ISSN 0031918X, The Physics of Metals and Metallography, 2011, Vol. 112, No. 7, pp. 711–744. © Pleiades Publishing, Ltd., 2011.

Magnetism of Compounds with a Layered Crystal Structure N. V. Baranova, b, E. G. Gerasimova, and N. V. Mushnikova a

Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 18, Ekaterinburg, 620990, Russia b Institut of Natural Sciences, Ural Federal University, pr. Lenina 51, Ekaterinburg, 620083 Russia Abstract—This review presents the results of investigations of the crystal structure, magnetic ordering, magnetic anisotropy, and magnetic phase transformations in compounds of the RT2Z2 and RT6Z6 type (R is a rareearth metal; T is a transition metal; and Z = Si, Ge, or Sn) and also in intercalated dichalcogenides of transition met als, such as MxTX2 and RxTX2. A specific feature of these compounds is a layered character of their crystal struc tures, in which the atoms that have a magnetic moment are located in separate crystallographic layers. Inside the layers of magnetic atoms and between the layers, there act different (in energy) exchange interactions of different type, which leads to a variety of magnetic structures and magnetic phase transitions in these compounds and makes them suitable objects for the investigation of physical phenomena inherent in quasitwodimensional magnetic systems. DOI: 10.1134/S0031918X11070039

INTRODUCTION Among inorganic substances, there exist com pounds that can be considered as natural analogs of multilayers and quasitwodimensional magnets rep resenting ideal monatomic multilayered structures and, thereby, as ideal model objects for the investiga tion of physical phenomena inherent in multilayers and quasitwodimensional structures. These are, in particular, intermetallic compounds of the RT2Z2 type with a layered tetragonal structure (R is a rareearth metal, T is a transition metal, and Z = Si or Ge) and compounds of the RT6Z6 type with a hexagonal crystal structure, in which the Z atoms are Sn or Ge, which can partly or completely be replaced by Ga or In. In the RT2Z2 and RT6Z6 compounds, atoms of the rare earth and transition metals are located in separate crystallographic layers; as a result, the exchange inter actions that act inside the layers and between the layers are of different type. Another impressive example of lay ered magnetic systems are Group IV–VI transition metal dichalcogenides of the TX2 type (X = S, Se, Te) intercalated with atoms of 3d or 4f metals. Since the threelayered blocks X–T–X, inside which there exist strong covalent bonds, are connected between them selves by only weak van der Waals interaction, various atoms, molecules, and structural fragments can be incorporated in spaces between the X–T–X sand wiches. The intercalated compounds are good objects for studying physics and chemistry of twodimen sional state. They manifest superconducting proper ties, transitions into the states with chargedensity waves (CDWs). The intercalation of atoms of 3d (M) or 4f (R) metals that have magnetic moments between the threelayered X–T–X blocks makes it possible to obtain structures consisting of layers of magnetic atoms separated by nonmagnetic interlayers.

The substitution for the rareearth or transition atoms in RT2Z2 and RT6Z6 compounds, just as the intercalation of various 3d or 4f atoms into the struc ture of the TX2 compounds, makes it possible to vary the magnitude of intralayer and interlayer exchange interactions in wide limits and to obtain layered mag netic systems with various types of magnetic ordering. In this review, we present the results of recent investi gations of specific features of the crystal structure, magnetic structure, magnetic anisotropy, and mag netic phase transformations in compounds with a lay ered structure of the RT2Z2 and RT6Z6 type and in intercalated transitionmetal dichalcogenides of the MxTX2 and RxTX2 type. 1. TERNARY RT2Z2 AND RT6Z6 COMPOUNDS WITH A TETRAGONAL LAYERED STRUCTURE In layered RT2Z2 compounds, there is observed a very wide spectrum of physical phenomena, including superconductivity, intermediate (mixed) valence of rareearth ions, crystalfield effects, heavy fermions, and various types of magnetic ordering and magnetic phase transitions [1]. The most thoroughly studied phe nomenon is at present the magnetism of rareearth ele ments in RT2Z2 compounds, whereas the nature of the magnetic behavior of 3d transition metals in layered compounds remains mainly unclear. First of all, this concerns the magnetic structures and magnetic phase transitions in the RT2Z2 compounds with T = Mn. Below, we give a brief review of the results of recent investigations of various magnetic phase transitions in RT2Z2 compounds with T = Mn and of the reasons for the absence of a local moment at atoms of 3d transition metals in the RT2Z2 compound with T ≠ Mn.

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Z T Z R

a Fig. 1. Crystal structure of RT2Z2 compounds.

1.1. Crystal Structure of RT2Z2 Compounds The intermetallic compounds of the RT2Z2 type (R = rareearth element; T = Mn; Z = Si or Ge) have a crystal structure of the ThCr2Si2 type (space group I4/mmm). The like atoms in the crystal structure are located in separate atomic planes (layers) alternating along the с axis in the following rigorous sequence: ⎯T–Z–R–Z–T– (Fig. 1). The atoms R, T, and Z occupy in the crystal structure positions 2a (0, 0, 0), 4d (0, 1/2, 1/4), and 4c (0, 0, z – 0.38), respectively. The spacing between the neighboring R(001) or T(100) planes is ≈0.52 nm, which is much greater than

the spacings between the nearestneighbor atoms in the planes (dRR ≈ 0.4 nm; dММ ≈ 0.28 nm) [1, 2]. The layered structure of the RMn2Z2 compounds makes it possible to consider them as a unique natural model object for the investigation of phenomena inherent in multilayer films and quasitwodimen sional objects. An analysis of the voluminous literature shows that the ternary intermetallic compounds RT2Z2 with a ThCr2Si2 structure can include a good many of ele ments of the periodic table and their number increases continuously (Fig. 2): —as the R element, not only any rareearth metal can enter into these compounds, but also Y, Lu, Ca, Sr, Ba, Ti, Th, or U; —as the T element, these compounds can contain 3d metals (from Cr to Cu), 4d metals (from Ru to Ag), and 5d metals (from Re to Au) of the transition rows; —in this review, we consider RT2Z2 compounds in which the Z element is Si or Ge. However, it should be noted that sometimes the compounds with a stoichiom etry of 1 : 2 : 2 and a structure of the ThCr2Si2 type can be formed also when Z = P, As, Sb, Sn, Se [1, 3–5]. The consideration of such compounds is beyond the framework of this work. It can be supposed that it is precisely the layered crystal structure of the RMn2Z2 compounds and also the combination of crystallographic layers containing atoms of different groups of the periodic table that cause the variety of physical phenomena observed in them.

Fig. 2. Elements that can enter into the intermetallic compounds of the RT2Z2 type. THE PHYSICS OF METALS AND METALLOGRAPHY

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La(Fe1 – xVx)2Si2

0.016

χ, (mol)–1

0.014 0.012 0.010 0.008

x = 0.5

0.006 0.004

x = 0.35 x = 0.25

0.002

x=0 0

50

100

150 T, K

200

250

300

Fig. 3. Temperature dependences of the magnetic susceptibility χ of La(Fe1 – xVx)2Si2. The dashed lines show the calculated Curie–Weiss dependences.

1.2. Magnetism of 3d Transition Metals in RT2Z2 Compounds In RT2Z2 compounds with various 3d transition metals, the T atoms have a nonzero magnetic moment only in compounds with Mn. The atoms of iron, cobalt, and nickel have no magnetic moment in the RT2Z2 compounds. All RT2Z2 compounds with T ≠ Mn, Cr, and nonmagnetic rareearth elements (R = Y, La, Lu) are Pauli paramagnets with a temper atureindependent magnetic susceptibility [6]. The iron atoms exhibit diamagnetic properties even when they are partly replaced by Mn in R(Fe1 – xMnx)2Ge2 solid solutions [7, 8]. In quasiternary compounds of the R(Mn1 – xTx)2Z2 type (T = Fe, Co, Ni), the substi tution of the magnetic Mn atoms for Fe, Co, and Ni leads to the same changes in the magnetic properties of the compounds as in the case of their replacement by a nonmagnetic 3d element [9]. An analogous situa tion is observed also in many other ternary intermetal lic compounds with a natural layered crystal structure. It was supposed that in the RT2Z2 compounds there occurs a strong hybridization of the 3d electron states of transitionmetal atoms with the p (s) states of the Z metals, which leads to the complete occupation of the 3d band of the transition metals [10]. The presence of a magnetic moment at Mn atoms in the RT2Z2 compounds can be related to the fact that in the row of magnetic transition metals of the iron group (Mn, 3d54s2; Fe, 3d64s2; Co, 3d74s2; Ni, 3d84s2) the Mn atoms have the least filled 3d shell. Therefore, it was supposed that one of the ways of the influence on the magnetic state of 3d transition metals in RT2Z2 compounds can be the partial substitution of atoms of 3d transition metals that have the least filled 3d shell for Mn, Fe, Co, and Ni. The authors of [11] tried to affect the degree of the occupation of the 3d band and the magnetic state of iron atoms in LaFe2Si2 by the partial replacement of Fe by V, which has the initial THE PHYSICS OF METALS AND METALLOGRAPHY

electron configuration 3d34s2 with a less filled, as com pared to Fe (3d64s2) 3d shell. To this end, they studied the magnetic properties of La(Fe1 – хVх)2Si2 in the range of concentrations х corresponding to solid solutions. It has been shown, in particular, that such a substitution leads to the appearance of a localized magnetic moment at Fe atoms at intermediate concentrations of the sub stituting element in the La(Fe1 – хVx)2Si2 compounds. In the initial ternary compound LaFe2Si2, the magnetic susceptibility χ is virtually temperatureindependent, which is a characteristic property of Pauli paramagnets (Fig. 3). In the compounds with vanadium, the temper ature dependence of the magnetic susceptibility obeys the Curie–Weiss law with negative values of the para magnetic Curie temperature (Θp from –9 to –21 K) and with the magnitude of the effective magnetic moment μeff ≈ 0.42–2.48 μB/Fe. The maximum magnitude of the effective magnetic moment proved to be close to the magnitude of the effective magnetic moment of Fe atoms in iron. The most significant changes in the magnitudes of χ0 and μeff with an increase in the vanadium concentration, which indicate a strong change in the electron energyband structure of the La(Fe1 – хVx)2Si2 compounds, are observed in the compound with х = 0.5, in which there occurs a signif icant increase in the lattice parameter а, correspond ing to a strong change in the intralayer interatomic spacings. The results obtained permit one to expect that in compounds of the RT2Z2 type the magnetic moment at the atoms T = Fe, Co, and Ni can arise upon a partial replacement of these metals by 3d tran sition metals with the least filled 3d shell. A specific feature of all quasiternary R(T1 – хVx)2Si2 compounds is an anisotropic variation of the lattice parameters with increasing vanadium concentration (Fig. 4) [12]. The lattice parameter а remains virtually independent of the vanadium concentration, despite that vanadium has a greater atomic radius; the parameter с and the unit cell volume increase monotonically. A similar unusual Vol. 112

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Y(Mn1 – xVx)2Si2

La(Mn1 – xVx)2Si2

1.07 1.06 Y(Mn1 – xVx)2Si2

1.05 La(Fe1 – xVx)2Si2

1.04 1.03 La(Fe1 – xVx)2Si2

1.02 0

0.1

0.2

0.3 x

0.4

V, nm3

1.065 1.060

0.5

0

0.1

0.2

0.3 x

0.4

V, nm3

c, nm

1.070

0.181 0.180

La(Mn1 – xVx)2Si2

0.179 0.163 0.162 Y(Mn1 – xVx)2Si2

0.161 V, nm3

La(Mn1 – xVx)2Si2

c, nm

0.416 0.415 0.414 0.413 0.412 0.411 0.410 0.409 0.396 0.395 0.394 0.393 0.392 0.391 0.390 0.389 0.388 0.412 0.411 0.410 0.409 0.408 0.407 0.406 0.405 0.404

c, nm

a, nm

a, nm

a, nm

714

0.5

0.174 0.172 0.170 0.168 0.166

La(Fe1 – xVx)2Si2 0

0.1

0.2

0.3 x

0.4

0.5

Fig. 4. Concentration dependences of the lattice parameters in La(Fe1 – xVx)2Si2, Y(Mn1 – xVx)2Si2, and La(Mn1 – xVx)2Si2 compounds.

anisotropic concentration dependence of the lattice parameters was observed also in R(Fe1 – хCrx)2Si2 solid solutions [13]. In the cases where Mn or Fe are replaced by elements with a 3d shell filled more than in the case of Cr, there are usually observed a mono tonic variation of all lattice parameters. The reasons responsible for the anisotropic concentration depen dence of the lattice parameters in the compounds of the R(T1 – хVx)2Si2 and R(Fe1 – хCrx)2Si2 type remain unclear. However, it is obvious that with increasing vanadium concentration in compounds, such an anisotropic behavior of the lattice parameters leads to a stronger hybridization of the electron shells of 3d metals in layers (basal planes) as compared to the interlayer hybridization of 3d electron states of the atoms of tran sition metals with the p (s) states of silicon. The experimental investigations of the electron contribution to heat capacity also reveal an anisotro pic dependence of the density of states at the Fermi level in RT2Si2 compounds on the lattice parameters [14]. The density of states at the Fermi level depends strongly on the intralayer interatomic spacings (lattice parameter а) and is virtually independent of the inter layer spacings (lattice parameter с) (Fig. 5). This agrees with the appearance of a local magnetic moment at the Fe atom in La(Fe1 – хVx)2Si2 com pounds, which is accompanied by a strong change in the intralayer interatomic spacings. Thus, there exists a possibility of the appearance of a localized magnetic moment at the atoms of Fe, Co, and Ni in both the RMn2Z2 compounds and in other quasiternary compounds with a naturally layered crystal structure. Nevertheless, initially, it is only Mn that has a magnetic moment in the RMn2Z2 com pounds, and it is precisely in the compounds with Mn that there is observed an extremely wide spectrum of

magnetic structures and magnetic phase transitions in the 3d magnetic subsystem, which will be considered below. 1.3. Magnetic Structures in the Manganese Sublattice and Exchange Interactions in RMn2Z2 Compounds The layered compounds are, as a rule, character ized by a strong intralayer exchange interaction and weak interlayer exchange interaction. The magnitude of the interlayer exchange interaction and, conse quently, the type of interlayer magnetic ordering depend most strongly on the interlayer spacing. One of the most unusual features of the magnetic properties of the RMn2Z2 compounds consists in the existence of an (unusual for layered compounds) cor relation between the type of interlayer Mn–Mn exchange interactions and the intralayer spacings between the Mn atoms. The existence of the unusual character of the interlayer Mn–Mn exchange interac tion was suggested based on the study of magnetic properties of ternary compounds [1, 15]. It turned out that in the ternary compound RMn2Z2 with different R and Z elements the type of the interlayer magnetic ordering of magnetic moments of Mn atoms correlates only with the lattice parameter а, which determines the intralayer Mn–Mn spacings dMn–Mn (dMn–Mn = a/ 2 ) and does not correlate with the lattice parameter с, which determines the interlayer Mn–Mn spacings d1 (d1 = c/2). There exists a certain critical distance dc ≈ 0.285–0.287 nm such that at dMn–Mn > dc the magnetic moments of manganese atoms in neighboring layers are ordered ferromagnetically and at dMn–Mn < dc, anti ferromagnetically. Inside each layer there usually is formed a canted ferromagnetic structure with an angle

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θ = 40°–60° and with a resultant magnetic moment directed along the c axis.

20

2.5 2.0

UNi2Si2 YMn2Si2

1.5

15

γ, mJ/(mol K2)

1.0 10 0.390 0.395 0.400 0.405 0.410 0.415 a, nm 40 35

LaMn2Si2 LaFe2Si2

30 25

3.0

La0.7Y0.3Mn2Si2

2.5 UNi2Si2

NdFe2Si2

La0.75Y0.25Mn2Si2

2.0

20

1.5

YMn2Si2

15

10 0.94 0.96 0.98 1.00 1.02 1.04 1.06 c, nm

1.0

N(EF), states/(eV atom)

30 25

3.0

LaMn2Si2 La0.7Y0.3Mn2Si2 NdFe2Si2 LaFe2Si2 La0.75Y0.25Mn2Si2

The most wellknown compound is the ternary compound SmMn2Ge2, in which dMn–Mn ≈ dc and the type of the interlayer Mn–Mn ordering proves to be unstable; as a result, there are observed both spontaneous and magneticfieldinduced firstorder phase transitions from an antiferromagnetic to a ferromagnetic interlayer Mn–Mn ordering [15–19]. In the quasiternary inter metallic compounds of the R1 – x R 'x Mn2Z2 (R and R' are the rareearth elements) and RMn2(Si1 – xGex)2 types, there is a possibility of smoothly changing lattice param eters with changing concentration x from dMn–Mn > dc to dMn–Mn < dc by changing the type of the interlayer Mn–Mn exchange ordering.

N(EF), states/(eV atom)

γ, mJ/(mol K2)

40 35

Because of the existence of a critical intralayer spacing dc, the main magnetic structures that are observed in RMn2Z2 compounds in the manganese sublattice can be subdivided into groups according to the magnitude of intralayer spacings between manga nese atoms. Figure 6 displays the main types of mag netic structures characteristic of the manganese sub lattice in RMn2Si2 compounds on the example of a compound of composition La0.75Sm0.25Mn2Si2 [20], in which dMn–Mn is approximately equal to dc and all magnetic structures are realized with changing tem perature. As is seen from Fig. 6, in La0.75Sm0.25Mn2Si2 there are observed four different magnetically ordered states with the following critical temperatures of the magnetic phase transitions: AF''–P, TP = 405 K; F⎯AF', ТС = 305 K; AF–F, TAF = 160 K; and AF'–AF, TSm ≈ 14 K. At temperatures T > TP, La0.75Sm0.25Mn2Si2 is in the paramagnetic state (P); at ТС < T < TP, there occurs a collinear antiferromagnetic ordering of the magnetic moments of manganese atoms in the layers (inplane antiferromagnetism, AF''); at ТAF < T < TC, a canted ferromagnetic structure with a ferromagnetic ordering of magnetic moments of man ganese atoms in neighboring layers (F) is realized; at ТSm < T < TAF, an antiferromagnetic interlayer order

LaMn2Si2

30 25

3.0

LaFe2Si2 La0.7Y0.3Mn2Si2

2.5 UNi2Si2

La0.75Y0.25Mn2Si2

NdFe2Si2

2.0

20

1.5 YMn2Si2

15

1.0

10 0.15

0.16 0.17 V, nm3

N(EF), states/(eV atom)

γ, mJ/(mol K2)

40 35

0.18

Fig. 5. Variations of the electronic contribution γ to the heat capacity of compounds and the density of states at the Fermi level N(EF) as functions of the lattice parameter in RT2Si2 compounds.

AF'

715

F

AF

AF''

La, Sm Mn Mn Sm Mn

T = 4.2 K

θ

θ

Mn

Mn

Mn

Mn

T = 200 K

T = 78 K

T = 350 K

Fig. 6. Magnetic structure of La0.75Sm0.25Mn2Si2 at various temperatures. Twosublattice models of interlayer magnetic ordering in the compound are shown schematically. THE PHYSICS OF METALS AND METALLOGRAPHY

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6

K1

40

4

Ha, kOe

K1, K2 × 106, erg/cm3

8

20 2

K2 0

0

50

100

150 T, K

200

250

300

Fig. 7. Temperature dependence of the constants of mag netic anisotropy K1 and K2 and of the field of magnetic anisotropy Ha of the La0.75Sm0.25Mn2Si2 compound (solid symbols) and of the LaMn2Si2 compound (open symbols) in the temperature range of existence of the F structure.

ing is observed (AF); and at T < TSm, a ferromagnetic ordering of magnetic moment of Sm occurs in the basal plane, which leads to a distortion of the antifer romagnetic structure in the manganese sublattice (AF'). As is seen from Fig. 6, four main types of mag netic structures can be distinguished in the manganese sublattice in RMn2Z2 compounds. The F and AF magnetic structures are character ized by a ferromagnetic and antiferromagnetic inter layer Mn–Mn ordering and by the existence of a canted magnetic structure in a layer: —the AF structure exists in the compounds with dMn–Mn < dc; at low temperatures (T < 50 K), there occurs a ferromagnetic ordering of magnetic moments of rareearth ions in the basal plane and a partial dis tortion of the antiferromagnetic interlayer ordering of the magnetic moments of Mn because of the R–Mn exchange interaction, which leads to the appearance of “reentrant” ferromagnetism, i.e., of a ferromag netic component of the magnetic moment at manga nese atoms in the basal plane (an AF’ structure); —the F structure exists in compounds with dMn ⎯ Mn > dc; a characteristic feature of the compounds with dMn–Mn > dc with the F structure is also the exist ence of an inplane intralayer antiferromagnetic ordering of the magnetic moments of manganese (AF'' structure), which precedes the transition of the compounds into the paramagnetic state with increas ing temperature. As is seen from Fig. 6, at least four types of exchange interactions can be distinguished in RMn2Z2 compounds: (i) an interlayer Mn–Mn exchange interaction (λMn–Mn), which determines the type of the interlayer Mn–Mn magnetic ordering;

(ii) competing antiferromagnetic and ferromag netic intralayer Mn–Mn exchange interactions intra ( λ Mn–Mn ), which lead to the appearance of a canted ferromagnetic structure in the layer; (iii) an exchange interaction between the magnetic moments of Mn atoms and rareearth elements (λR–Mn); (iv) an exchange interaction between the magnetic moments of rareearth ions (λR–R). According to different estimates [21–23], the fol lowing relationships are fulfilled between the parame ters of exchange interactions in the RMn2Z2 com intra

pounds: λ Mn–Mn > λMn–Mn > λR–Mn > λR–R. The stron gest interactions are the intralayer Mn–Mn exchange interactions; in the magnetic fields realistically attain able in experiments (H < 400 kOe) no substantial change in the angle Θ of the intralayer canted ferro magnetic structure occurs. Therefore, in the majority of cases the magnetization curves of compounds can be described in terms of twosublattice models of col linear interlayer Mn–Mn ordering, in which the mag nitude of the magnetic moment of each magnetic sub lattice is equal to the projection of the total magnetic moment of Mn onto the с axis. 1.4. Magnetic Anisotropy of RMn2Z2 Compounds The formation of magnetic structures in com pounds should be affected substantially by magnetic anisotropy. It is known that in RMn2Z2 compounds containing magnetic rareearth elements the magnetic anisotropy at low temperatures (T < 50 K) is almost completely determined by the anisotropy of the rare earth sublattice [1, 24]. The anisotropy of the manga nese sublattice in the RMn2X2 compounds was studied in some detail only recently. The magnetic anisotropy of the manganese sublat tice was studied in the ternary compound with a non magnetic rareearth element LaMn2Si2 and in the quasiternary compound La0.75Sm0.25Mn2Si2 in the temperature range of existence of the F and AF'' struc tures and in the paramagnetic state [23, 25]. The inves tigations performed showed that in all the cases the manganese sublattice in the compounds has a strong uniaxial magnetic anisotropy with an easy axis с. It is no grounds to assume that the type of anisotropy of the manganese sublattice can be different in the com pounds with an AF' and AF structures. The tempera ture dependences of the constants of magnetocrystal line anisotropy and of the field of magnetic anisotropy НА=2(K1 + K2)/2 of the compounds are shown in Fig. 7. As is seen, these compounds have a significant uniaxial magnetocrystalline anisotropy up to tempera tures close to ТС. The magnitudes of the constants K1 and K2 of LaMn2Si2 at T = 4.2 K (К1 = 6.4 × 106 erg/cm3, K2 = 1.26 × 106erg/cm3) are close to the values of anisotropy constants obtained in [24] for GdMn2Ge2 (К1 = 5.4 × 106 erg/cm3, K2 =3.6 × 106 erg/cm3), in

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Table 1. Magnitudes of the paramagnetic Curie temperature θP, the effective magnetic moment μeff, and the constant χ0 of the singlecrystal and polycrystalline samples of the La0.75Sm0.25Mn2Si2 compound

Polycrystal Parallel to c axis Perpendicular to c axis

θp, K

μeff, μB/f.u.

μeff*, μB/Mn

χ0, mol–1

310 336 301

4.20 3.84 4.27

2.95 2.70 3.01

–1.46 × 104 –0.62 × 104 +3.12 × 104

* The values of µeff per Mn atom were calculated on the assumption that the effective magnetic moment of the Sm ion is µeff = 0.84 µB/Sm.

which the rareearth ion Gd has a zero orbital mag netic moment and the contribution of the rareearth sublattice to the total anisotropy of the compound is minimum as compared to other magnetic rareearth ions. The anisotropy of Mn yields the main contribu tion to the total anisotropy of RMn2Z2 compounds also in the case of magnetic rareearth ions at high temperatures, when the rareearth magnetic sublattice is disordered and the allowance for the magnetic anisotropy of the Mn sublattice yields new additional possibilities for the investigation of the nature of vari ous magnetic phase transitions in compounds. The strong uniaxial anisotropy with an easy axis с is also retained at high temperatures, in the paramagnetic state. The values of the paramagnetic Curie tempera ture θP obtained by fitting the experimental tempera ture dependences of the inverse paramagnetic suscep tibility χ–1(T) to the Curie–Weiss law, the effective magnetic moment μeff, and the constant χ0 for the quasisinglecrystal and polycrystalline samples of La0.75Sm0.25Mn2Si2 are given in Table 1. As is seen, the difference in the values of the paramagnetic Curie temperature of the compounds along the с axis and in the basal plane reaches 35 K. The higher value of the paramagnetic Curie temperature obtained from mea surements in the basal plane θ⊥ = 301 K indicates that in the paramagnetic state there is retained a significant uniaxial magnetic anisotropy with the easy axis с. The values of the effective magnetic moment per Mn atom are close to typical values of the effective magnetic moment of manganese in RMn2Z2 compounds. As is seen from Table 1, there is also observed a small differ ence between the values of the effective magnetic moment of the compound along the c axis and in the basal plane. The magnitude of the effective magnetic moment of the compound in the basal plane proves to be greater by 0.43 μB/f.u. As a rule, the strong magnetocrystalline anisotropy and the anisotropy of the paramagnetic Curie temper ature are observed in two types of compounds. First, in the compounds containing 4f and 5f metals with strongly localized f shells and nonfrozen values of the orbital magnetic moment. Second, in nonmetallic compounds containing 4f and 5f rareearth metals, and 3d transition metals (in this case, the 3d ions, just as f metals, possess a nonzero orbital magnetic moment). In the case of metallic compounds based on THE PHYSICS OF METALS AND METALLOGRAPHY

3d elements, such as the RMn2Z2 compounds, the magnetocrystalline anisotropy and the anisotropy of the paramagnetic Curie temperature are usually small, which is related to the freezing of the orbital magnetic moment. The strong anisotropy effects revealed in La0.75Sm0.25Mn2Si2 in the paramagnetic state can be related both to a partial unfreezing of the orbital mag netic moment of manganese in the compound and to the specific features of the crystal structure of the com pound, which represents a natural layered crystal structure. The large magnetic anisotropy connected with the unfreezing of the orbital magnetic moment, was observed, e.g., for Co and Mn in compounds such as YCo5 [26] and MnBi [27]. It is also known that in multilayered film structures the magnetic anisotropy can by an order of magnitude exceed the magnetic anisotropy of bulk materials [26]. 1.5. InterlayerAntiferromagnet–Interlayer Ferromagnet FirstOrder Magnetic Phase Transition As was already noted above, in the RMn2Z2 com pounds there exists a critical spacing between Mn atoms in a layer dc ≈ 0.285–0.287 nm such that at dMn⎯Mn > dc the magnetic moments of manganese atoms in neighboring layers are ordered ferromagneti cally (F structure), and at dMn–Mn < dc they are ordered antiferromagnetically (AF structure, Fig. 6). In the compounds with dMn–Mn ≈ dc, there is observed a spon taneous and a magneticfieldinduced firstorder phase transition of the interlayerantiferromagnet– interlayerferromagnet (AF–F) type. The nature of the AF–F transition in the RMn2Z2 compounds remains unclear up to date. On the one hand, it is supposed that at this phase transition there can occur a change in the energyband structure of the compounds, since the value of dc is close to critical, at which there occurs a delocalization of 3d electrons of Mn in binary alloys [1, 10, 15]. However, at present no proofs exist indicating a change in the electronic struc ture of these compounds. In particular, the magnitude of the magnetic moment of manganese remains almost unchanged upon the AF–F phase transition, and no significant changes are observed in the electron contribution to the heat capacity of the compounds, which characterizes the density of electron states at the Fermi level [14]. On the other hand, the AF–F Vol. 112

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Temperature, K

Temperature, K

Paramagnetic

Paramagnetic

400 300 F 200

AF 100 0

(b)

500

0.2

0.4 0.6 0.8 Pressure, GPa

1.0

400

AF''

300 200

AF

F

100

1.2 0

0.2

0.4 0.6 Concentration x

0.8

1.0

Fig. 8. (a) P–T phase diagram of the La0.75Sm0.25Mn2Si2 compound and (b) concentration phase diagram of the La1– xSmxMn2Si2.

phase transition can qualitatively be described in terms of the phenomenological model of localized magnetic moments on the assumption of the existence of a strong dependence of the interlayer Mn–Mn exchange interac tion on the interatomic spacings [21, 28–30]. The effect of interatomic spacings on the magnetic phase transition in RMn2Z2 compounds can be studied by two methods. First, in quasiternary intermetallic compounds of the R1 – xR’Mn2Z2 and RMn2(Si1 – xGex)2 6 5

(a)

La0.75Sm0.25Mn2Si2 H=0

Rc

R, Ω

4 3 Ra

2 1

(b) 12 ΔV/V

ΔV/V, λ(10–3)

10 8 6

AF

F

λa

4 2 0

λc 50

100 150 200 Temperature (K)

250

300

Fig. 9. Temperature dependences of (a) the spontaneous linear magnetostriction and (b) electrical resistance of the La0.75Sm0.25Mn2Si2 compound measured along the c axis (Rc, λc) and in the basal plane (Ra, λa). The volume sponta neous magnetostriction was calculated as ΔV/V = 2λa + λc.

type, in which the intralayer interatomic Mn–Mn spac ings can be changed from dMn–Mn > dc to dMn–Mn < dc, by changing the concentration x. Second, in the com pounds with dMn–Mn ≈ dc, this can be done by studying the effect of an external hydrostatic pressure on the critical temperatures of various nanoaggregate phase transitions. Figure 8a shows a P–T phase diagram which sums the results on the effect of pressure on spontaneous magnetic phase transition in the compound La0.75Sm0.25Mn2Si2 in which dMn–Mn is close to dc and all main magnetic structures inherent in the RMn2Z2 compounds are realized. In Fig. 8b, there is given a concentration x–T magnetic phase diagram of the La1 – xSmxMn2Si2 compounds, in which a monotonic decrease in the lattice parameters and in the unitcell volume of the compounds occurs [29, 30]. As can be seen form Fig. 8, the P–T phase diagram of La0.75Sm0.25Mn2Si2 is qualitatively similar to the concen tration x–T phase diagram of the La1 – xSmxMn2Si2 compounds. The critical temperatures of magnetic ordering with increasing hydrostatic pressure change in La0.75Sm0.25Mn2Si2 just as in La1 – xSmxMn2Si2 compounds with increasing concentration x. The only exception is the critical temperature of the existence of the AF structure, which increases in La1 – xSmxMn2Si2 because of the growth of concentration of magnetic Sm ions. On the whole, the effect of an external hydrostatic pressure on the magnetic state of La0.75Sm0.25Mn2Si2 is equivalent to a “chemical” pressure. A decrease in the interatomic spacings in both cases leads to the stabiliza tion of an antiferromagnetic interlayer ordering in the compound, a decrease in the temperature range of existence of the F and AF'' structures, and an increase in the temperature range of existence of the AF structure. The greatest effect of the hydrostatic pressure proves to be on the interlayer Mn–Mn exchange interaction, i.e., on the temperature of the AF–F transition. The spontaneous AF–F phase transition is accom panied by strong anisotropic changes in the lattice parameters and electrical resistance (Fig. 9). In the

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE T=4K

3 T = 80 K

(a)

2

H || c

M, μB /f.u.

M, μB /f.u.

3

H || a

1

λa

0

(b)

λa

λ, 10–3

H || c

H || a λc

λc

(b) λa

0.5 0 –0.5

H || a λc

λc (c)

2.8 R, Ω

R, Ω

λa

H || c

H || c

H || c

2.25

H || a

1

(c)

2.30

(a)

H || c

2

0 1.5 1.0 λ, 10–3

0 1.5 1.0 0.5 0 –0.5 –1.0

719

H || a

2.00 1.99

2.7 0

10

20 30 40 50 Magnetic field, kOe

60

70

0 10 20 30 40 50 60 70 80 90 100 Magnetic field, kOe

Fig. 10. (a) Magnetization curves, (b) field dependences of the linear magnetostriction, and (c) electrical resistance of the La0.75Sm0.25Mn2Si2 compound measured in magnetic fields directed along the c axis (open symbols) and in the basal plane (solid symbols) at temperatures of 4 and 80 K.

temperature dependence of the resistance of the com pound measured along the c axis there is clearly seen a jump at the temperature of the spontaneous AF–F phase transition. In the basal plane, no anomaly is observed. The resistance in the ferromagnetic state is lower than that in the antiferromagnetic state. No noticeable anomalies in the behavior of the tempera ture dependence of the resistance upon measurements both along the c axis and in the basal plane have been observed. The spontaneous firstorder AF–F phase transition at the temperature TAF = 150 K is accompa nied by a jumplike increase in the lattice parameter a (Δa/a ≈ 1.5 × 10–3) and a decrease in the parameter c (Δc/c ≈ –0.75 × 10–3). Along with changes in the linear magnetostriction, a significant increase in the volume of the compound (ΔV/V ≈ 2.0 × 10–3) occurs upon the spontaneous AF–F magnetic phase transition. Upon the AF–AF' spontaneous magnetic phase transition, no noticeable changes in either linear or bulk magne tostriction occurs. At temperatures T < TSm, a magneticfieldinduced firstorder AF'–F phase transition occurs in La0.75Sm0.25Mn2Si2. The AF'–F phase transition occurs upon magnetizing both along the c axis and in the basal plane, though at critical magnetic fields dif fering in magnitude (H||, H⊥) (Fig. 10, T = 4 K). The firstorder AF–F magnetic phase transition induced by the magnetic field is accompanied by a jumplike increase in the magnetostriction in the basal plane THE PHYSICS OF METALS AND METALLOGRAPHY

(Δλa ≈ 1.5 × 10–3) and by a decrease in the magneto striction along the c axis (Δλc ≈ –0.75 × 10–3). These values of the magnetostriction coincide with those observed upon the spontaneous AF–F phase transi tion. In the dependence of the electrical resistance on the external magnetic field upon magnetizing both along the c axis and in the basal plane, jumps are observed in critical fields corresponding to the critical fields H|| and H⊥ of the AF–F phase transition induced by the magnetic field (Fig. 4c). The magnitude of the magnetoresistance upon the AF'–F phase transition measured along the c axis (ΔRc/Rc ≈ + 3%) is almost 30 times greater than that in the basal plane (ΔRa ≈ +0.1%). Upon demagnetizing, in the Rc(H) depen dence at the F–AF' transition there is also observed a jump in the resistance, but of the opposite sign; in addition, the resistance of the sample increases in the zero magnetic field. Upon the demagnetizing in the basal plane, in the Ra(H) dependence the sign of the change in the resistance is retained at the F–AF' transition, and again there is observed an increase in the residual resistance of the sample in the zero mag netic field. In magnetic fields that are greater or less than the critical field of the AF'–F phase transition, there is observed a negative magnetoresistance: the magnitude of the electrical resistance decreases lin early with increasing strength of the magnetic field, which is characteristic of the majority of antiferromag nets and ferromagnets. Vol. 112

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In the temperature range of TSm < T < TAF, in the La0.75Sm0.25Mn2Si2 compound there occurs a first order AF–F magnetic phase transition induced by magnetic field (Fig. 10, T = 80 K). The magnetic fieldinduced firstorder AF–F phase transition again is accompanied by a jumplike increase in the magne tostriction in the basal plane (Δλa ≈ 1.5 × 10–3) and by a decrease in the magnetostriction along the c axis (Δλc ≈ –0.75 × 10–3). The values of the magnetostric tion again coincide with those observed upon the spontaneous AF–F phase transition. In the depen dence of the electrical resistance on the external mag netic field there is also observed a jump; the magne toresistance is positive (ΔRc/Rc ≈ +8.5%). Just as in the case of the AF'–F transition, when the magnetic field decreases, the resistance jump changes sign upon the AF–F phase transition and an increase in the resistance is observed in a zero magnetic field. Thus, both the spontaneous and magneticfield induced AF–F phase transitions are accompanied not only by large anisotropic changes in the lattice param eters (Δa/a ≈ 1.6 × 10–3, Δc/c ≈ 0.75 × 10–3) but also by a significant change in the volume (ΔV/V ≈ 2 × 10–3. The change in the volume measured upon the phase transition quantitatively coincides with the estimates performed on the basis of thermodynamic relation ships that relate the change in the temperature of the transition TAF as a function of pressure to the change in the volume [30]. The AF–F magneticfield induced phase transition exists in magnetic fields directed both along the c axis and in the basal plane and, irrespective of the direction of the external mag netic field, is accompanied by equal magnetostrictive distortions of the crystal lattice. The data on the magnetoresistance prove to be by no means unambiguous. First, it should be noted that the magnetoresistance is always positive, both for dif ferent samples and in measurements along the c axis and in the basal plane. Second, the values of the mag netoresistance along the c axis are much higher than those in the basal plane. Nevertheless, the magnetore sistance varies strongly from measurement to mea surement, and in the RMn2Z2 compounds different signs of the magnetoresistance are observed [31]. The discrepancies are mainly observed for polycrystalline samples. It seems that the strong changes in the lattice parameters that arise upon the AF–F phase transition lead to the formation of microcracks in the samples, which in turn strongly affects the residual resistance of the compounds in the zero magnetic field. The exist ence of microcracks affects most strongly the mea surements of magnetoresistance in polycrystalline samples, where there exist grain boundaries as the sources of microcracks. The giant magnetostriction changes, which arise upon phase transitions, in the presence of microcracks lead to changes in the topol ogy of the flowing current (due to an increase or decrease in the thickness of the microcracks) and, in turn, to a change in the electrical resistance of the

samples. In this case, both positive and negative values of magnetoresistance can arise. It is known that the spindependent magnetoresis tance is related to the existence of scattering of con duction electrons by the magnetic moments of atoms and of magnetic impurities. In the case of a noncol linear magnetic ordering, the resistance is, as a rule, greater than upon collinear ordering. In the antiferro magnetic state, the electrical resistance is also, as a rule, greater than in the ferromagnetic state. The mag netoresistance observed in the RMn2Z2 compounds can be due to two reasons. First, upon a phase transi tion changes in the electron energy band structure of the compound can arise. The energybandrelated character of the phase transition follows from the fact that the magnetoresistance is positive upon measure ments both along the c axis (in which case the type of the interlayer ordering of magnetic moments of man ganese changes) and in the basal plane (where the type of magnetic ordering remains unaltered). The large magnitude of the bulk magnetostriction upon the AF–F phase transition also can indicate the band character of the phase transition. The anisotropic behavior of the magnetoresistance can be affected also by the spindependent mechanism of magnetoresis tance, since the largest magnetoresistance is observed along the c axis, where the magnetic structure of the compound is changed, while the magnetoresistance is virtually absent in the basal plane, where the magnetic structure inside the layers remains virtually unaltered upon the phase transition. A specific feature of firstorder magneticfield induced AF'–F and AF''–F phase transitions is that they can exist in magnetic fields directed both along and across the anisotropy axis and that the values of the critical fields are equal to or are less than the field of magnetic anisotropy (Figs. 10, 11). In addition, the AF'–F and AF''–F phase transitions are accompa nied by large changes in lattice parameters. The above features of the firstorder magnetic phase transitions are also characteristic of band metamagnets, in which there occurs a change in the electronic structure upon the phase transition. Without considering a particular mechanism of the change in the sign of the interlayer exchange interaction in the compounds and assuming only that at the point of the phase transition the mag nitude of interlayer Mn–Mn exchange interactions changes jumpwise, the following expressions can be obtained for the metamagnetic transitions [29]:

(

)

AF F AF 1 H ||0 = 1 H Mn −Mn + H Mn −Mn = H Mn −Mn + Δ H , (1) 2 2

H ⊥0 = H S − H S 2 − H S (H A + 2H ||0)

(2) = H S − −H S Δ H , where HS is the saturation field in the magnetization AF F AF curve H S = H A + 2H MnMn ; Δ H = H Mn −Mn − H Mn −Mn is the change in the field of the interlayer exchange

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE

H || ≈

H ||0

(

)

H2 − Sm H ||0 + 1 H A , 2 H S2

7 6 Magnetic field, T

interaction upon the transition from the antiferromag netic to ferromagnetic interlayer Mn–Mn ordering; and HA is the field of magnetic anisotropy. In terms of such an approach, the change in the interlayer exchange interaction can formally be caused either by changes in the electronenergyband structure of the compounds or by the existence of a strong dependence of the interlayer exchange interactions on the lattice parameters. With the allowance for the effect of the molecular exchange field of the samarium sublattice, the above expressions take on the following form:

721

5

H⊥

HA

4 3 H||

2 1

(3)

(4) H⊥ = − H Sm. The expressions (1)–(4) make it possible to suffi ciently well (both qualitatively and quantitatively) describe phase transitions. However, although the AF–F phase transition is qualitatively well described in terms of the phenomenological models of localized magnetic moments, which mean the existence of a strong dependence of the interlayer exchange interac tions on the interatomic spacings, the nature of the AF–F magnetic phase transition in the RMn2Z2 com pounds remains unclear, as before. First of all, in terms of these models it is impossible to understand why the interlayer Mn–Mn spacings depend predominantly on the intralayer interatomic spacings and why there exists a critical spacing dc between the Mn atoms. In addition, the AF–F transition possesses all main external features characteristic of itinerantelectron (band) magnets. The following factors indicate in favor of the band character of the F–F transition. First, the transition is accompanied by strong volume changes. Second, the magneticfieldinduced transi tion exists in magnetic fields directed both along and across the anisotropy axis. And, third, the AF–F tran sition is accompanied not only by a change in the interlayer Mn–Mn exchange interactions, but also by a change in the sign of the dependence of the intralayer Mn–Mn exchange interactions on the interatomic spacings. The theoretical calculations of the band structure of the RMn2Z2 compounds also confirm that there is a correlation between the density of states at the Fermi level and the type of the interlayer Mn–Mn magnetic ordering. Correspondingly, in the Hubbard model the sign of the interlayer Mn–Mn magnetic ordering in compounds with a layered crystal structure can depend on the density of states at the Fermi level, and the magnitude of the magnetic moment of Mn can remain virtually unaltered.

H ⊥0

1.6. Ferromagnet–InPlaneAntiferromagnet Magnetic Phase Transition The reasons for the appearance of conditions for the existence of the AF'' state, and the nature of the F–AF'' magnetic phase transition are least studied at present THE PHYSICS OF METALS AND METALLOGRAPHY

0

50

100 150 200 Temperature, K

250

300

Fig. 11. Temperature dependences of the critical fields of the metamagnetic transition H|| and H⊥ and of the field of anisotropy HA of the La0.75Sm0.25Mn2Si2 compound. The dashed line shows the temperature dependence of the field of magnetic anisotropy of the LaMn2Si2 compound.

in the compounds of the RMn2Z2 type. This is mainly caused by the fact that the very existence of the AF'' state was for the first time revealed exclusively in Mössbauer experiments and in experiments on mag netic scattering of neutrons and virtually did not man ifest itself in the experiments on the investigation of magnetic properties of the compounds [6, 23, 33]. It long was considered that in the RMn2Z2 compounds with dMn–Mn > dc with an F structure above the ТС tem perature there occurs a transition into the paramag netic state. The discovery of a new magnetic structure of the AF'' type existing at Т > ТС stimulated a large number of neutron diffraction studies of magnetic structures of the compounds, which confirmed the existence of an AF'' structure in all RMn2Z2 com pounds with dMn–Mn > dc. Initially, it was assumed that the F–AF'' phase transition can be considered as a spin reorientation of the magnetic moments of man ganese at Т = ТС [32]; however, as was shown in [23, 25], the F–AF'' phase transition cannot be con sidered as a spin reorientation and occurs as the “dis appearance” of the ordering of the projections of the magnetic moments of manganese atoms onto the c axis with the retention of the magnetic ordering of the projections of the magnetic moments of manga nese atoms in the basal plane. The investigation of the nature of the F–AF'' transition was mainly restrained by the absence of macroscopic proofs of the existence of the AF'' state. Initially, as the macroscopic sign of the AF'' state there was considered a small deviation from the Curie–Weiss dependence in the temperature dependences of the inverse paramagnetic susceptibil ity χ–1(Т) [33]. However, as was shown in [25], in the case of polycrystalline samples of the compounds, the anomalies indicating the existence of an AF'' structure can be absent because of the strong anisotropy of the manganese sublattice. It was only quite recently that Vol. 112

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Table 2. Structures characteristic of the RT6Z6 compounds Pr

Nd

Sm

Gd

Tb

Dy

Ho

Er

Tm

Lu

Sc

Y

RMn6Sn6 RMn6Ge6

?

RFe6Sn6

?

RFe6Ge6

?

? ?

– Hexagonal

HfFe6Ge6 (P6/mmm)

– Orthorhombic

HoFe6Sn6 (Immm)

– Hexagonal

YCo6Ge6 (P6/mmm)

– Orthorhombic

TbFe6Sn6 (P6/mmm)

– Orthorhombic

GdFe6Ge6 (Pnma)

there were revealed anomalies in the temperature dependence of heat capacity [34] and in the thermal expansion coefficient [35] in the region of the AF''–P phase transition, which can be considered to be the first reliable macroscopic proofs of the existence of the AF'' state in the compounds and give the possibility for a further investigation of the F–AF'' phase transition and the nature of the AF'' state in RMn2Z2 com pounds. 2. RAREEARTH COMPOUNDS WITH A STRUCTURE OF THE HfFe6Ge6TYPE 2.1. Crystal and Magnetic Structures of RT6Z6 Compounds The specific features of the magnetism of com pounds with a natural layered structure clearly mani fest themselves in the group of intermetallic com pounds with a general formula RT6Z6, where R is a rareearth element or Sc and Y; T is a 3d transition metal; and Z is Sn or Ge, which can be partially or completely replaced by Ga or In. These compounds crystallize into structures of different types (Table 2), most of which are closely related to one another. The basic structures for all types are the structures of the HfFe6Ge6 and ScFe6Ga6 types, which were described for the first time in [36, 37]. Both structures can be

represented as being derived from a hexagonal struc ture of the CoSn type [38], which contain kagomé planes of T atoms, octahedra of Z atoms, and coarse R atoms located in the centers of bipyramids. The vari ous hexagonal and orthorhombic structures listed in Table 2 can be represented in the form of fragments of the HfFe6Ge6 and ScFe6Ga6 structures taken in differ ent combinations [38]. It can be seen from Table 2 that most frequently the RT6Z6compounds have a hexagonal crystal structure of the HfFe6Ge6 type (space group P6/mmm). Such a structure is shown in Fig. 12. It represents a set of alternating layers R(Z)–T–Z–Z–Z–T–R(Z) packed along the crystallographic с axis. The carriers of mag netism in these compounds are atoms of transition 3d metals and also R atoms with an incompletely filled f electron shell. The compounds of these types do not form for R = La, Ce, Pm, and Eu. At T = Co, the compounds have a hexagonal structure of the YCo6Ge6 type irrespective of R. The magnetic atoms of each type are located in separate crystallographic layers. The strong exchange interaction in the layers containing atoms of the T metal ensures high temperatures of magnetic ordering (400–600 K). This interaction is usually ferromag netic, and all magnetic moments of 3d atoms within

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE

n=2 J2 J3

n=1 J1 n=0 J2

J3

n = –1

R

Mn

X

Fig. 12. Crystal structure of the HfFe6Ge6 type and the interlayer Mn–Mn exchange integrals in RMn6Sn6 com pounds.

each layer are parallel to one another. At the same time, the interaction between the layers of atoms T is weakened, since there are layers of nonmagnetic met als between them. Depending on the magnitude and sign of interlayer exchange interactions, different magnetic structures are formed in the RT6Z6 com pounds.

723

As an example, Fig. 13 displays the magnetic struc tures of RMn6Z6 compounds with nonmagnetic atoms R = Y, Lu, which were determined by the magnetic neutron diffraction method [39, 40]. The neutron diffraction measurements show that for both in YMn6Ge6 and LuMn6Sn6 the exchange interaction of Mn atoms through a layer containing R atoms (J2 in Fig. 12) is antiferromagnetic, whereas within the structural block Mn–Z–Z–Z–Mn the exchange Mn–Mn interaction (J1 in Fig. 12) is ferro magnetic. The difference in the orientations of mag netic moments in these compounds indicates a weak magnetic anisotropy. In YMn6Sn6, there arises a more complex magnetic structure. The magnetic moments of the Mn atoms lie in the basal plane, but upon the transition from layer to layer they rotate relative to one another (Fig. 13c). The angle of rotation is variable: it is small (~10°) upon the transition through the Z–Z–Z layers, but is 100°– 130° upon the transition through the R(Z) layer. Thus, the magnetic structure represents a double spiral swirl ing along the c axis. Let us now consider a phenome nological model that explains the formation of spiral magnetic structures in layered magnets with non equivalent layers [41, 42]. 2.2. Formation and Destruction of Magnetic Structures of a Double Flat Spiral Type The spiral magnetic structures were earlier revealed in a whole number of magnets, including MnO2 [43], Mn

c'

c'

Mn(7/4) Y Mn(5/4)

c

2

c

Mn(3/4) Mn(3/4)

Mn(3/4) Y(1/2)

Y

Lu(1/2) Mn(1/4)

Mn(1/4)

b

a

b

b a

Mn

a (a)

Mn(1/4)

c

(b)

(c)

Fig. 13. Magnetic structures of (a) YMn6Ge6, (b) LuMn6Sn6, and (c) YMn6Sn6 compounds [39, 40]. THE PHYSICS OF METALS AND METALLOGRAPHY

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⎡ ⎛ ⎞⎤ δ = − sign ( J 1J 3 ) arccos ⎢−J 2 J 3 ⎜ 1 2 − 12 + 12 ⎟⎥ ⎣ ⎝ 4J 3 J 1 J 2 ⎠⎦ (6) ⎡1 ⎛ 1 ⎞⎤ 1 1 Φ = arccos ⎢ J 1J 2 ⎜ 2 − 2 − 2 ⎟⎥ . ⎣2 ⎝ 4J 3 J 1 J 2 ⎠⎦

QF

0 x = J2/J1

1

J1 < 0

y = J3/J1

3 2 1 0 QAF –1 –2 –3 –1

π 2 < δ ≤ π). The angles in both spiral structures are given by the relationships

J1 > 0

y = J3/J1

3 2 1 QF 0 –1 –2 –3 –1

QAF

0 x = J2/J1

1

Fig. 14. Magnetic phase diagram of a layered magnet with two nonequivalent layers and three integrals of exchange interaction.

MnAu2 [44], rareearth metals and their compounds [45]. If the intralayer exchange interaction substan tially exceeds the interlayer interaction, then upon an analysis of a magnetic structure, the interactions between the atoms can be replaced by an effective interaction between the resultant moments of the lay ers. It is known that for the formation of a magnetic spiral it is necessary to take into account the interac tion between not only firstneighbor layers but also between secondneighbor and thirdneighbor layers [46]. Since in the RT6Z6 compounds structural blocks of two nonequivalent type exist, the exchange integrals between a given manganese layer and its nearest neigh bors from above and from below (J1 and J2 in Fig. 12) can differ. The exchange integral between the second nearest neighbors J3 is the same for all layers. It follows from the above data that the magnetic structure in YMn6Sn6 represents two spirals with the same period Φ inserted into one another and shifted by a certain angle δ. With allowance for three types of exchange interaction, the energy per two layers in such a struc ture is

E = −J 1 cos δ − J 2 cos ( Φ − δ) − 2J 3 cos Φ.

(5)

The minimization of this energy with respect to δ and Φ yields six possible types of magnetic ordering: collinear ferromagnetic; three collinear antiferro magnetic; and two spiral (quasiferromagnetic (QF, δ ≤ π 2 ) and quasiantiferromagnetic (QAF,

Figure 14 displays magnetic phase diagrams con structed in J2/J1 and J3/J1 coordinates for the case of J1 > 0 and J1 < 0 (on the assumption that |J1| > |J2|). It is seen that the helicoidal phase QF arises between the ferromagnetic and antiferromagnetic structures at positive J1, and the QAF phase, between two antiferro magnetic phases when J1 < 0. If we consider the phase diagram shown in Fig. 14 for the case of RMn6Z6 com pounds, we see that the case of J1 > 0 is realized for them, since upon alloying in one of the sublattices there is observed a transition from ferromagnetic to helicoidal and further to antiferromagnetic ordering [47]. The relationships between the parameters of exchange interaction at which the angles of the rota tion of magnetization upon the transition from layer to layer prove to be close to the experimentally observed values Φ = 100° and δ = 11° for YMn6Sn6 are J2/J1 = 0.22 and J3/J1 = –0.12. Let us consider the distortion of a spiral structure in a magnetic field. If switchingon a magnetic field per pendicular to the plane of ordering of the moments, the solution can be obtained in an analytical form [41]. The allowance for interlayer exchange interactions leads only to a renormalization of the 2ndorder mag netic anisotropy constant. Its magnitude proves to be equal to

K eff ⎧J J ⎡ ⎛ ⎞⎤ ⎫ (7) = K + 1 ⎨ 1 2 ⎢1 + J 32 ⎜ 12 + 12 ⎟⎥ − ( J 1 + J 2 + 2J 3 )⎬ . 2 ⎩ J 3 ⎣4 ⎝ J 1 J 2 ⎠⎦ ⎭ where K is the magnetocrystalline anisotropy con stant. The projection of the magnetization M onto the field in this case grows linearly with increasing field from M = 0 at B = 0 to the saturation M = Ms at B = Ba, where Ba = 2Keff/Ms is the anisotropy field. If the magnetic field is applied in the plane of the layers, an analytical expression for the magnetization curve can be obtained only for a simple spiral [44]. With increasing field, the simple spiral first becomes distorted smoothly and then transforms jumpwise into a fanlike structure. In the case of a double flat spiral, the experiments performed on YMn6Sn6 single crys tals show the existence of several jumps in the curve of magnetizing in the basal plane [48]. In terms of the suggested model, the exact results for the calculation of the magnetization curves of the double spiral could not be obtained. The results of numerical simulation are given in Fig. 15.

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2.3. Magnetic Structures in RT6Z6 Compounds with Magnetic RT6Z6 Atoms The aboveconsidered structures referred to RT6Z6 compounds in which the R atoms are diamagnetic. In the compounds with magnetic R atoms there addition ally arises an R–T exchange interaction. In all R–T intermetallic compounds without exception, this interaction tends to orientate the spins of the R and T atoms antiparallel to one another. At the same time, it THE PHYSICS OF METALS AND METALLOGRAPHY

725

(a)

–1.02 –1.04 –1.06 –1.08 –1.10

H AF

–1.12 –1.14 0

0.02

1.0 M/Ms

The field dependences of the energies of the spiral and antiferromagnetic structures are shown in Fig. 15. It is seen that near the field BMs/J1 = 0.02 marked by a vertical dashed line the energy of the initially col linear antiferromagnetic state becomes equal to the energy of a distorted spiral. In the presence of a domain structure, a jump in the magnetization can exist at these points, with a transition onto the curve corresponding to the deformed AF phase. With increasing field, the difference in the energies between the spiral and antiferromagnetic structures first increases, but then decreases. At BMs/J1 = 0.046, this difference becomes very small. At the same time, the magnetization of the spiral structure in these fields is noticeably greater than that of the antiferromagnetic structure. This can lead to a next jump in the magneti zation, which will decrease the magnetoelastic energy that was not earlier included into consideration. Finally, in the range of fields BMs/J1 ~ 0.06 the situa tion changes to the opposite one; the antiferromag netic curve already reaches saturation, whereas that corresponding to the spiral structure does not yet sat urate. In this case, there again is possible a magnetiza tion jump. The magnetization curve obtained, shown by a solid line in Fig. 15b, is quite similar to that exper imentally observed for YMn6Sn6 in the case where the field is applied in the basal plane [48]. The simple model given above makes it possible to explain the main features of magnetic structures in the first approximation. However, a detailed analysis of neutrondiffraction patterns of YMn6Sn6 shows that in the crystal there coexist two (and even three, at high temperatures) magnetic phases of the doublespiral type with wave vectors of different magnitudes directed along the с axis [49, 50]. In [51, 52], there was set and solved a problem of the development of a tech nique that makes it possible to mathematically rigor ously determine the entire set of magnetic structures stable in an arbitrary layered magnet. It was shown that in a sample containing S different magnetic layers only spiral structures can be formed. At S = 2, only one sta ble double spiral can exist in the magnet. The apparent contradiction can be eliminated if we take into account the magnetic anisotropy in the basal plane, since its presence leads to the division of the homoge neous magnetic spiral into separate fragments (domains), which can give contributions with different wave vectors to the neutronscattering pattern [53].

E/J1

MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE

0.04 (b)

0.06

0.08

0.8 0.6 0.4

x = J2/J1 = 0.21 y = J3/J1 = –0.12

0.2 0

0.02

0.04

0.06

0.08

BMs/J1 Fig. 15. (a) Dependence of the energy of the helicoidal (H) and antiferromagnetic (AF) structure on the magnitude of the field applied in the plane of the helicoid; (b) magneti zation curves corresponding to the helicoidal structure (dotted line), antiferromagnetic structure (dashed line), and structure that corresponds to the minimum energy (solid line). The highfield jumps are shown only qualitatively).

is seen from Fig. 13 that the R atoms are located in a layer that is equispaced from two layers of T atoms whose magnetic moments (in the absence of an R–T interaction) are also oriented antiparallel. Conse quently, if the R–T interaction is weak, it is frustrated and then the magnetic R atoms virtually do not affect the structure of the T sublattice. If the energy of the R–T interaction is greater than the energy of the inter layer Mn–Mn interaction J2, then the frustration will be eliminated and there will occur a transition to a fer rimagnetic structure. Therefore, in compounds with magnetic R atoms there are observed quite various magnetic structures and magnetic phase transitions induced by temperature or magnetic field. In the compounds with T = Fe, the R–Fe exchange interaction is relatively weak and the effect of the mag netic sublattices of R and Fe on one another is negligibly small. Therefore, here there arises an effect that is rarely observed in twosublattice magnets, namely, the mag netic sublattices become ordered at different tempera tures [54]. The Fe sublattice is ordered antiferromag netically below the Néel temperatures, i.e., ~485 K for RFe6Ge6 and ~555 K for RFe6Sn6 (the magnetic order is analogous to that shown in Fig. 13b). The ferromag netic order in the R sublattice arises at substantially lower temperatures and virtually does not affect the order in the Fe sublattice. The crystal structures and the temperatures of magnetic ordering of the RFe6Ge6 and RFe6Sn6 compounds are given in Table 3 accord ing to [54]. Vol. 112

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Table 3. Space groups, structure types, Néel temperatures of the Fe sublattice, and Curie temperatures of the R sublat tice of RFe6Ge6 and RFe6Sn6 compounds [54] Space group

Structure type

TN(Fe) (K)

Cmcm P6/mmm Cmcm Cmcm Cmcm Immm Immm P6/mmm

TbFe6Sn6 YCo6Ge6 TbFe6Sn6 TbFe6Sn6 TbFe6Sn6 HoFe6Sn6 HoFe6Sn6 HfFe6Ge6

486 489 490 489 484 484 482 481

LuFe6Ge6 P6/mmm

HfFe6Ge6

485

– 29.3 7.8 7.5 8.0 3.1 – – –

YFe6Sn6 GdFe6Sn6 TbFe6Sn6 DyFe6Sn6 HoFe6Sn6 ErFe6Sn6 TmFe6Sn6 LuFe6Sn6

HoFe6Sn6 TbFe6Sn6 TbFe6Sn6 TbFe6Sn6 HoFe6Sn6 ErFe6Sn6 HfFe6Ge6 HfFe6Ge6

558 554 553 559 559 560 562 540

– 45 19 14 8 4 – –

Com pound YFe6Ge6 GdFe6Ge6 TbFe6Ge6 DyFe6Ge6 HoFe6Ge6 ErFe6Ge6 TmFe6Ge6 YbFe6Ge6

Immm Cmcm Cmcm Cmcm Immm Cmcm P6/mmm P6/mmm

TC(R) (K)

The stronger interaction between the magnetic R and T sublattices is realized in the compounds with T = Mn. In RMn6Sn6 compounds with diamagnetic R atoms (Sc, Y, Lu), the paramagnetic Curie temper atures are greater than the temperatures of magnetic ordering [55]. which indicates a strong ferromagnetic interaction within the Mn layers. For the compounds with magnetic R (Gd–Tm), there is observed a decrease in the paramagnetic Curie temperature with increasing de Gennes factor of the rareearth ion [55], which is connected with an enhancement of the anti ferromagnetic interaction between the R and Mn sub lattices. For R = Tm and Er, this interaction is rela

Paramagnet

400

T, K

300 200 100

0

Er–P Mn–AF Er–P Mn–AF

0.5

1.0

Ferrimagnet Er–F Mn–F 1.5 2.0 μ0H, T

2.5

tively weak and, similar to the compounds with Fe, the magnetic sublattices of R and Mn in TmMn6Sn6 and ErMn6Sn6 become ordered at different temperatures [55]. The investigation of the magnetic properties of single crystals of these compounds made it possible to determine the magnetic structures at different temper atures and in magnetic fields of different strength. For example, Fig. 16 displays the magnetic phase diagram of the ErMn6Sn6 compound constructed in [56] based on the data of magnetic measurements along the crys tallographic c axis. Upon cooling of the sample from high temperatures, the Mn sublattice is ordered anti ferromagnetically at T = 355 K. In the absence of a magnetic field, the Er sublattice remains paramag netic upon cooling down to 65 K. The magnetic field exerts a strong effect on the magnetic structure of the compound. In the temperature range from 65 to 355 K, the application of a magnetic field causes a metamagnetic transition in the Mn sublattice. In this case, the exchange Er–Mn interaction increases sharply, the Er sublattice becomes ordered and is ori ented antiparallel to the Mn sublattice, forming a col linear ferrimagnetic structure. Below 65 K in the zero magnetic field, both magnetic sublattices are antifer romagnetic. The application of a magnetic field less than 0.2 T induces a metamagnetic transition in the Mn sublattice, which leads to a metamagnetic transi tion in the Er subsystem and to the formation of a fer rimagnetic structure. In magnetic fields applied along the crystallo graphic c axis, the changes in the magnetic structure prove to be analogous, but the magnitudes of the criti cal fields of the metamagnetic transition exceed by several times the corresponding magnitudes for the case of H || a. The strongest R–Mn exchange interaction should be expected in GdMn6Sn6, since the Gd ion possesses the maximum spin in the row of rareearth metals. In spite of the presence of two magnetic atoms, this com pound has one temperature of magnetic ordering equal to 435 K, below which there is formed a ferri magnetic structure. The spontaneous magnetic moment of the compound is 6.0 μB/f.u., which, with allowance for the magnetic moment of Gd μGd = 7 μB, corresponds to 2.17 μB per Mn atom. From the mea surements of the magnetization curves on textured (with rotation) powder samples, it was established that in GdMn6Sn6 the magnetic moments of the sublattices are oriented in the basal plane of the crystal [57, 58]. 2.4. Magnetic Anisotropy and Magnetic Phase Transitions in GdMn6Sn6 and TbMn6Sn6 Compounds

3.0

Fig. 16. Magnetic phase diagram of the ErMn6Sn6 com pound for the case of H||a [56].

Since the Gd3+ ion has no orbital magnetic moment, the contribution to the anisotropy of inter metallic compounds from the gadolinium sublattice is usually small. The study of the anisotropy of GdMn6Sn6 permits one to make conclusions on the

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25 GdMn6Sn6

–0.2

M, A m2/kg

0 K1, K2, MJ/m3

727

K2 K1

–0.4 –0.6

20 15 10 230 K 210 K 250 K 270 K

5

–0.8

280 K 290 K 300 K 310 K

–1.0 80

120

160

200 T, K

240

0

260

1

2 3 μ0H, T

4

5

Fig. 17. Temperature dependences of the magneticanisot ropy constants K1 and K2 of the GdMn6Sn6 compound [58].

Fig. 18. Magnetization curves of TbMn6Sn6 measured per pendicularly to the texture axis at various temperatures [61].

anisotropy of the Mn sublattice in RMn6Sn6 com pounds. The description of the magnetization curves of highly anisotropic uniaxial crystals is usually per formed on the basis of a standard phenomenological expansion of their energy:

decreases more rapidly than μMn, and up to the Curie temperature TC = 420 K the magnetic moment of the Mn sublattice (6 μB) exceeds the magnetic moment of the Tb sublattice [63]. With increasing temperature, the magnetic moments of Tb and Mn reorient from the c axis toward the basal plane because of the com petition between the contributions to the magnetic anisotropy from the sublattices of manganese and ter bium [55]. It has been establish on the basis of neu trondiffraction data [60] that the spin reorientation occurs through a state corresponding to a cone of easy axes and is terminated at a temperature Tsr ≈ 310 K.

2

4

6

E = K 1 sin θ + K 2 sin θ + K 3 sin θ + … – M s H cos θ,

(8)

where K1, K2, K3, … are the magneticanisotropy con stants, Ms is the saturation magnetization, H is the internal magnetic field, and θ is the angle between the vector Ms and the c axis. The first three terms in (8) determine the energy of the magnetocrystalline anisot ropy; the last term determines the Zeeman energy of the crystal. For an oriented powder sample, the analysis of the magnetization curves also requires the allowance for the angle of misorientation of the c axes of the crystal lites [57, 58], which typically is 5°–8°. The temperature dependences of the magnetic anisotropy constants K1 and K2 of the GdMn6Sn6 com pound, for which the calculated magnetization curves coincide best with the experimental data, are given in Fig. 17. In the temperature range of 77–280 K, the con stant K1 is negative; i.e., the manganese sublattice exhibits an easyplane anisotropy. In RMn6Sn6 compounds with highly anisotropic R ions, there is possible a competition between the anisotropies of different magnetic subsystems, which leads to the appearance of magnetic phase transitions. The magnetic properties of the TbMn6Sn6 compound have been studied in much detail both by neutron dif fraction [57, 60] and by magnetic measurements using single crystals and textured polycrystalline samples [56, 61]. According to neutrondiffraction measurements [60, 62], the magnetic moment of terbium and manga nese in TbMn6Sn6 are μTb = 8.6 and μMn = 2.4 μB, are directed along the c axis, and are oriented antiparallel to one another. With increasing temperature, μTb THE PHYSICS OF METALS AND METALLOGRAPHY

The magnetization curves of TbMn6Sn6 indicate the presence of magneticfieldinduced phase transi tions in this compound. In the magnetization curve of an isotropic sample at room temperature there is observed an anomaly in the form of a strongly smeared magnetization jump in a field of ~0.4 T, which was ascribed by the authors of [63] to spinflop or meta magnetic transition. However, the measurements on an oriented polycrystalline sample [61] and on a sin glecrystal TbMn6Sn6 sample [56] contradict this assumption, since the magnetization jump is observed upon the magnetization along hard rather than easy axis as it should occur in the case of a spinflop or metamagnetic transition. Figure 18 displays the magnetization curves of a textured sample of TbMn6Sn6 measured perpendicu larly to the texture axis (crystallographic c axis) at var ious temperatures. The jumplike changes in the mag netization are observed at temperatures below 160 K. It is seen that the critical field of the transition decreases with approaching the spinreorientation temperature. At a temperature above Tsr, there also is observed a firstorder phase transition, but only in a magnetic field applied along the c axis. Such a behav ior is characteristic of magneticfieldinduced first order magnetization processes (FOMPs) [64] which occur due to specific features of the magnetocrystal line anisotropy of the compounds. An exhaustive clas sification of such transitions and their phenomenolog Vol. 112

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c axis H

A1

A1, P1

H

P1 H M c axis

c axis H A1C

A1C, P1C

H

P1C H M A2, P2 c axis

c axis H

A2

H

P2 H

Fig. 19. Angular dependences (schematic) of the energy of a ferromagnet and its magnetization curves [64].

ical description on the basis of relationship (8) are given in [64]. The magneticfieldinduced jumplike change in the magnetization of a ferromagnet is related to a non monotonic angular dependence of its energy (Fig. 19). In this case, upon the application of a magnetic field along the hard axis the smooth rotation of the magne tization vector is impeded, since the system should pass through a local energy maximum. As a result, in the magnetization curve there arises a jump. On the whole, there exist six types of FOMPs (see Fig. 19). Three of them are realized upon the application of the field along the c axis (their designation, according to

K1, K2, 106 J/m3

2.5 2.0 K1

1.5 1.0

0.3 K1 0.2 0.1 0 K 2 –0.1 280 300 320

0.5 0

K2

–0.5 150

200

250 T, K

300

350

Fig. 20. Temperature dependences of the magneticanisot ropy constants K1 and K2 of the TbMn6Sn6 compound [58].

[64], contains a letter A) in the crystal with an easy plane anisotropy; and three, in a uniaxial crystal in a field oriented in the basal plane (designated by P). After a jump, the magnetization can either reach satu ration (A1, P1) or not reach saturation (A2, P2). Finally, there also is possible a jump from a phase char acterized by a cone of easy axes (A1C, P1C). To simu late the magnetization curve with an FOMP on the basis of expansion (8) with allowance for only two anisotropy constants, the values of K2 should be nega tive, whereas K1 can be both positive (FOMP of type A1 at |K2| > K1 or of type P1 at |K2| < K1) and negative (FOMP of type A1). The conditions for the realization of an FOMP in this case are written in the following form [64, 65]: K 1 > 0,

K 2 < 0,

6 K2 > K1 ,

K 1 > 0,

K 2 < 0,

4 K2 > K1 .

(9)

Since at low temperatures the easy axis in TbMn6Sn6 is oriented along the crystallographic c axis, an FOMP of the P1 type is realized in this com pound. The anisotropy constants obtained from an analysis of the magnetization curves of TbMn6Sn6 [58, 66] are given in Fig. 20. At low temperatures, the magnetization process is described by a positive anisotropy constant K1 and a negative anisotropy con stant K2. At a temperature of 315 K, the K1(T) depen dence passes through the zero and a spontaneous reorientation of the magnetization vector occurs from the c axis toward the basal plane of the crystal.

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Table 4 lists the magnitudes of the magnetic moments of the Tb and Mn sublattices and the angles they make with the c axis that were calculated from the neutron diffraction patterns taken from a nonoriented sample in various magnetic fields [62]. The average moments of the Tb and Mn sublattices and the magni tude of the angle (7°) they make with the c axis mea sured in a zero magnetic field agree well with the data of previous studies [57]. Some increase in the mag netic moments of the sublattices under the effect of the field can be related to the ordering effect of the field on the Mn sublattice, in which the magnetization direc tion coincides with the direction of the external mag netic field. In this case, there also occurs an increase in the magnetic moment of the Tb sublattice due to a strong intersublattice exchange interaction. According to the theory of singleion anisotropy, the higher the order of the anisotropy constant, the more rapidly it should decrease with increasing tem perature. In TbMn6Sn6 the anisotropy constant K2 decreases slowly with increasing temperature and remains sufficiently high at room temperature, which is untypical of the crystalfield model. To explain this fact, other mechanisms should be used. In [67], it was shown that the FOMP can be caused by the presence of a magnetoelastic contribution to the anisotropy energy, which changes the magnitude of K2. However, according to our estimates [59], the magnitude of the magnetoelastic contribution is less than 2% of the magnitude of K2 for the Tb sublattice. For a more cor rect description of the magneticfieldinduced phase transitions, the possibility of the formation of a non collinear magnetic structure should apparently be taken into account [68]. Indeed, according to the neu trondiffraction data (Table 4), the magnetic moments of the Tb and Mn sublattices are not strictly antiparal lel in a magnetic field. THE PHYSICS OF METALS AND METALLOGRAPHY

5

(002)

8

(001)

4

(003)

H⊥ C (006)

2

3 2

0

H || C

1

I, 103 counts

4

6 I, 103 counts

Although the transitions of the FOMP type are encountered relatively frequently in intermetallic compounds (R2Fe14B, R2Fe17, RFe11Ti and in some others), the neutrondiffraction studies of magnetic moments in the process of such transitions are rather rare, since, as a rule, they occur in large magnetic fields. The small magnitude of the field of a spinreori entation transition at room temperature in TbMn6Sn6 permitted us to study this transition by neutron dif fraction [62]. Figure 21 displays the neutrondiffrac tion patterns of an oriented sample of TbMn6Sn6 taken in a magnetic field of 0.5 T (exceeding the criti cal field of the transition at a given temperature) applied perpendicular and parallel to the c axis (T = 293 K). It is seen well that the magnetic line (001) related to the projection of the magnetic moment onto the basal plane is absent upon the magnetization along the c axis and appears upon the magnetization perpen dicular to the c axis, which agrees well with the data of magnetic measurements and confirms that this transi tion is neither spinflop nor metamagnetic.

729

–2 0 –4 0 10 20 30 40 50 60 70 80 90 2θ, deg Fig. 21. Neutron diffraction patterns of a textured sample of TbMn6Sn6 taken in a magnetic field of 0.5 T applied parallel (lower curve) and perpendicular (upper curve) to the texture axis [62].

When Gd substitutes for Tb in the quasiternary Tb1 – xGdxMn6Sn6 system, there is formed a disor dered solid solution in the rareearth sublattice. This makes it possible to smoothly control the magnetic anisotropy and exchange interactions and to shift the temperatures and fields of magnetic phase transitions. The temperature dependences of the critical fields Hcr of magnetic phase transitions are shown in Fig. 22. It is seen that the FOMP is observed both above and below the temperature of spin reorientation Tsr. The magnitudes of Hcr decrease with approaching the spin reorientation temperature from both the higher and lower temperatures and are equal to zero at T = Tsr. The materials with a sharp change in the orientation of magnetization in relatively low fields near room tem perature can find application as the elements of sensors and actuators responding to changes in temperature and magnetic field. There are known development works that demonstrate the conversion of the thermal energy into electrical energy based on the spinreorien tation transitions [69]. At the same time, for the appli cations based on the magnetocaloric and magnetoresis Table 4. Magnetic moments of the Tb and Mn sublattices and the angles of their orientation relative to the c axis in various magnetic fields for the TbMn6Sn6 compound Magnetic field

Sublattice

H=0 µ0H = 0.4 T µ0H = 0.5 T

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Tb Mn Tb Mn Tb Mn 2011

Magnetic moment (µB/atom) 5.2(1) 1.89(8) 5.8(2) 2.1(1) 5.9(1) 2.1(1)

Angle relative to the c axis (deg) 7(1) 7(1) 44(3) 37(5) 51(3) 37(5)

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BARANOV et al.

μ0Hcr, T

15

revealed in the compounds Y0.5Ho0.5Mn6Sn6 [71] and Y0.7Ce0.3Mn6Sn6 [72]. The transition from a noncollinear spiral structure to a collinear ferromagnet structure can also be observed in Y1 – xTbxMn6Sn6. The magnetic phase dia gram of this system is given in [73, 74]. At x ≥ 0.2, the compounds are ferrimagnetic. At smaller Tb concen trations, a spiral structure is retained, which, however, can easily pass into a ferrimagnetic one in the presence of a magnetic field. Figure 23a shows magnetization curves of YMn6Sn6 measured in magnetic fields to 5 T under an external hydrostatic pressure to 0.6 GPa. It is seen that the field necessary for the collinear ordering of mag netic moments decreases with increasing pressure. Note that the application of an external pressure usu ally stabilizes antiferromagnetic interactions. The Y0.85Tb0.15Mn6Sn6 compound exhibits a spiral magnetic ordering, but its ground state is maximally close to a ferromagnetic state. At atmospheric pres sure, this compound passes into a ferromagnetic state in a field that is significantly lower than in the case of YMn6Sn6 (Fig. 23b). In the region of the transition, a hysteresis of magnetization is observed, which indi cates that this is a secondorder phase transition. A sharp increase in the hysteresis as compared to YMn6Sn6 appears to be related to an enhancement of magnetic anisotropy upon the incorporation of highly anisotropic Tb ions. Upon the application of an exter nal pressure, a significant residual magnetization arises, which is characteristic of ferromagnetic order ing. At the same time, the hysteresis loop has a con striction and is typical of a sample in which there coex ist ferromagnetic and antiferromagnetic components in approximately equal amounts. The coexistence of two magnetic phases is a sign of a magnetic inhomogeneity of the sample. The energies of the ferromagnetic and antiferromagnetic phases are

Tb1 – xGdxMn6Sn6 x=0 x = 0.2 x = 0.4 x = 0.6 x = 0.8 x = 0.9

10

5

0

50

100 150 200 250 300 T, K

Fig. 22. Temperature dependences of the critical field of the magnetic phase transition (FOMP) of the Tb1 ⎯ xGdxMn6Sn6 compounds [58].

tance effects it is transitions with a change in the mag netic order, in particular, antiferromagnet–ferromagnet transitions that are more attractive. 2.5. Spontaneous and MagneticFieldInduced Magnetic Phase Transitions between Antiferromagnetic and Ferromagnetic States The spiral antiferromagnet YMn6Sn6 can be trans formed into a ferromagnetic state by substitution of gallium for part of tin [70]. In the YMn6Sn6 – xGax sys tem, the ferromagnetism arises near room temperature already at x = 0.1; at lower temperatures, there is observed a transition from the antiferromagnetic into ferromagnetic state upon an application of a magnetic field. The magnetoresistance in such a transition reaches 35% in a field of 5 T at T = 5 K and 15% at 200 K [70]. As was already mentioned above, analo gous transitions are observed upon a partial substitu tion of some lowmagneticallyactive rareearth ions for yttrium. A significant magnetoresistance was

60

YMn6Sn6 40

T = 4.2 K M, A m2/kg

T = 4.2 K M, A m2/kg

Y0.85Tb0.15Mn6Sn6

P=0 0.3 GPa 0.6 GPa M(μ0H, T) 10

20 5

P=0 0.6 GPa

40

20

μ0H (T) 0 0

2

4 μ0H, T

5

10 15 20 6

8

0

0

2

μ0H, T

4

6

Fig. 23. Magnetization curves of polycrystalline samples of (a) YMn6Sn6 and (b) Y0.85Tb0.15Mn6Sn6 measured at various pres sures. The inset shows the magnetization curve of YMn6Sn6 in pulsed fields (to 20 T) at atmospheric pressure. THE PHYSICS OF METALS AND METALLOGRAPHY

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE 6 RMn6Sn6 ΔV/V (10–3)

4

R=Y R = Tb

X T X

731

M

X T X

2 0

Fig. 25. Intercalation of dichalcogenides of transition met als (schematic).

–2 0

0.5

1.0 T/TC

1.5

Fig. 24. Variation of the lattice volume ΔV/V as a function of the reduced Curie temperature T/TC for the YMn6Sn6 and TbMn6Sn6 compounds [75].

very close to one another near the transition. There fore, the fluctuations of the alloy components, which are caused, in particular, by the difference in the atomic radii of Y and Tb, lead to the formation of tem perature and concentration ranges in which a mixture of magnetic phases is stable. Since the lattice compression strengthens the fer romagnetic interactions, the appearance of a negative volume magnetostriction is expected upon the passage of the alloy into the magnetically ordered state. We studied the thermal expansion of the Y1 – xTbxMn6Sn6 compounds by Xray diffraction in a wide temperature range [75]. Above the Curie temperature, the lattice expansion agrees well with the Debye–Grüneisen model with a Debye temperature of 336 K. The mag netic ordering leads to an insignificant change in the thermal expansion along the c axis, whereas for the parameter a there is observed a strong deviation from the dependence expected for the Debye–Grüneisen model below the ordering temperature [75]. The spontaneous magnetostriction is positive for YMn6Sn6 and is negative in a wide temperature range for TbMn6Sn6. Figure 24 displays the temperature dependences of the change in the lattice volume for RMn6Sn6 com pounds with R = Y and Tb. It is seen that the appear ance of a ferrimagnetic order is accompanied by a sig nificant negative volume magnetostriction and that the ferrimagnetic compound with Tb has a smaller volume than the spiral magnet YMn6Sn6. The unusual properties observed under pressure and the anomalous expansion of the lattice appear to be related to the specific features of the exchange interactions in these materials. As was noted above, the formation of a doublespiral structure means the existence of at least three interplanar exchange inter actions, namely, J1 and J2 between nearest planes and J3 between nextnearest planes (Fig. 12). It is seen from the magnetic phase diagram of the spiral magnet shown in Fig. 14 that the difference between the ener THE PHYSICS OF METALS AND METALLOGRAPHY

gies of the spiral and ferrimagnetic states will decrease if the ratio J2/J1 or J3/J1 increases with increasing pres sure. Therefore, for the structure of the double flat spi ral type the antiferromagnetic interactions will be weakened with reducing volume, e.g., because of a rapid decrease in the (most strong) ferromagnetic interlayer exchange interaction J1. 3. MAGNETIC PROPERTIES OF INTERCALATED DICHALCOGENIDES OF TRANSITION METALS WITH A LAYERED STRUCTURE One of the most widely used ways of producing quasitwodimensional systems, including magnetic systems, is the intercalation of some atoms, mole cules, or structural fragments into the interlayer space of crystal substances with a layered structure, such as dichalcogenides of transition (T) Group IV–VI metals of the TX2 type (X = S, Se, Te). In the TX2 compounds, the ions of the T metal and chalcogen inside threelay ered blocks X–T–X are related to one another by strong (predominantly covalent) bonds, whereas the binding between the X–T–X blocks is weak (mainly of the van der Waals type). This makes it possible to introduce atoms of other elements, or even molecules, into the gaps between the X–T–X sandwiches (Fig. 25) and thereby create new layered structures [76, 77]. The hexagonally packed layers of T and X atoms can be shifted relative to each other, so that there can be realized octahedral or trigonal surround ings of T atoms by the chalcogen atoms in the sand wich. Different ways of packing of such sandwiches in the direction perpendicular to the layers leads to dif ferent structural modifications of dichalcogenides TX2, which can differ strongly in their physical proper ties. They can exhibit superconductivity, transition into states with a chargedensity waves (CDWs), and also can find application as materials for the electrodes of lithiumion batteries [76, 77]. The dichalcogenides of transition metals TX2 (X = S, Se, Te) exhibit Pauli paramagnetism with a suscep tibility χ ~ 10–6 to 10–5 cm3/mol at room temperature. At low temperatures, there can appear a Curie–Weiss contribution from localized moments of impurity atoms. In a whole number of TX2 compounds (T = V, Vol. 112

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V Cr Mn Fe Co Ni

MxTiS2

V Cr Mn Fe Co Ni V Cr Mn Fe Co Ni 0

MxTiSe2

MxTiTe2

0.2

0.4

0.6

0.8

1.0

Fig. 26. Diagram of existence of intercalated compounds MxTiX2 [84].

Ti, Nb, Ta; X = S, Se), in the temperature dependences of the magnetic susceptibility anomalies related to the formation of CDWs were revealed [76, 77]. The intercalation of titanium dichalcogenides with atoms of 3d transition metals (M) of rareearth ele ments (R) that have incompletely filled 3d or 4f elec tron shells makes it possible to obtain structures with alternating layers of magnetic and nonmagnetic atoms [78–81]. By changing the concentrations of interca lated magnetic atoms of various types, one can vary in wide limits the exchange interactions inside the layers and between the layers and obtain magnetic ordering of various type and thereby produce objects with vari ous magnetic characteristics. Below, we consider the main features of the magnetic properties of MxTX2 compounds depending on the type and concentration of atoms of 3d metals. 3.1. Methods of Production of Intercalated Dichalcogenides of Transition Metals and Their Crystal Structure To synthesize dichalcogenides of transition metals, the method of solidstate reactions from correspond ing elements in evacuated quartz ampoules was used. The intercalated materials on their basis can be obtained by the same method [80, 81]. For the inter calation of rareearth elements, electrochemical and chemical methods are also used. Thus, in [82, 83] for the preparation of intercalated compounds YbxTiS2 and EuxTiS2, there were first synthesized precursor Rx(NH3)yTiS2 compounds (R = Eu, Yb) and then the

deintercalation of NH3 and N H 4 groups was per formed by annealing at 270°C. The singlecrystal samples of transitionmetal dichalcogenides are grown by the method of gas transport reactions, as a rule, using I2 or Cl2 as trans port agents. The single crystals of TX2 compounds are obtained in the form of thin plates with an area S ~ 5– 25 mm2 and thickness of 30–50 μm. The same method can be used to obtain single crystals of some interca lated compound MxTX2 [79], although such single crystals as a rule contain a different amount of the intercalant as compared to the initial polycrystalline sample. In the row of compounds TS2 → TSe2 → TTe2, there occurs an increase in all crystallographic param eters because of an increase in the radius of the chal cogen ion. In this case, the thickness of the X–T–X sandwich also increases. However, the relative spacing between the layers of chalcogens expressed through the sandwich thickness decreases. Upon the transition from TS2 to TTe2 there occurs a decrease in the physical width of the spacing (gap) between the sandwiches in this row. This should lead to different limiting concentrations of the inter calated atoms and also should affect the properties of compounds obtained by the incorporation of atoms of one type into different matrix TX2 compounds. Figure 26 displays a diagram of the existence of intercalated compounds MxTiX2 depending on the type and con centration of the intercalant, which illustrates the concentration of atoms of transition metals in the lat tice of titanium dichalcogenides [84]. As is seen, the boundary of the intercalation of atoms of transition met als in the TiX2 matrices shifts toward smaller concentra tions with increasing atomic number of the chalcogen in the row of compounds TiS2–TiSe2–TiTe2. For some sys tem on the basis of the titanium ditelluride (M = V, Mn), instead of the continuous series of solid solu tions, the singlephase compounds were obtained only for concentrations x = 1/2 and 1/3. Depending on the type and concentration of intercalated atoms and also on the conditions of the synthesis, in the MxTiSe2 compounds there can form superstructures related to an ordered arrangement of intercalated atoms in the van der Waals gaps. With increasing temperature, phase transformations of the order–disorder type can be observed in such systems, upon which a disordering in the system of interca lated atoms can occur. In this connection, a very sub stantial factor is the regime of heat treatment and the rate of cooling of the final materials, since the sam ples synthesized at different temperatures and cooled at different rates can differ in their physical proper ties [85]. The titanium dichalcogenides TiX2 (X = S, Se, Te), which are the initial phases for the obtaining interca lated compounds, have a hexagonal crystal structures

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THE PHYSICS OF METALS AND METALLOGRAPHY

Se Ti Se c b

a

O

O

O M

O

Fig. 27. Disposition of atoms in the structure of the MxTiSe2 compounds (schematic).

Mn

c, Å

6.1 Gd

6.0

Cr Fe Ni Co

5.9 0

0.1

0.2

0.3 x

0.4

0.5

Fig. 28. Concentration dependences of the lattice param eter c of the MxTiSe2 compounds.

6.2 1.0 6.1 0.9 rM, Å

c, Å

of the CdI2 type (space group P 3 m1) [76, 77]. The titanium atoms have an octahedral surroundings of chalcogen atoms (Fig. 27). The structure of this type is called a 1T modification. The vacant positions in the van der Waals gaps can be completely or partially filled by foreign atoms or molecules. The investigations of the crystal structure of the MxTiX2 compounds show that the structure of the X–Ti–X sandwiches does not suffer substantial changes. The introduction of 3d ions into the gap between the sandwiches is, as a rule, accompanied by an increase in the interatomic spac ings in the directions parallel to the layers, whereas in the perpendicular direction there occurs either a compres sion or an expansion of the lattice, depending on the type and concentration of the intercalant [78, 86, 87]. Figure 28 shows the variation of the lattice param eter c as a function of the concentration of metal atoms M in the MxTiSe2 compounds. The figure also displays the concentration dependence of the parameter c for the case of intercalation of the titanium diselenide with gadolinium. As is seen, the intercalation of the titanium diselenide with atoms of 3d metals to x = 0.25 in most cases leads to a decrease in the parameter c, which characterizes the average interlayer spacing. An increase in the concentration of Gd in the GdxTiSe2 system also leads to a compression of the lattice [88], which, however, is less pronounced than in the case of the intercalation with 3d metals. The only exception is Mn, whose introduction is accompanied by an expan sion of the lattice in the direction perpendicular to the layers. The compression of the crystal lattice of the MxTiSe2 compounds along the c axis upon the interca lation with 3d ions is ascribed to the formation of cova lentlike bonds as a result of the hybridization of 3d orbitals of the intercalated atoms with the 3d states of titanium and p states of the chalcogen [86, 87]. The existence of such a hybridization was confirmed by experiments on the angleresolved photoelectron spectroscopy (ARPES), which were performed using single crystals of a number of intercalated MxTiX2 compounds [89, 90]. The investigation of the ARPES spectra showed that in the electron structure of the MxTiX2 compounds there appears a dispersionless band lying approximately 1 eV below the Fermi level. The main contribution to this band comes from the hybridized M 3d–Ti 3d states [89, 90]. The effect of intercalation of various 3d atoms on the deformation of the lattice in the direction perpen dicular to the layers is clearly seen in Fig. 29, which demonstrates the dependence of the lattice parameter c of the M0.25TiSe2 compounds on the atomic number of the 3d element. As is seen, the variation of c agrees qualitatively with the change in the ion radii in the row of 3d metals. Except for chromium, which has a valence +3, the other 3d metals intercalated into the titanium disulfide, exhibit the valence +2. An analo gous correlation was obtained for other MxTX2 systems [78, 79]. It has bee established that the intercalation of

733

6.0 0.8 M0.25TiSe2

5.9

0.7 Cr

Mn

Fe

Co

Ni

Fig. 29. Lattice parameter c and the radii of M ions depending on the atomic number of a 3d element. For Co2+, the values of rM for the (䊏) highspin and (䊐) low spin states are given. Vol. 112

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4.00

0.016 CrxTiSe2 0

–0.016

CrxTiTe2 0

0.2

0.4

0.6

x

μeff(μθ)

(C – C0)/C0

0.032

Cr Mn Fe Co Ni

2.00

0.20

0

0.1

0.2

0.3 x

0.4

0.5

Fig. 30. Variation of the relative changes in the lattice parameter c depending on the chromium concentration in the CrxTiS2, CrxTiSe2, and CrxTiTe2 systems.

Fig. 31. Concentration dependences of the effective mag netic moment per intercalated atom M in MxTiSe2 com pounds.

atoms of one and the same type into different matrix compounds TX2 affect differently their crystal struc ture. As an example, Fig. 30 displays the concentration dependences of c for the CrxTiX2 systems intercalated by chromium [91]. In contrast to CrxTiTe2 and CrxTiSe2, in the system on the basis of the titanium disulfide CrxTiS2 there is observed a monotonic growth of the parameter c with increasing chromium concen tration, which is characteristic of compounds in which the intercalated atom forms ionic bonds with the neighboring chalcogen atoms. The difference in the change of lattice deformation upon intercalation of atoms into CrxTiX2 depending on the type of the chal cogen atom can be related to an increase in the degree of covalence of the bond formed by chromium atom introduced between the X–Ti–X blocks with increas ing atomic number of the chalcogen in the sequence TiS2–TiSe2–TiTe2 [91].

concentration to x = 0.25 in all MxTiSe2 systems except for MnxTiSe2 leads to a lattice compression in the direction parallel to the c axis, which can be related to an increase in the degree of hybridization of M 3d electrons with the bands of the TiSe2 matrix. It is natural to suppose that in this case there should occur a change in the magnetic moment of the intercalated atoms. Indeed, an analysis of the behavior of the effec tive magnetic moment depending on the concentra tion x shows that in all MxTiSe2 compounds, except for the case of intercalation by manganese, an increase in x to 0.25 leads to a decrease in μeff per atom (see Fig. 31). The magnitude of μeff appears to be affected also by the collectivization of the M 3d electrons with increasing concentration x, since in this case there occurs a simultaneous increase in the width of the additional band arising upon intercalation and a growth of the density of states at the Fermi level [92].

3.2. Effective Magnetic Moment of 3d Atoms Intercalated into the TiSe2 Structure The intercalation of titanium dichalcogenides with ions of 3d transition metals or by molecules containing ions with incompletely filled d shells leads, along with structural changes, to substantial changes in both the magnitude and the type of the temperature depen dences of the susceptibility. At low temperatures, the χ(T) dependences of intercalated MxTiX2 compounds in most cases exhibit anomalies related to changes in their magnetic state. In the paramagnetic state, the temperature dependence of the magnetic susceptibil ity of intercalated compounds MxTiX2 is satisfactorily described by the expression χ(T) = χ0 + C(T – Θp)–1, where χ0 = χP + χdia is the term caused by the Pauli paramagnetism of conduction electrons (χP) and by the diamagnetic contribution (χdia); C is the Curie constant; and Θp is the paramagnetic Curie tempera ture. As was noted above, an increase in the intercalant

Figure 32 displays the values of the effective mag netic moment calculated by the formula μeff = 2μB[S(S + 1)]1/2, and the values of μeff obtained from the measurements of the paramagnetic susceptibility of the compounds M0.25TiSe2 as functions of the atomic number of the elements. For chromium, a value of μeff corresponding to Cr3+ was taken in calcu lations; for the other 3d elements, the values of μeff for the divalent ions (M 2+). As is seen, the minimum dif ference between μexper and μtheor is observed for Cr. This difference increases with increasing atomic number of the element and reaches a maximum value for Ni, which can be an additional argument in favor of an assumption on an increase in the degree of hybridiza tion of the 3d electrons of M atoms with the 3d states of titanium and 4p states of selenium. The smaller val ues of the effective magnetic moments as compared to the spin values of μeff for M ions and of the lattice parameter c with increasing content of incorporated M atoms in the MxTiSe2 compounds indicate that the magnetism of these compounds cannot be described

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE

in terms of the model of localized moments. These compounds appear to occupy an intermediate position between the systems with localized magnetic moments and itinerantelectron magnets. In the behavior of such compounds, a noticeable role can apparently belong to spin fluctuations. In contrast to systems on the base of titanium dichalcogenides, in the com pounds of the MxTaX2 and MxNbX2 type in most cases the values of the effective magnetic moments prove to be close to calculated spin values [79]. This means that upon the intercalation of atoms M into the structure of tantalum and niobium dichalcogenides the 3d elec trons remain well localized. From an analysis of the magnetic susceptibility of ironintercalated dichalco genides FexNbS2 and FexTaS2 there have been obtained values of the effective magnetic moment per Fe2+ ion that noticeably exceed the calculated spin value 4.9 μB, which is ascribed to the existence of an orbital contribution [79]. The existence of a partly unfrozen orbital moment in these compounds is sup ported by the fact that a large magnetocrystalline anisotropy of singleion nature has been revealed in them [79, 93]. 3.3. LongRange Magnetic Order and Magnetic Structures in Intercalated MxTX2 Compounds At small concentrations of intercalated 3d atoms (x < 0.25), the majority of the investigated compounds of the MxTX2 type at low temperatures exhibit a behav ior characteristic of spin and cluster glasses [78, 81], which is ascribed to the competition between the intralayer exchange interaction between 3d electrons of the intercalated atoms through the conduction elec trons and the interlayer exchange interaction with the participation of p electrons of the chalcogen. Upon the intercalation of vanadium [78] and nickel [78, 92] atoms into the structure of titanium chalcogenides, the paramagnetic state was retained in a wide range of concentrations up to x = 0.5. Among the intercalated titanium dichalcogenides, the majority of studies of magnetic properties were performed for FexTiS2 [78, 94], FexTiSe2 [95, 96], and CrxTiSe2 [87, 97], in which the presence of a longrange magnetic order was revealed with the ordering temperatures of up to 140 K. Upon the intercalation of atoms of 3d metals into the structure of tantalum and niobium dichalco genides in a number of systems a longrange magnetic order was also revealed to form at the concentrations of the intercalated atoms x = 1/4 and x = 1/3 [79]. The data on the type of magnetic ordering and values of the temperatures of phase transitions in the MxTX2 sys tems (T = Ti, V, Nb, Ta) with a large concentration of intercalated atoms M are given in Table 5. In contrast to titanium dichalcogenides MxTiX2 and vanadium dichalcogenides MxVX2 intercalated with 3d metals [98], in which the longrange magnetic order is observed at high concentrations of atoms M (x ~ 1/2), in the compounds based on TaX2 and NbX2 THE PHYSICS OF METALS AND METALLOGRAPHY

735

(a)

μeff, μB

6

μeffteor

4 μeffexp

2 0

μeffexp/μefftheor

(b) M0.25TiSe2 1.0

0.5

0

Cr

Mn

Fe

Co

Ni

Fig. 32. (a) Calculated and experimental values of the effective magnetic moment of 3d atoms in the M0.25TiSe2 compounds; and (b) relative changes in μeff.

with a trigonalprismatic surroundings of T metals by chalcogen atoms (modification 2H), the magnetic ordering is realized also at smaller concentrations (x = 1/4, x = 1/3) [79]. In the FexTaX2 and FexNbX2 com pounds intercalated with Fe atoms, already at an iron concentration x = 1/4 there can be observed an F or AF ordering with critical temperatures of 130–160 K [79]. The measurements of the magnetic susceptibility performed on single crystals of MxTaX2 and MxNbX2 samples made it possible to conclude that in most compounds the magnetic moments of the intercalated atoms in the magnetically ordered state lie in the plane of layers. The exceptions are the compounds FexTaX2 and FexNbX2, in which the magnetic moments of Fe appear to be oriented along the hexagonal axis perpen dicular to the plane of layers, which is explained by the spin–orbital interaction and by the effect of the crystal field of octahedral symmetry [79]. The investigations of singlecrystal samples of Fe0.25TaS2, which exhibits a ferromagnetic ordering below TC = 160 K, revealed the existence in it of a giant magnetocrystalline anisot ropy. The field of magnetocrystalline anisotropy in this compound is about 590 kOe [93], which is comparable with the anisotropy observed in rareearth com pounds, and the coercive force upon the magnetiza tion reversal reaches 50 kOe at low temperatures [99]. The measurement of magnetic properties of CrxTiSe2 compounds intercalated by chromium revealed the existence of an AF ordering in samples with a large content of the intercalant (x = 0.5) at tem Vol. 112

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Table 5. Type of magnetic ordering and the values of critical temperatures of magnetic transformations for MxTiX2 com pounds [78, 85, 79, 91, 98] V M1/2TiS2

Type of ordering Critical temperature

M1/2TiSe2

Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature Type of ordering Critical temperature

M1/2TiTe2 M1/2VS2 M1/2VSe2 M1/3TaS2 M1/4TaS2 M1/3TaSe2 M1/3NbS2 M1/4NbS2 M0.33NbSe2

Cr

Mn

F 115

F 55

F 120 AF 115–127

F 100–105

peratures below TN = 44 K [85]. At moderate chro mium concentrations, the CrxTiSe2 compounds, just as other MxTiX2 systems, at low temperatures exhibit a behavior characteristic of the state of spin glass (at x = 0.1) or cluster glass (at x = 0.25). The tempera ture of the transition into the spinglass state (Tf) for Cr0.1TiSe2 is virtually independent of the regime of cooling, whereas the critical temperatures for the compounds with x > 0.25 differ substantially [85]. The difference in the temperatures of magnetic ordering between the slowly cooled and quenched samples of CrxTiSe2 increases with increasing chromium content. At x = 0.5 and 0.6, the values of the critical tempera tures for these samples differ almost twofold. This fol lows from the data on the investigation of the behavior of the magnetic susceptibility of CrxTiSe2 shown in Figs. 33 and 34. Figure 34 displays, along with the freezing temperature Tf and Néel temperature TN, also the concentration dependence of the paramagnetic Curie temperature Θp, which corresponds to the aver age of the algebraic sum of energies of exchange inter actions. First, with increasing concentration of the intercalated chromium atoms to x = 0.25, the para

Co

Ni

AF 35

AF 120

AF 25

AF 90

F 80F 140A'F AF 135

AF 42 F 78

F 35

Fe

F 70 F 80

F 40–53 F 120

AF 135 AF 94.5 F 35 F 160

AF 45 AF 137 AF 135

magnetic Curie temperature is negative and increases in the absolute value, which indicates the predomi nance of antiferromagnetic exchange interactions. However, at x > 0.25 there occurs a decrease in |Θp| and even a change in the sign to positive at x > 0.33. At x = 0.6, Θp reaches 82 K. The alternatingsign variation of the paramagnetic Curie temperature with increasing content of chromium atoms intercalated into the gaps between the Se–Ti–Se threelayer blocks indicates the existence of competing exchange interactions. In contrast to the compounds with a small chromium concentration, the different regime of cooling of the highly intercalated samples (x = 0.5, 0.6) leads to qualitative differences in the behavior of the magneti zation under the effect of a field. In the field depen dence of the magnetization of a slowly cooled sample (see Fig. 35) there is observed a sharp increase in the magnetization after a critical field Hc is reached, whose magnitude is about 10 kOe. The existence of a hysteresis near Hc indicates that in these compounds there occurs a magneticfield induced firstorder phase transition from the AF to F state. The moderate value of the critical field indicates

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE 100

(a)

CrxTiSe2

Cr0.5TiSe2

12

θp 80

100 Oe 10 kOe

8

Tf, TN, Θp, K

60 4 χ, rel. units

737

(b)

TN

40 Tf Tf

20

4 0 2 –20 0.2 20

40 T, K

60

80

Fig. 33. Temperature dependences of the magnetic suscep tibility of (a) quenched and (b) slowly cooled samples of the Cr0.5TiSe2 compound.

that the energy of the negative interlayer exchange interaction is substantially less than the ferromagnetic interaction inside the layers, since the neighboring chromium layers are separated by nonmagnetic Se⎯Ti–Se sandwiches. This assumption is confirmed by the fact that, in spite of the AF character of the ordering, the paramagnetic Curie temperature of Cr0.5TiSe2 is positive. The magnetic neutrondiffrac tion investigations of the slowly cooled Cr0.5TiSe2 sample [97] confirmed the antiferromagnetic charac ter of its magnetic structure. As is seen from the scheme shown in Fig. 36, the magnetic moments of chromium atoms located in the same van der Waals gap in the Cr0.5TiSe2 compound are ordered almost parallel to one another along the chains aligned with the direction of the b axis. The interaction between the chromium ions located in the neighboring van der Waals gaps is antiferromagnetic. The measurements of the magnetization curves of the antiferromagnetic compounds CrxTiSe2 (x = 0.5, 0.6) in high pulsed fields showed that the magnetization in a field of 420 kOe reaches 2.5 μB per Cr atom, which agrees well with the neutrondiffraction data (2.4 μB [97]). The magnitude of the magnetic moment of the chromium atom in the saturation state proved to be less than 3 μB, which could be expected based on the assumption on the localized character of 3d electrons of the Cr3+ ion. The quenching of the compound Cr0.5TiSe2 leads to a substantial decrease in the temperature of the THE PHYSICS OF METALS AND METALLOGRAPHY

0.6

Fig. 34. Concentration dependences of the paramagnetic Curie temperature Θp, Néel temperature TN, and freezing temperature Tf for CrxTiSe2 samples obtained by slow cooling (solid symbols) and by quenching (empty sym bols).

magnetic transformation (to 23 K, Fig. 33) and to a change in the type of the field dependence of the mag netization of the quenched sample of Cr0.5TiSe2 (Fig. 35, curve 1). The quenching appears to result in a state of the clusterglass type. The change in the character of magnetic ordering and a significant decrease in the temperature of the magnetic transfor mation in quenched samples of CrxTiSe2, as compared 30 20

2 Cr0.5TiSe2

1

T=2K M, G cm3/g

0

0.4 x

10 0 –10 –20 –30 –40

–20

0 H, kOe

20

40

Fig. 35. Field dependences of the magnetization measured at T = 2 K using (1) quenched and (2) slowly cooled sam ples of the Cr0.5TiSe2 compound. Vol. 112

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which affect the magnitude and character of exchange interactions. The lowtemperature measurements of the magnetization of CrxTiSe2, CrxTiTe2, and CrxNbSe2 compounds, which exhibit longrange mag netic order, showed that the magnitude of the average magnetic moment per Cr ion reaches in high fields 2.3–2.4 μB, i.e., is lower that that expected for Cr3+ ion (3 μB) according to the model of localized magnetic moments.

Fig. 36. Scheme of ordering of magnetic moments of Cr in the Cr0.5TiSe2 compound [97].

to slowly cooled samples, can be related to a partial mutual substitution of Cr and Ti atoms in view of the close magnitudes of their ionic radii. The results obtained for CrxTiSe2 show that a change in the regime of heat treatment of intercalated compounds can serve as a tool for a purposeful change in their magnetic state. In contrast to the AF ordering in CrxTiSe2, the inter calation of chromium atoms into the structure of the titanium ditelluride TiTe2 to a concentration x ≥ 0.5 leads to the formation in CrxTiTe2 of a longrange fer romagnetic order with a Curie temperature to 120 K [9]. At a less content of chromium in the CrxTiTe2 compounds, just as in other intercalated titanium dichalcogenides, at low temperatures there are observed states of the spinglass or clusterglass type. The ferromagnetic behavior at temperatures below 100 K was revealed in Cr0.33NbSe2 [100], whereas in the CrxNbS2 there is formed a longperiod helicoidal magnetic structure [101] and in CrxVSe2 no long range magnetic order is observed in the subsystem of intercalated chromium atoms up to the concentration of x = 0.5 [100]. These results show that the key factor that determines the character of the magnetic ordering of magnetic moments of intercalated atoms at a given concentration is the type of the matrix compound in whose structure they are incorporated. Since the inter calated atoms, as a rule, occupy in the TX2 lattice octa hedral positions between X–T–X blocks, the CrxTX2 compounds at a given concentration differ from one another in the magnitudes of the intralayer and inter layer spacings and in the electronic characteristics,

Among the MxTiX2 systems, most works were devoted to the investigation of magnetic properties of titanium disulfides and diselenides intercalated with iron. At small concentrations (x < 0.2) in both systems a spinglass state is observed; at intermediate concen trations (0.2 < x < 0.4), a clusterglass state exists. Note that the freezing temperatures in both systems at x = 0.2–0.4 differ only insignificantly. An analysis of the paramagnetic susceptibility showed that in FexTiS2 compounds the paramagnetic Curie temperature is positive and increases monotonically with increasing x [102], which indicates the predominance of a ferro magnetic exchange interaction between the 3d elec trons of iron atoms intercalated into the van der Waals gaps of the titanium disulfide. The available data on the magnetic ordering in FexTiS2 compounds with a large concentration of Fe atoms are contradictory. It is assumed that, first, upon cooling to below TN = 132– 140 K [103, 104], there arise either ferromagnetic clusters in the antiferromagnetic matrix or a long range ferromagnetic order at below the critical tem perature TC, which, according to different works, var ies from 52 to 111 K [103, 104]. In compounds based on the titanium diselenide, FexTiSe2, in contrast to the system FexTiS2, an AF ordering occurs at x > 0.4, although in this case, just as in the CrxTiSe2 system, the paramagnetic Curie tem perature is positive. The authors of [102, 105] made an attempt to describe the magnetic state of the FexTiS2 and FexTiSe2 in terms of the Ruderman–Kittel– Kasuya–Yosida model, in which the exchange inter action between the 3d electrons of the intercalated Fe atoms occurs through conduction electrons. Since in these compounds the conductivity in X–Ti–X layers is substantially higher than that perpendicular to the layers [78, 79], the calculation was performed on the assumption that the exchange interaction in the layer of Fe atoms is dominant and the changes in the elec tronic structure upon the intercalation reduce to only an increase in the Fermi level (model of a “rigid band”). In addition, it was assumed that no ordering of Fe atoms and vacancies occurs in the van der Waals gap. Using such simplifications, the authors have been able to qualitatively describe the variation of the para magnetic Curie temperature with concentration in both FexTiX2 (X = S, Se) systems. These results indi cate a large role of the indirect exchange interaction through the conduction electrons in the establishment of magnetic order in these compounds.

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MAGNETISM OF COMPOUNDS WITH A LAYERED CRYSTAL STRUCTURE (a)

Fe0.66TiS2 40 M, G cm3/g

Fe Ti

T = 4.2 K

–40

M, μB/Fe

c a

Fe0.5TiSe2

0

0 –50 H, kOe

–100

0.6

Fe0.5TiSe2

0.2

0

THE PHYSICS OF METALS AND METALLOGRAPHY

50

100 (b)

77 K

0.4 4.2 K

Fig. 37. Magnetic structure of the Fe0.5TiSe2 compound [96].

According to neutron diffraction data [96], the Fe0.5TiSe2 compound at temperatures below the Néel temperature (135 K) possess a canted antiferromag netic structure, in which the magnetic moments of Fe atoms are ordered antiferromagnetically inside the layers and are located at an angle of about 74.4° to the plane of layers. A schematic representation of the magnetic structure of the Fe0.5TiSe2 compound is shown in Fig. 37. This model of the magnetic structure differs from that suggested earlier [95], where it was assumed that the magnetic moments of Fe atoms are oriented strictly perpendicular to the plane of layers. The magnitude of the magnetic moment of Fe in Fe0.5TiSe2 is 2.98 ± 0.05 μB, according to neutron dif fraction data. The underestimated value of μFe appears to be a consequence of the participation of the 3d elec trons of the intercalated Fe atoms in the formation of covalentlike bonds and the hybridization with the 3d states of Ti and 4p states of Se. The magnetic unit cell in the magnetic structure of Fe0.5TiSe2 is doubled along the c and a axes. The magnetic moments of Fe atoms located in the same layer but lying in neigh boring chains along the b axis have opposite orienta tions. According to neutrondiffraction data, the tita nium atoms also have a small magnetic moment (~0.4 ± 0.3 μB), which is due to the effect of the inter calated Fe atoms. The existence of a canted magnetic structure in Fe0.5TiSe2 can be a result of a competition between the effects of the crystal field, dipole–dipole interaction, and exchange interactions inside the lay ers and between the layers. As was established by mea surements at different temperatures, the antiferromag netic ordering in Fe0.5TiSe2 is accompanied by anisotro pic spontaneous magnetostrictive deformations of the crystal lattice, which appears to be due to a spin–orbital interaction and the effect of crystal field [96].

739

100

200 H, kOe

300

400

Fig. 38. Field dependences of the magnetization of the (a) Fe0.66TiS2 and Fe0.5TiSe2 compounds at T = 4.2 K in static magnetic fields and (b) of Fe0.5TiSe2 at 4.2 and 77 K in pulsed fields.

The difference in the magnetic state of highly inter calated FexTiS2 and FexTiSe2 compounds is clearly illustrated in Fig. 38, which represents the field depen dences for the ferromagnetic compound Fe0.66TiS2 with the Curie temperature TC = 140 K [80] and for the antiferromagnetic compound Fe0.5TiSe2 with the Néel temperature TN = 135 K. As is seen, at low temperatures in the ferromagnetic compound Fe66TiS2 there is observed a wide hysteresis loop with a coercive force Hc greater than 40 kOe (Fig. 38a). Such a behavior appears to be related to a large magnetocrystalline anisotropy, whose presence in this compound is caused by a partial unfreezing of the orbital moment of intercalated Fe2+ ions. The existence of an orbital contribution to the total mag netic moment of iron ions is confirmed by experi ments on magnetic circular dichroism [106]. As was noted above, the large hysteresis upon magnetization reversal was also observed at low temperatures for a singlecrystal sample of the ferromagnetic Fe0.5TiS2 compound [99]. The antiferromagnetic Fe0.5TiSe2 demonstrates almost linear variation of the magneti zation with changing field from –90 to +90 kOe (Fig. 38a). However, the measurements of the magne tization of this compound in strong pulsed magnetic fields revealed deviations from linearity in fields of ~280 kOe, which can indicate the beginning of the AF–F phase transition. In contrast to the CrxTiSe2 system, the change in the regime of cooling exerts no significant effect on the main magnetic characteristics Vol. 112

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Fe0.5TiS2 – xSex

100

Θp, K

Tcrit, K

100 50

50 0 0 Fe0.5TiS2

0.5

1.0 x

1.5

2.0 Fe0.5TiSe2

0

0.5

1.0 x

1.5

2.0

Fig. 39. Magnetic phase diagram of the Fe0.5TiS2 – xSex compounds.

Fig. 40. Concentration dependence of the paramagnetic Curie temperature Θp for the Fe0.5TiS2 – xSex compounds.

of the FexTiSe2 compounds, although at large concen trations of iron (x ~ 0.5) the structures of the slowly cooled samples and samples subjected to rapid quenching do differ.

the change in the sign of Θp upon the substitution of selenium for sulfur. Note that the compounds FexTiS2 and FexTiSe2, according to the data available in the lit erature [107], have metallic conductivity. Since upon the substitution of selenium for sulfur no changes in the electron concentration occurs, it can be assumed that the main factor responsible for the change in the character of the magnetic ordering from ferromag netic to antiferromagnetic in the Fe0.5TiS2 – xSex sys tem is a change in the interatomic spacings in the lay ers of intercalated Fe atoms with increasing Se con centration.

The magnitude of the effective magnetic moment μeff per Fe ion in all FexTiX2 compounds is 2.6–4.2 μeff and exhibits a weak dependence on the concentration x. The investigation of mixed compounds Fe0.5TiS2 – xSex showed that the substitution of selenium for sulfur leads to the disappearance of the region of F ordering already at the content of selenium x > 0.5. The mag netic phase diagram constructed on the basis of data on the measurements of the susceptibility is shown in Fig. 39. As is seen, the substitution of selenium for sul fur in the matrix does not lead to a significant change in the Néel temperature, which varies between 107 and 135 K, but leads to qualitative changes in the mag netic ordering of the compounds in the ground state: there occurs a transition from an F to AF ordering at Se concentrations x > 0.5. The concentration depen dence Θp(x) is nonmonotonic (Fig. 40); the maximum positive values of Θp (~80–100 K) are observed for the compounds with small concentrations of Se, in which at low temperatures there is realized an F state. The antiferromagnetic compounds with a Se concentra tion x = 1 and x = 2 have positive Θp < 50 K; only for x = 1.5 the paramagnetic Curie temperature is nega tive (Θp = –15 K). In the case of the simple twosub lattice antiferromagnet, the positive sign of the para magnetic Curie temperature indicates that the ferro magnetic exchange inside the sublattices exceeds the antiferromagnetic intersublattice interaction. In the Fe0.5TiS2 – xSex the situation is apparently more com plex, since the ordering of magnetic moments is a result of a competition of exchange interactions that have different mechanisms; in particular, inside the layer of intercalated iron atoms, the indirect RKKY exchange interaction is oscillating. The existence of such a competition manifests itself, in particular, in

Note a significant (by a factor of more than 20) dif ference in the values of the critical field that leads to the phase transition from the antiferromagnetic into ferromagnetic state for CrxTiSe2 (Fig. 35) and FexTiSe2 (Fig. 38) systems at x ~ 0.5–0.6. The reason is in the difference in the exchange interactions inside the layer of intercalated atoms of iron and chromium. As was noted above, the magnetic moments of chromium atoms exhibit predominantly ferromagnetic ordering inside the layer and the location of moments in neigh boring chromium layers has an antiferromagnetic character [97]. The interlayer Cr–Cr interaction is weak as compared to the intralayer interaction, since the neighboring chromium layers are separated by nonmagnetic Se–Ti–Se sandwiches. Therefore, the F ordering in the Cr0.5TiSe2 compound can be destructed by a relatively weak field (~10 kOe), whereas in Fe0.5TiSe2 the antiferromagnetism is not destructed even in fields of ~350 kOe. The large differ ence in the critical field of the AF–F transition in Fe0.5TiSe2 is due to the fact that the AF ordering in this compound is formed in the layer of intercalated Fe atoms [96] and, therefore, the magnitude of the criti cal field necessary for the AF–F transition is deter mined in this compound by strong interlayer exchange interaction.

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3.4. Magnetic Properties of Titanium Dichalcogenides Intercalated with RareEarth Elements

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30

20

8 6 4 2

M, μB/Gd

M, G cm3/g

The compounds on the basis of layered dichalco genides of transition metals (TX2) have been studied substantially less as compared to the MxTiX2 systems. The available works were mainly devoted to studying incommensurate phases (RS)xTS2 (T = Nb, Ta) with a structure consisting of alternating sandwiches S–T–S and twolayer blocks RS [108, 109]. In most such com pounds, the R ions have effective magnetic moments close in magnitude to those characteristic of free ions R3+. In some (RS)xTS2 compounds, there was revealed an antiferromagnetic ordering with Néel temperatures equal to a few kelvins [109]. In [110], it has been shown on the example of the (CeS)1.16[Fe33(NbS2)2] that upon the simultaneous intercalation with atoms of 3d and 4f metals there is realized a greater degree of twodimensionality because of the weak interlayer exchange interaction. With decreasing temperature, there are observed two magnetic transitions in this compound, at 22 K and at 3.4 K, into antiferromagnetic states in the Fe and Ce subsystems, respectively. The authors of [88] used a twostep ampoule syn thesis to obtain titanium diselenidebased compounds intercalated with gadolinium with the Gd concentra tion to x = 0.33. The behavior of the magnetic suscep tibility χ(T) of the GdxTiSe2 (0 < x ≤ 0.33) compounds in the temperature range of 50–350 K are described well by the generalized Curie–Weiss law. In all these compounds, the magnitude of the effective magnetic moment is about 7.9 μB, which agrees well with the value for free Gd3+ ion (7.94 μB). Such a behavior dif fers from that of the aboveconsidered MxTiSe2 sys tems, which can be explained by the strong localiza tion of the 4f electrons of Gd in contrast to the 3d elec trons of M ions, which hybridize with the 3d states of Ti and 4p states of Se. For the GdxTiSe2 there was obtained a value of the paramagnetic Curie tempera ture Θp = –12 K. The negative sign of Θp indicates the predominant antiferromagnetic exchange between the Gd ions, which appears to be indirect and to be imple mented through the conduction electrons, since the conductivity of these compounds has a metallic char acter. At low temperatures, the χ(T) dependences of the GdxTiSe2 compound exhibit an anomaly near 9 K, which shifts toward lower temperatures with increas ing magnetic field, indicating the transition into the antiferromagnetic state at below 9 K. The existence of an antiferromagnetic ordering in GdxTiSe2 com pounds is confirmed by the results of measurements of field dependences of the magnetization (see Fig. 41). In all M(x) dependences obtained at T = 2 K, i.e., below TN, there is observed a change in the slope and a noticeable hysteresis in a field of about 18 kOe. As the field reaches a critical value, a spinflop transition appears to occur in the subsystem of magnetic moments of Gd. The small magnitude of Hc is related

741

x = 0.33 T = 4.2 K x = 0.2

x = 0.25 x = 0.2

0

100 200 300 H, kOe 10 T = 2 K

x = 0.1 GdxTiSe2

0

20

40 H, kOe

60

Fig. 41. Field dependences of the magnetization of inter calated GdxTiSe2 compounds at T = 2 K [88]. In the inset, the magnetization curve for Gd0.2TiSe2 in pulsed fields at 4.2 K is given.

to the relatively low energy of the antiferromagnetic exchange interaction between the 4f electrons of Gd and suggests the existence of a significant anisotropy. Since Gd has a zero orbital moment, it can be assumed that the magnetic anisotropy in these compounds is due to the dipole–dipole interaction and to the anisot ropy of exchange interaction because of the layered character of the crystal structure and the anisotropy of conductivity. As follows from the inset in Fig. 41, which presents the magnetization curve for Gd0.2TiSe2 in pulsed fields at 4.2 K, the magnetization reaches saturation in a field Hs ~ 90 kOe. In the saturation state, the magnetic moment per Gd ion is μs = 7.4 ± 0.3 μB, which agrees with the value gJ μB = 7 μB for the free Gd3+ ion. Thus, the results of [88] show, on the example of the GdxTiSe2 system, the possibility of direct intercalation of rareearth ions into the struc ture of the titanium dichalcogenides to significant concentrations (x ~ 1/3). As in the case of intercala tion of 3d metals, the introduction of Gd leads to a slight compression of the lattice in the direction per pendicular to the layers (Fig. 28), which can be due to the formation of covalentlike bonds between the Se–Ti–Se sandwiches with the participation of 5d electrons of Gd. Just as in other compounds, the electrons of the incompletely filled 4f shell of Gd remain well localized and do not participate in the hybridization with the electronic states of the matrix TiSe2, in contrast to the 3d electrons of the interca lated ions of transition metals. 4. CONCLUSIONS The consideration of the results of the investigation of magnetic properties of compounds of the RT2Z2, RT6Z6, and MxTX2 types shows that these compound exhibit an extremely wide spectrum of magnetic struc tures and magnetic phase transitions both upon the variation of the temperature and upon the application Vol. 112

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of a magnetic field or hydrostatic pressure. Such their behavior is due to the layered character of their crystal structure, in which the atoms having a magnetic moment are located in separate crystallographic lay ers. As a result, inside the layers and between the layers there exist exchange interactions of different type and of different energy. The exchange interaction between the layers are weaker than the intralayer interactions, since they are separated by layers of nonmagnetic atoms. The magnitude of the interlayer exchange interaction and, consequently, the type of interlayer magnetic ordering depend most strongly on the spac ing between the layers. Depending on the magnitude and sign of the interlayer and intralayer exchange interactions and also on the type of magnetic anisot ropy of the sublattices, a ferromagnetic or an antifer romagnetic order is observed in such compounds, fre quently with a complex arrangement of magnetic moments. In some compounds, an independent ordering of magnetic moments in different sublattices occurs at different temperatures. Neutrondiffraction studies revealed noncollinear, canted, and spiral mag netic structures in the RT2Z2, RT6Z6, and MxTX2 com pounds. It has been shown that the magnetizations of layered compounds possessing spiral magnetic struc tures can be described in terms of a model that takes into account the exchange interactions with the near est layers and nextnearest layers, as well as the mag netic anisotropy. The magnetic phase transitions that occur under the effect of a magnetic field in layered compounds are accompanied by significant changes in the electrical resistance, large magnetocaloric effects, and magnetostrictive deformations, which can be of large interest from the viewpoint of practical applica tions. It should be noted that, although the general understanding of the magnetic behavior of com pounds with a layered structure has already been achieved to date, a whole number of problems remain unclear and require further investigations. Among such problems, the mechanism of the formation of the magnetic moment and the nature of magnetic anisot ropy in the sublattice of 3dmetal atoms can be men tioned. The results obtained indicate that in the RT2Z2 compounds there occurs a strong hybridization of electronic 3d states of atoms of the T metal and p (s) states of the Z metals. A similar situation is observed in intercalated MxTX2 compounds, in which also there was revealed a hybridization of 3d states of intercalated M atoms with the electronic states of the matrix com pound TX2. Such a hybridization affects the magni tude of the magnetic moment and the exchange inter actions in the sublattice of 3d atoms. Owing to the layered character of the crystal struc ture, such compounds can serve as model objects for studying the specific features of exchange interactions and the nature of magnetic anisotropy in quasitwo dimensional systems, and for establishing main factors

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