Glass Physics and Chemistry, Vol. 31, No. 5, 2005, pp. 563–582. Original Russian Text Copyright © 2005 by Fizika i Khimiya Stekla, Tver’yanovich, Kim, Rusnak.

Effect of Light on the Magnetic Properties of Semiconductors Yu. S. Tver’yanovich, D. S. Kim, and A. N. Rusnak Faculty of Chemistry, St. Petersburg State University, Universitetskii pr. 26, Petrodvorets, 198504 Russia Received December 10, 2004

SPINTRONICS—PROMISING DIRECTION OF DEVELOPMENT OF INFORMATION TECHNOLOGIES In modern semiconductor electronics, effort has been made to use spin degrees of freedom of electrons in addition to charge degrees of freedom for information processing. This new developing branch is referred to as spintronics [1]. The use of the electron spin rather than the charge is promising for the design of a new generation of semiconductor storage units and signal processing devices based on new principles of operation [1–7]. The electron spin properties in metals have long been used for information storage. In particular, the giant magnetoresistance effect, according to which the resistance of a ferromagnet–diamagnet thin-film sandwich depends substantially on the magnetic field [8, 9], has been applied in the majority of computer hard disks. In recent years, special attention has been focused on spin-dependent phenomena in semiconductors. A device that can potentially be implemented is a spin field-effect transistor in which a collector and an emitter are ferromagnets [10]. If the magnetizations of both regions are aligned parallel to the same direction, the spin-polarized current behaves like a normal current of a transistor. When their magnetizations are oriented in opposite directions, the transistor is switched off. This can be accomplished in a dynamic manner, which makes it possible to design microprocessors that can change the configuration of their functional structure in real time. The main impediment to the practical implementation of the above concepts is the necessity of efficient injection and transport of carriers with the spin polarization. Traditional ferromagnetic materials are frequently incompatible with the existing semiconductor technology. Moreover, the efficiency of spin injection often appears to be very low due to the difference in the electric properties and the formation of Schottky barriers [11–13]. The main way of overcoming this problem is the use of so-called diluted magnetic semiconductors. These materials are alloys in which a number of atoms forming the lattice are replaced by transition metal atoms. Such alloys possess semiconductor properties and also can have pronounced magnetic (for example, paramagnetic, antiferromagnetic, ferromagnetic) properties that are absent in traditional semiconductors [1, 6, 7]. Therefore, these alloys can potentially

be used for spin injection and control of spin properties in contacting nonmagnetic semiconductor layers. Owing to the discovery of ferromagnetism in (In,Mn)As [14, 15], diluted magnetic semiconductors have become the main materials of spintronics as a result of their compatibility with the semiconductors used in modern electronics. However, the Curie temperatures TC of diluted magnetic semiconductors are insufficiently high for real applications. Practically, it is necessary to design diluted magnetic semiconductors with ferromagnetic properties at room temperature. For the most part, the first works in this field conII cerned II–VI semiconductors of the A 1 – x MnxBVI type in which a number of Group II element atoms are randomly replaced by Mn atoms. The presence of magnetic atoms in these systems affects the behavior of free carriers through the sp–d exchange interaction between localized magnetic moments and spins of mobile carries. These interactions are responsible for the numerous magnetoelectric and magneto-optical phenomena, including the large Faraday rotation and the formation of magnetic polarons [12, 13]. Owing to the use of molecular-beam epitaxy for growing MnxGa1 – xAs, Ohno [16] succeeded in introducing up to 0.1 of atomic fraction of Mn, which considerably exceeds the solubility of Mn in this material. Unfortunately, materials thus prepared are thermodynamically nonequilibrium. As a consequence, devices fabricated on their basis can undergo degradation during service. Furthermore, these materials are ferromagnets with a Curie temperature of ~110 K, which is insufficient for practical applications. Numerous phenomena observed in “diluted magnetic semiconductor– nonmagnetic semiconductor” heterostructures, including the spin injection from MnGaAs into GaAs and the electrically controlled magnetism in MnInAs, have been described to date [16–19]. In this respect, it is appropriate to note the paper with the symptomatic title “How to Make Semiconductors Ferromagnetic: A First Course on Spintronics” [20]. In this paper, the rapidly developing field of ferromagnetism in diluted magnetic semiconductors, in which a semiconductor host is doped with a transition metal to produce a ferromagnetic semiconductor (e.g., Ga1 − xMnxAs with x < 1–10 at %), is discussed with the emphasis on explaining the physical mechanisms

1087-6596/05/3105-0563 © 2005 Pleiades Publishing, Inc.

564

TVER’YANOVICH et al.

responsible for the magnetic properties. Main works in this field are reviewed with critical discussions of the role of disorder, localization, band structure, defects, and the choice of materials in producing required magnetic properties, including a high Curie temperature. The correlation between the magnetic and transport properties is argued to be a crucial factor for the full understanding of the properties of ferromagnetic semiconductors. NATURE OF MAGNETIC SEMICONDUCTORS AND THE ROLE OF FREE CARRIERS The magnetic properties of semiconductor compounds of transition and rare-earth elements depend substantially on the density of mobile carriers, because carriers provide the indirect exchange between the magnetic moments of the d and f unfilled electron shells. The ferromagnetism induced by carriers is a unique property of magnetic semiconductors. The mechanism of this phenomenon is as follows. The spin of a free electron moving over a crystal is conserved. If the spin of an atom to which the electron is transferred is parallel to the spin of the atom from which the electron is transferred, the exchange energy between the electron and the magnetic atom after transfer is not changed and remains minimum. When the spins of the magnetic atoms are antiparallel, the spin of the electron after transfer to the neighboring atom appears to be oriented in an unfavorable (antiparallel) direction with respect to the spin of this atom. As a result, the electron energy should increase, and, hence, these transitions are impossible. On the other hand, if the transition is forbidden and the electron is localized on a particular atom, the electron energy according to the uncertainty principle turns out to be higher than the energy of the electron capable of transferring to other atoms. Therefore, the electron energy is minimum when the spins of all atoms are parallel to each other [21]. Consequently, an antiferromagnetic semiconductor or a paramagnetic semiconductor (a ferromagnetic semiconductor at a temperature somewhat higher than the Curie point) at a sufficiently high density of free carriers should undergo a transition to the ferromagnetic state. However, if the carrier density is not high enough for the crystal to transform into the ferromagnetic state, the energy gain can be achieved when free electrons are concentrated in specific crystal regions and make them ferromagnetic. In particular, a single electron can produce a ferromagnetic microregion and be self-localized in it. The energy expended for flipping the spins is compensated for by the gain in the electron energy, because the ferromagnetic region is a potential well for the electron in the antiferromagnetic semiconductor (or paramagnetic semiconductor) material. Nagaev [22] was the first to prove the existence of similar objects. According to [21, p. 212], the magnetic moment of ferrons can be larger than the electron mag-

netic moment by four orders of magnitude. In this case, the material has an inhomogeneous magnetic structure. Rho et al. [23] investigated Eu1 – xGdxO semiconductors (x = 0, 0.006, 0.035) by Raman spectroscopy. It was found that, in the vicinity of the Curie temperature TC, the material is characterized by the phase inhomogeneity manifesting itself in Raman scattering that corresponds to the spin flip in zero field due to the formation of magnetic polarons. The evolution and behavior of these polarons were studied as a function of the temperature, disordering, and Gd concentration. It is of interest that the Raman spectra over a rather wide range of temperatures in the vicinity of the Curie point TC can be adequately described by a superposition of Raman signals that correspond to the predominance of collision and spin-flip processes only under the assumption of phase inhomogeneity in the vicinity of the Curie temperature TC. This inhomogeneity is associated with the magnetic polarons coexisting with residual regions of the paramagnetic phase. In other investigations of magnetic semiconductors [24, 25], similar Raman signals were also identified as a result of spin flip in zero field due to the presence of polarons. Taking into account the foregoing, it becomes clear that ideas of controlling the magnetic states of magnetic semiconductors with the use of different physical actions have been widely discussed in the literature. For example, Dietl [26] noted that recent studies in the field of spintronics involve virtually all families of materials; however, ferromagnetic semiconductors are of special interest, because they combine the potentialities of semiconductors and ferromagnets. Since the magnetic properties of Cr- and Mn-based compounds are governed by band carriers, efficient methods developed for modifying the carrier density by electric fields and light in semiconductor quantum structures can be applied to control the magnetic order [26]. For AIIBVI diluted magnetic semiconductors, these potentialities can be illustrated using (Cd,Mn)Te quantum wells (Fig. 1) [27, 28]. It is important that the magnetization reversal is isothermal and reversible. Despite the absence of special investigations, it is expected that this phenomenon is associated with the sufficiently fast processes. Since the background hole density in AIIBVI quantum wells based on manganese is low, the relative change in the Curie temperature for these materials, as a rule, is larger than that for AIIBV compounds. Kimura et al. [29] measured the reflection spectra of Cd2S3 magnetic semiconductor in the photon energy range 0.05–0.5 eV at a temperature of 14 K in magnetic fields up to 5 T. An increase in the magnetic field leads to a shift in the position of the peak at approximately 0.1 eV toward the low-energy range and its broadening. This behavior was assumed to be proof that the above absorption peak is associated with the deep levels of magnetic polarons. On the basis of these experimental results, the authors of [29] proposed the energy scheme depicted in Fig. 2. It is significant that the observed

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS p–i–p

Intensity, arb. units

p = 16 × 1010 cm–3 (a) T, K 4.2

T = 1.34 K 1010 cm–3

p, 2.7

2.7

5.2

2.4

7.1

2.1

10

1.8

12

1.2

16

T, K 4.2

(c)

Vα = 7 V

T, K 4.2

3.7

3.5

3.2

3.2

3.1

2.2

1.7 1.5

1.7

1685

(b)

p–i–n

Vα = 0 V

565

(d)

1.5 1695

1705 1685 Energy, meV

1695

1705

Fig. 1. Effect of the (a, c, d) temperature, (b) exposure, and (c, d) bias voltage Vd on the photoluminescence line for the (Cd,Mn)Te quantum well placed at the center of (a, b) p–i–p structure and (c, d) p–i–n diode. The splitting and shift of the line indicate the appearance of ferromagnetic ordering, which can be affected by exposure to (b) light and (c, d) electric field through the change in the hole density p in the quantum well [26].

polarons have a very high binding energy (0.1 eV). Consequently, it is expected that there can exist magnetic polarons with a very high stability and a long lifetime.

T = 14 K, H = 0 T 0.1 eV 10 meV

Kasuya [30] examined a very interesting phenomenon, namely, the Bose condensation of magnetic polarons. Beginning with the discovery of a layered structure of CuO2 oxide characterized by a high critical temperature of magnetic ordering [31], different experimental investigations have been carried out with the aim of elucidating the physical mechanism of magnetic ordering. However, the proposed models contradict each other, and this phenomenon has defied explanation. In [32–34], Kasuya proposed the model of paired magnetic polarons and their Bose condensation. It is reasonable to expect that polarons are formed in systems with low carrier densities. Therefore, the liquid state of magnetic polarons could explain the unusual temperature dependence of the antiferromagnetic spin correlation length ξ inside CuO2 layers in La2 – xSrxCuO4 compounds [35]. Subsequently, detailed experimental and theoretical investigations were underGLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

7 meV

Gd 5d

Magnetic polaron

T = 14 K, H = 5 T

EF

Energy

Gd 5d

Magnetic polaron

EF

Energy

Fig. 2. Scheme of the state of a bound magnetic polaron in GdzS3 and the influence of the magnetic field on the polaron state [28]. 2005

566

TVER’YANOVICH et al.

Curie temperature, K 600 500

Mn, 5%

(Ga,Mn)N

400 300 200

(Ga,Mn)As

100 0 10

8 6 4 2 0 2 4 Concentration of Concentration of additional holes, % additional electrons, %

Fig. 3. Dependences of the Curie temperature on the concentration of additional carriers for the (Ga,Mn)N and (Ga,Mn)As semiconductors. Holes in both diluted magnetic semiconductors are generated by Mg acceptors. In the GaN compound, electrons are generated by O donors. In the GaAs compound, As interstitial atoms hypothetically serve as donors.

taken not only for CuO2-based systems but also for other systems, including cerium monopnictides with a low carrier density, in which different aspects of an unusual behavior of a magnetic-polaron liquid were observed [34, 36]. Specifically, Kohgi et al. [37] revealed the condensation of a liquid formed by weak magnetic polarons into strong magnetic polarons with ordering of spins and charges. On the basis of the results obtained in these studies, the assumption was made that condensation of magnetic polarons occurs along the boundary between magnetic polarons. In this case, there arise strong magnetic polarons in the same way as in cerium monopnictides [34, 35] and charges and spins progressively form a stripe structure similar to that found in La2 – x – yNdySrxCuO4 compounds at x = 1/8 [38]. It was also demonstrated that other anomalous properties, such as an anisotropic pseudogap of the x2 – y2 type [39] observed at temperatures above the Curie point TC, can be adequately interpreted in terms of the aforementioned model. METHODS FOR CONTROLLING THE MAGNETIC STATE OF SEMICONDUCTORS Doping Ferrones can be formed by introducing donor dopants into a magnetic semiconductor [21]. A ferron formed by an electron localized on a donor can be termed a magnetic polaron. According to [21], this doping can bead to a considerable increase in the magnetic susceptibility, a change in the Weiss constant, and even the formation of spontaneous magnetization [21, p. 225]. However, this method for controlling the mag-

netic properties of semiconductors in information devices most likely has no practical value. Investigations in this direction have been carried out in order to produce new magnetic semiconductors with high Curie temperatures. As an example, let us consider the results obtained by Sato et al. [40]. These authors studied the influence of electrically active dopants on the magnetic properties of (Ga,Mn)N and (Ga,Mn)As semiconductors. The dependences of the Curie temperature TC on the concentration of additional electrons and holes are plotted in Fig. 3. In both compounds, holes are formed through substitution of manganese for gallium. Additional electrons in the (Ga,Mn)N compound are formed through substitution of oxygen for nitrogen. In the (Ga,Mn)As semiconductor, As interstitial atoms hypothetically serve as donors. For both compounds (Ga,Mn)N and (Ga,Mn)As, the Curie temperature TC decreases drastically with an increase in the electron concentration (Fig. 3). The behavior of the Curie temperature TC upon electron doping is quite consistent with the experimental observations [41] and can be adequately explained in the case of the (Ga,Mn)As semiconductor with allowance made for the compensation for carriers of opposite sign. Control of Free-Carrier Density by a p–n Junction The solution to the problem of the control of the magnetic properties of materials is of great importance from the standpoint of both basic science and high technologies, in particular, in view of the last developments in the field of magnetoelectronics and spintronics. Diluted magnetic semiconductors, in which the ferromagnetic interactions are caused by the free carriers, are of special interest, because the magnetic properties of these materials can be changed as a result of a variation in the carrier density [18]. Therefore, it is quite reasonable that there arises an idea to apply the method for controlling the free-carrier density with the use of a p−n junction, which is widely employed in semiconductor engineering. The first investigation was performed by Beschoten et al. [18] with AIIIBV diluted magnetic semiconductor layers embedded in a Schottky diode. It was revealed that a voltage of 125 V across a gate leads to a change in the Curie temperature in a field-effect transistor based on an (In,Mn)As thin layer by approximately 1 K. Compared to AIIIBV magnetic semiconductors, manganese in AIIBVI magnetic semiconductors is isoelectric and does not result in the appearance of carriers. Consequently, the ferromagnetic interactions can be induced by holes due to the variation in doping of heterostructures. The possibility of controlling the ferromagnetism in Cd0.96Mn0.04Te quantum wells by electric fields was demonstrated in [42–44]. The method proposed by Matsukura et al. [45] for controlling the magnetic state with the use of electric fields is similar to that described above. The carrier-

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS (a)

567

(b) VG > 0

VG < 0

Mn spin Hole

Metal Insulator (In,Mn)As

Buffer layer

Ground

Fig. 4. Scheme of ferromagnetism control by the electric field. (a) Application of the positive bias voltage across a gate induces the paramagnetic phase due to the decrease in the hole density and, hence, leads to a weakening of the magnetic interaction of Mn atoms. (b) Application of the negative bias voltage has an opposite effect and enhances the ferromagnetism.

induced ferromagnetism in a field-effect transistor based on the (In,Mn)As magnetic semiconductor can be controlled by the electric field. By varying the electric field of a gate, it is possible to control isothermally and reversibly the transition temperature of the ferromagnetic state. The essence of the method consists in increasing the free-carrier density in some region of the material by applying the external field through an insulator layer (Fig. 4). Carrier Photogeneration The exchange interaction between carriers and magnetic ions introduced into an alloy provides a way of observing a number of phenomena that obey quantum regularities. In particular, photons generate excitons (whose spin correlates with localized magnetic spins) with the formation of the so-called exciton magnetic polaron. This phenomenon is illustrated in Fig. 5. Electronically, the formation of the exciton magnetic polaron leads to the localization of the exciton with release of the relaxation energy. From the viewpoint of magnetism, the exciton magnetic polaron induces a uniform spin orientation within the range of the exciton wave function and forms a ferromagnetic “bubble.” Although different models of this phenomenon have been proposed to date [46, 47], attempts to include the exciton effect in a complex self-consistent theory of magnetic polaron have not met with success. At quantum dots located in diluted magnetic semiconductors, different nonmagnetic mechanisms of localization, such as potential fluctuations and (or) disordering at interfaces, mask phenomena associated with the formation of exciton magnetic polarons. Takeyama et al. [48] studied the photoluminescence in different systems formed by quantum wells in diluted magnetic semiconductors with the use of the following experimental setup. A dye laser (R : 6G) pumped by an Nd : YAG laser was used as a excitation GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

source. The energy of excitation pulses was lower than 1 nJ. The photoluminescence signal was recorded by a streak camera with a charge-coupled device. The time resolution of the setup was of the order of 20–30 ns. The photoluminescence spectra of quantum wells (Ar laser excitation; wavelength, 514.5 nm) were carefully analyzed over a wide range of temperatures (2–60 K). The energies of exciton magnetic polarons were determined from the photoluminescence spectra (Fig. 6). The energy increases with a decrease in the quantum well size. Exciton magnetic polarons are not formed in quantum wells with sizes larger than 4 nm. It can be seen from Fig. 6 that the data obtained in [48, 49] for similar systems are close to each other but differ from the results for bulk exciton magnetic polarons. The results of theoretical calculations [50, 51] are also presented in Fig. 6. In order to interpret these data, we analyze the steady-state photoluminescence spectra and the timeresolved photoluminescence spectra in the picosecond range. As can be seen from Fig. 7, the energy of the photoluminescence peak differs substantially from the energy obtained by extrapolating the high-temperature data (above 60 K) and indicates that the relaxation energy increases with a decrease in the temperature. The half-width of the photoluminescence peaks is larger than the half-width that could be expected from the high-temperature data (dotted line in Fig. 7b). The temperature dependence of the Stokes shift at t = 300 ps is shown in Fig. 7c. Even at 40 K, the exciton relaxation energy is equal to 5 meV. The Stokes shift below 40 K depends strongly on the temperature, reflecting the localization of exciton magnetic polarons. Judging from these results, we can assume that the exciton magnetic polaron is formed at temperatures lower than 40 K once the initial exciton is localized according to the nonmagnetic mechanism. Consequently, the exciton magnetic polarons found in the systems under consideration are localized magnetic 2005

568

TVER’YANOVICH et al.

Photon Mn spin

e: Exchange interaction

Mn spin

Exciton

h: Exchange interaction

Energy of exciton magnetic polarons, meV 35 CdTe–Cd1–xMnxTe 30 Data taken from [48] 25 Data taken from [49] 1 20 15 10

2

5 0

Exciton magnetic polaron

0

1

2

3

4 Lz, nm

Fig. 6. Dependences of the energy of exciton magnetic polarons on the quantum well size Lz in the CdTe– Cd1 − xMnxTe (x = 0.24) semiconductor. The data taken from [48] and the results obtained by selective photoluminescence spectroscopy [49] are compared with the results of theoretical calculations (1) at x = 0.26 and (2) within the variational theory [50, 51].

Mn spin

Fig. 5. Illustration to the formation of photoinduced magnetic polarons (exciton magnetic polarons).

polarons. Possibly, this explains good agreement between the data of luminescence and selective photoluminescence spectroscopy. Therefore, the experimental data obtained in [48] not only demonstrate that the photoferromagnetism can occur in principle but also enable one to make the inference regarding an increase in the binding energy of magnetic polarons with a decrease in the localization region size. Karpenko and Berdyshev [52] assumed that the photoexcitation of free carriers should result in an increase in the Curie temperature of ferromagnetic semiconductors. However, the theoretical estimates showed that the effect is very weak [52]. This is the reason why the photoferromagnetism phenomenon could not be found for many years [53]. Only precision experiments revealed the influence of light on the magnetization of the EuS ferromagnetic semiconductor [54]. Unfortunately, substantial experimental problems did not make it possible to perform parallel measurements of photoconductivity [54] and the contribution of photoelectrons to the observed effect remained unclear. The freecarrier density calculated from the shift of the Curie temperature under exposure to laser radiation is approximately equal to 1018 cm–3 [54]. The probability of generating such a high free-carrier density is unrealistic taking into account that the measurements were carried out using films with a high defect concentration at temperatures in the vicinity of the Curie point at which a sharp minimum of the photoconductivity is usually observed [53]. However, it should be noted that the minimum of the photoconductivity is most likely

not associated with the photogeneration of carriers. Possibly, this contradiction can be explained either by the formation of localized magnetic polarons, which are not involved in charge transfer but increase the magnetization of the material, or by the fact that, at temperatures in the vicinity of the Curie point, free carriers are concentrated in particular regions and transform them into the ferromagnetic state. These regions do not form an infinite cluster, and, hence, free carriers do not participate in through conduction. Photogeneration of Virtual Carriers One more method for controlling the magnetic state of materials consists in photogenerating virtual carriers. The model of this phenomenon was developed by Nagaev [55]. The basic principles of the model are given below. The case in point is the ferromagnetic effect that is not associated with the optical generation of carriers. In this case, the degree of ferromagnetic order can be increased even at frequencies corresponding to the transparency range of a crystal. The effect is governed by the virtual transitions of electrons from the valence band to the conduction band with the formation of virtual conduction electrons and holes. These terms imply the change in the states of the valence band under irradiation due to the admixture of the valence states to the conduction band states. It should be kept in mind that electrons occurring in the valence band before irradiation remain in it, even though the band itself is changed.

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS

In many magnetic semiconductors (for example, in EuO [53]), the valence band states are predominantly formed by p orbitals of nonmagnetic anions and the conduction band states are formed by outer orbitals of magnetic cations. The overlap of the orbitals of partially filled cation shells with the orbitals of outer shells of the same cations is considerably stronger than that with the anion orbitals. Therefore, the exchange interaction of localized d and f moments with conduction electrons is significantly stronger than that with valence electrons. Under these conditions, the mixing of conduction and valence band states under irradiation substantially enhances the exchange interaction of valence electrons with localized moments. Depending on the orientation of the electron spin with respect to the magnetic moment of the crystal, this enhancement of the exchange interaction can increase or decrease the electron energy. If the degree of mixing does not depend on the electron spin, the energy of exchange between the electrons of the completely filled valence band and the localized moments does not completely change. However, in ferromagnetic semiconductors, the degree of mixing depends on the electron spin direction, because the energy bands in the presence of the magnetic moment of the crystal are spin-split bands (this is the Zeeman splitting of the electron energy in the molecular field of the crystal). Consequently, the spin orientation also affects a gap that occurs between the valence band and the band gap and governs the degree of mixing. In terms of virtual conduction electrons, we can say that they are spin-polarized electrons and transitions whose spin projection provides an increase in the energy of exchange with localized moments should be dominant. Since this energy increases with an increase in the crystal magnetization, virtual electrons generated by radiation favor ordering and retention of order in the crystal. The above mechanism is also valid in the case when real carriers are generated under exposure to light. If the magnetization relaxation time is shorter than other characteristic times, the contributions from virtual and real electrons to the ferromagnetic effect can be separated according to the relaxation times (the former contribution is instantaneous, whereas the relaxation time of the latter contribution is equal to the photoconductivity relaxation time). The fact that the transitions of virtual electrons are not accompanied by the light absorption makes it possible to observe much simply the ferromagnetic effect in the transparency range of the crystal: irradiation does not lead to heating that can destroy the ferromagnetic order. According to calculations performed in [55] (for the magnetic semiconductor with Eg ~ 1 eV, m* = m0), the Curie temperature is shifted by 3 K. This estimate was obtained in the case of the most power lasers. The effect remains noticeable for laser whose power is lower by one order of magnitude. Since the laser frequency corGLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

569

Energy position, eV 1.860 (a) 1.855 1.850 1.845 1.840 Half-width, eV 20 (b) 18 16 14 12 10 Stokes shift, meV 0 (c) –5 –10 –15

0

20 40 Temperature, K

60

Fig. 7. Temperature dependences of the (a) position, (b) half-width, and (c) Stokes shift of the photoluminescence line for CdTe/Cd0.76Mn0.24Te quantum wells (Lz = 1.3 nm) [48].

responds to the transparency range of the crystal, the effect is stable, at least, for short pulses. When the valence band is formed by the f-type states, not only virtual photoelectrons but also virtual photoholes interact strongly with the magnetization of the crystal and, hence, carriers of both types contribute to the ferromagnetic effect. CHOICE OF EXPERIMENTAL CONDITIONS Choice of Method for Controlling the Magnetic State Three main methods for controlling the magnetic state and the examples of their applications were considered above. These are the introduction of electrically active dopants and defects, the modulation of the carrier density with the use of p–n junctions, and photogeneration. All three methods are used in research works. Now, we evaluate their potentialities for practical applications. By practical application is meant their use in information systems (control of signals, writing and processing of information, etc.). 2005

570

TVER’YANOVICH et al.

The introduction of electrically active dopants for these purposes cannot be used, because this method enables one only to prepare new materials rather than to control their properties in real time. The use of p–n junction for these purposes provides a way of achieving high densities of nonequilibrium carriers, which is a doubtless advantage of the method. In this method, a light beam is controlled by electric signals. However, at present, the attraction in information technologies is toward all optical processing, for example, all optical switching. Therefore, the phenomenon of photoinduced ferromagnetism is most promising for practical applications. In order to solve the stated problem, it is necessary to increase the probability of observing the photoferromagnetism to a maximum degree, namely, to increase the efficiency of photogeneration of carriers (including excitons and polarons) and their lifetime. In our opinion, the lifetime of nonequilibrium currents can be increased in a number of ways. First, it is necessary to use a magnetic semiconductor in the form of nanocrystals, because this leads to an increase in the binding energy of a magnetic polaron (to an increase in the depth of the quantum well containing the polaron) and, hence, its stability. Recall that Boukari et al. [28] observed magnetic polarons with a high binding energy of 0.1 eV. The spatial separation of positive and negative free carriers should decrease the probability of their recombination. The spatial separation can be provided by using, for example, p–n junctions arising at interfaces of composite semiconductor materials. However, the size of these phases should be comparable to the size of exciton magnetic polarons or ferrons (according to Nagaev). Otherwise, an increase in the Coulomb energy does not permit one to achieve the desired effect. Undeniably, a substantial role is played by the proper choice of the magnetic semiconductor. This implies that the magnetic semiconductor should possess a positive exchange interaction, which at a high free-carrier density ensures the Curie temperature TC no lower than room temperature. Moreover, the semiconductor can be obtained in a “deteriorated” form, namely, in the form of a paramagnet with a low freecarrier density. This can be achieved in at least two ways: either by nanodispersion that results in an increase in the band gap and a decrease in the free-carrier density due to the size effect or by increasing the temperature of the experiment to the Curie temperature at which the free-carrier density decreases. Choice of Materials for Investigation (Ferromagnetism of Semiconductors) We begin the analysis of this problem with consideration of different types of magnetic semiconductors. For many years, researchers have investigated different

aspects of magnetism in semiconductor materials, including spin glasses, the antiferromagnetic behavior of AIIBVI materials doped with Mn, and ferromagnetism of chalcogenide compounds with europium and Crbased spinels [56, 57]. The strong ferromagnetic interaction between localized spins was observed in Mndoped AIIBVI compounds with a high carrier density. Suski et al. [58] revealed the ferromagnetic properties in Pb1 – x – ySnyMnxTe (y > 0.6) semiconductors with a high hole density of the order of 1020–1021 cm–3. It was demonstrated that free holes in low-dimensional structures of diluted magnetic semiconductors based on AIIBVI compounds can induce the ferromagnetic order [59, 60]. In many semiconductor materials in a monolithic form, a low solubility of magnetic and electron dopants limits an increase in the density of magnetic moments and free carriers. However, this problem can be overcome using low-temperature epitaxial growth. The ferromagnetism at temperatures higher than 300 K was recently found in the GaN compound and chalcopyrite semiconductors doped with transition metals [61, 62]. This demonstrates the potentialities of spintronics technologies in achieving Curie temperatures comparable to room temperature. Dietl et al. [63] applied the Zener model of ferromagnetism (which is based on the exchange interaction between carriers and localized spins) to the explanation for the temperature of the transition to the ferromagnetic state in III–V and II–VI compound semiconductors. The theory includes ferromagnetic correlations caused by the holes due to the shallow acceptors in the matrix of localized spins in the magnetically doped semiconductor. The theoretical results obtained by Dietl et al. [64] suggest that the ferromagnetism in the n-type materials should be observed, if at all, at low temperatures and predict its occurrence at higher temperatures in the p-type materials. In particular, Mn ions replacing Group II or III elements provide the appearance of localized magnetic moments. In the case of III–V semiconductors, manganese also serves as an acceptor dopant. It is assumed that a high hole density is responsible for the ferromagnetic interactions between Mn ions. Experimental investigations revealed that the direct exchange between Mn ions in (Ga,Mn)As semiconductors doped with donors is antiferromagnetic. However, in the p-GaAs compound grown by molecular-beam epitaxy, doping with Mn in the concentration range 0.04 ≤ x ≤ 0.06 leads to the ferromagnetism. Therefore, the described model made it possible to explain successfully the relatively high temperature of the magnetic transition in the (Ga,Mn)As semiconductors. The carrier-induced ferromagnetism in semiconductors depends on the concentration of magnetic dopants, type of carriers, and their density. Since the magnetic behavior in semiconductor systems is similar to that observed in metal–insulator transitions at which the ferromagnetic transformation occurs with an increase in

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS

the carrier density, it is useful to examine the influence of localization on the appearance of the ferromagnetism. As the carrier density increases, the changeover from localized states to delocalized electrons occurs gradually. On the metallic side of the transition, certain electrons occupy extended states, whereas the other electrons are in states singly occupied by dopants. Upon the metal–insulator transition, extended states become localized (the localization radius decreases gradually from infinity to subatomic sizes). The electron wave function remains extended for interactions at distances shorter than the localization length. Theoretically, holes in extended or weakly localized states could induce long-range interactions between localized spins. This suggests that there can arise carrier-induced ferromagnetic interactions in materials with weak semiconductor properties as in heavily doped semiconductor oxides. The performed theoretical analysis allows us to make several interesting inferences and predictions. For materials, which have been studied in detail (semiconductors with a zinc-blende structure), magnetic interactions are favorable in semiconductors doped by holes owing to the interactions of Mn2+ ions with the valence band. This is in agreement with the aforementioned calculations of the exchange interaction between Mn2+ ions in II–VI compounds [64], which show that the main contribution is made by processes with the participation of two holes. Such a mechanism of superexchange can be treated as the indirect exchange interaction that is caused by the anions and, hence, involves the valence band. Note that, in II–VI compounds, the properties of the valence band are predominantly determined by the anions. The model proposed by Dietl et al. predicts that the transition temperature should be determined by the decrease in the atomic mass of forming elements and, hence, by the enhancement of the p– d hybridization and the weakening of the spin–orbit interaction. It is most important that the model predicts Curie temperatures TC higher than 300 K for the p-GaN and p-ZnO compounds. Therefore, the recent experimental observation of the ferromagnetism in the GaN compound turns out to be theoretically justified [65−74]. Katayama-Yoshida and Sato [75] reviewed the works devoted to systematic investigations into the design of ferromagnetic materials based on III–V and II–VI diluted magnetic semiconductors with the use of preliminary calculations in the local-spin density approximation. The electronic structures of the GaN compound doped with different 3d transition metals and the InN, InP, InAs, InSb, GaN, GaP, GaAs, GaSb, AlN, AlP, AlAs, and AlSb compounds doped with manganese were calculated by the Korringa–Kohn–Rostoker method in the coherent-potential approximation. It was found that the ferromagnetic ground states can be easily produced in the GaN compound doped with V, Cr, or Mn without introduction additional carriers. Moreover, it was shown that InN is the most promising candidate for the preparation of a high-temperature ferGLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

571

romagnet. The simple explanation was proposed for the behavior of magnetic states in III–V and II–VI compounds based on diluted magnetic semiconductors. Furthermore, it was demonstrated that the ZnS, ZnSe, and ZnTe compounds doped with V or Cr without additional p- or n-type doping are ferromagnets. However, the same compounds doped with Mn, Fe, Co, or Ni are in a spin-glass state. The ZnO compound doped with V, Cr, Fe, Co, or Ni without doping with carriers and the ZnO compound doped by Mn with additional p-type doping are characterized by the semimetallic ferromagnetism. MAGNETIC SEMICONDUCTOR SPINELS Let us dwell in more detail on the analysis of semiconductor spinels [76]. Among spinels, a large group is represented by spinels containing chromium, whose ions possess a magnetic moment and occupy octahedral sites in the crystal lattice. The magnetic order in spines with chromium depends on the distance between chromium ions in the octahedral sublattice. In turn, this distance is associated with the type (radius) of anions whose sublattice involves tetrahedral and octahedral sites. At small ionic radii of anions (for example, oxygen), magnetic moments localized at chromium ions are antiferromagnetically ordered with a negative paramagnetic Curie–Weiss temperature QC–W. Similar compounds, as a rule, behave as insulators [77]. At large ionic radii of anions, the magnetic ordering is spiral with a positive paramagnetic Curie–Weiss temperature QC–W or completely ferromagnetic. This depends on the type of cations in tetrahedral sites. For example, a simple spiral is observed for Zn, whereas the ferromagnetic order occurs for Cd or Hg. In both cases, spinels are semiconductors [78, 79]. A special group of spinels is formed by compounds with copper ions in tetrahedral sites. In this case, we are dealing with a very strong ferromagnetic interaction of magnetic moments localized on chromium ions. This is usually accompanied by the p-type metallic conductivity. Spinels (for example, ZnCr2Se4, CuCr2Se4) and solid solutions on their base are characterized by numerous structural, magnetic, and electric phase transitions and correlations between them. In particular, dilution of the magnetic sublattice with nonmagnetic ions frequently leads to the formation of the spin-glass state (e.g., upon replacement of Cr ions by Sb ions in CuCr2Se4 [80–82]. The chromium family of spinels is described by the following important parameters: the temperature TN (~20 K), the Curie temperature TC (~100 K; coppercontaining compounds, ~400 K), and the paramagnetic Curie–Weiss temperature QC–W (from –500 K to +450 K) [79, 80]. The magnetic and electrical properties of spinels are determined by the type of magnetic interaction, which, 2005

TVER’YANOVICH et al.

Cr2V4O13

0.41

Dominance of antiferromagnetic interaction

0.39 0.37 0.35 0.33

Zn0.5Ga2/5Cr2Se4 ZnCr2S4 ZnCr1.86In0.14Se4

0.31 0.29 0.27 0.25 0.25

CuCr2Se4

Dominance of ferromagnetic interaction

Cd0.8Cu0.2Cr2S4 CdCr2Se4

ZnCr2Se4

Insulator

0.43

ZnGa2O4 ZnCr2O4

Cr2V3.5M0.5O13.25

CdIn2S4 CdCr2S4

HgCr2S4 HgCr2Se4

Metallic conductivity

ro/ra 0.45

CuCr2S4

CuCr2Te4

0.30

Semiconductor

572

0.35

0.40

0.45

0.50

0.55 rt/ra

Fig. 8. Dependence of the ratio ro/ra on the ratio rt/ra as a phase diagram of the chromium compounds under investigation [82]. Points indicate the data for terminal compounds of solid solutions or solid solutions with the highest concentration in the case of limited solubility.

in turn, depends primarily on the valence of chromium ions. The superexchange interaction is dominant for compounds with bivalent and trivalent chromium ions, whereas double exchange interactions occur in compounds with a mixed valence of chromium ions (Cr3+– Cr4+), which is characteristic of copper-containing spinels. The latter interactions are dominant over the former interactions when the tetrahedral sublattice is completely occupied by chromium ions [77–80]. Different spinels and compounds of the spinel type with chromium were considered by Krok-Kowalski et al. [83] in order to construct the phase diagram, which represents correlations of the magnetic and electrical properties with the ionic radii of cations and anions. Figure 8 depicts this phase diagram in the form of the dependence of the ratio ro/ra on the ratio rt/ra, where rt is the ionic radius of cations in tetrahedral sites, ro is the ionic radius of cations in octahedral sites, and ra is the ionic radius of anions. The ionic radii rt, ro, and ra are taken from [84]. It is easy to distinguish two regions in Fig. 8 so that the antiferromagnetic interactions are dominant in region 1 (at ro/ra > rt/ra), and the ferromagnetic interactions are dominant in region 2 (at ro/ra < rt/ra). However, the electrical properties depend only on the ratio ro/ra; namely, as the ratio ro/ra decreases, the character of the electrical conductivity changes in the order: insulator–semiconductor–conductor [83]. PROPERTIES OF CuCr2Se4 SPINEL Spinel CuCr2Se4 is of importance as the main material for doped crystals of the spinel type. Substitution for cations [85] and anions [86] leads to a change in the

physical properties of the compound. Compounds with a chemical formula AB2X4 (where A and B are metal cations, and X is oxygen or a chalcogenide anion) often crystallize in a structure of the spinel type. The group of oxide spinels [87] is larger than the group of chalcogenide spinels (X = S, Se, Te) [88]. Oxide spinels are insulators or semiconductors, and chalcogenide spinels are semiconductors or metals (supersemiconductors at low temperatures) [87, 88]. The CuCr2Se4 compound belongs to chalcogenide spinels with the metallic conductivity [89]. This compound has a typical spinel structure with the space group Fd3m [89–91]. According to the neutron diffraction data, the CuCr2Se4 compound is characterized by a collinear ferromagnetic structure with magnetic moments of 2.8µB and 3µB per Cr atom at 4 and 77 K, respectively [90, 91]. Judging from the moments, chromium atoms are in the Cr3+ state and copper atoms are in the Cu+ state [90] (in [91], it was admitted that valence electrons of Cu+ ions participate in the formation of the conduction band). The saturation magnetization measured at the liquid-helium temperature is equal to 4.5–5.07µB per formula unit [92, 93]. The effective magnetic moment of chromium ions lies in the range from 4.3 to 4.5µB [92, 93]. The paramagnetic Curie– Weiss temperature QC–W falls in the range 436–465 K [76, 94]. The Curie temperature is equal to 414–460 K [76, 92]. Several models of the electronic structure were proposed for explaining the physical properties of the CuCr2Se4 compound. The hypothetical valence distributions are as follows: Cu2+[Cr3+]2[Se2–]4 [95], 3+

4+

Cu+[Cr3+Cr4+][Se2–]4 [76], and Cu+[Cr 1 + δ Cr 1 – δ ][Se2 – δ]4 (where δ = 0.1) [96]. The ion valences obtained by self-

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

60 54 48 42 36

3.5

Magnetization, µB

3.0 2.5 2.0

30 24

1.5 1.0 0.5 0 290 330 370 410 450 490 530 570 610 650 690 730 Temperature, K

18 12 6 0

573

Reciprocal of the magnetic susceptibility

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS

Fig. 9. Temperature dependences of the magnetization and the reciprocal of the magnetic susceptibility per CuCr2Se4 formula unit.

consistent calculations are represented by the formula Cu1.25+[Cr1.41+]2[Se1.02+]4 [97]. The X-ray photoelectron spectroscopic data indicate that the bonding is more likely to be covalent than ionic in character [98]. Belov et al. [99] reported on the first-order phase transition associated with the drastic decrease in the lattice constant at the Curie point. This phase transition should be accompanied by the change in the magnetic moment. Rodic et al. [100] examined the magnetic structure and the temperature dependence of the magnetic susceptibility of the CuCr2Se4 compound (Fig. 9) in order to determine the magnetic moment and the data on changes at the Curie point. The neutron diffraction experiments were performed with the use of a CuCr2Se4 powder sample at 10 and 295 K. The magnetic measurements were carried out in the temperature range 295–720 K. The magnetic moment was determined to be µ(Cr) = 2.81µB (at 10 K), and interatomic distances suggest that the oxidation state of chromium in the ferromagnetic phase is between +3 and + 4. However, the effective magnetic moment µeff(Cr) = 4.4µB obtained from the experimental data on the susceptibility in the paramagnetic phase corresponds to chromium in the oxidation state between +2 and +3. The firstorder transition with a change in the magnetic moment and chromium valence occurs at the Curie point TC = 450 K. Therefore, the phase transition attended by the change in the magnetic moment is observed at the Curie temperature. A sharp change in the lattice constant [84] and the magnetic moment indicates the first-order phase transition. These two effects are associated with each other. GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

Increase in the Lifetime of Magnetic Polarons upon Changeover to Nanocrystalline State of Materials In recent years, semiconductor nanocrystals, also called quantum dots, have been studied extensively [101, 102]. In particular, Murray et al. [103] and Norris et al. [104] prepared high-quality nanocrystals of AIIBVI compounds and investigated their optical properties, including the interband luminescence. The authors observed the blue shift of the fundamental absorption edge and discretization of the energy spectrum. Semimagnetic and diluted magnetic semiconductors based on AIIBVI compounds, such as Cd1 – xMnxTe, are famed for their magneto-optical properties and the formation of magnetic polarons [105]. The magnetic polarons are formed as a result of the strong sp–d exchange interaction between band carriers and Mn2+ ions. Magnetic polarons associated with the shallow dopants (acceptors, donors) have been investigated widely [46]. It was found that exciton magnetic polarons are formed in the bulk Cd1 – xMnxTe material and its epitaxial layer [106– 108] and also in CdTe–Cd1 – xMnxTe heterostructures [109, 110]. Acceptor-associated magnetic polarons favor saturation at low temperatures [111–117]. The mutual polarization between bound holes and Mn ions results in the formation of a ferromagnetic cluster. A similar situation is expected for optically excited diluted magnetic semiconductor nanocrystals. These quantum dots can serve as a model for a zero-dimensional exciton magnetic polaron, because the time of polaron formation is shorter than the lifetime of electron–hole pairs. Wang et al. [118] experimentally studied Zn0.93Mn0.07S diluted magnetic semiconductor nanocrystals. Crystals ≈25 Å in diameter were grown in a glass matrix. (This is not the sole example of growth of semimagnetic semiconductor nanocrystals in a vitreous host.) The observed photoluminescence peak at 2.12 eV corresponds to the well-known internal transition in Mn2+ ions. The photoluminescence excitation 2005

574

TVER’YANOVICH et al. E, meV 90

a = 1.5 nm

80 70 60 2.0

50 40

2.5

30

4.0

20

3.0

10 0

5.0 10

20

30

40

50 T, K

Fig. 10. Dependences of the polaron binding energy (meV) on the temperature T in zero field for Cd0.89Mn0.11Te quantum dots. Numerals near curves indicate the values of a = 1.5, 2.0, 2.5, 3.0, 4.0, and 5.0 nm [101].

spectrum exhibits a blue shift by 0.23 eV due to the quantum confinement. The static magnetic permeability in the temperature range 2.3–314 K was also measured in [118]. The experimental data are described by the Curie–Weiss law with a negligible Weiss constant. This indicates that the contribution of the Mn–Mn antiferromagnetic interaction in quantum dots is smaller than the corresponding contribution in bulk samples. Recently, Bhargava et al. [119] synthesized Mn-doped ZnS particles whose diameter varies in the range from 35 to 75 Å. Special attention was concentrated on the characteristics of the Mn2+ luminescence. Possibly, diluted magnetic semiconductors, such as Zn1 – xMnxS, with a band gap larger than 2.12 eV for bulk materials cannot be used to investigate magnetic polarons, because the emission spectrum of manganese dominates over the photoluminescence spectrum. This is explained by the short time of energy transfer (<500 ps) from an electron–hole pair to a d shell of manganese [119]. It is possible that this time corresponds to the polaron formation time (~100 ps in the bulk material) [106–108]. In this respect, investigations into Cd1 − xMnxSe nanocrystals embedded in a silica glass [120] are of considerable interest. Actually, the exciton luminescence data prove the existence of magnetic polarons. It was found that the Stokes shift of the photoluminescence upon selective excitation decreases in the magnetic field and reaches a maximum in a field of 6 T. This behavior is typical of exciton magnetic polarons. Furthermore, picosecond time-resolved spectroscopy revealed that the lifetime in a magnetic field of 5 T decreases from 900 to 400 ps. In [101], magnetic polarons associated with the electron–hole pairs in diluted magnetic semiconductor

quantum dots were theoretically studied within the effective mass approximation, which includes the interaction between the light- and heavy-hole bands. The magnetic polaron arising from the sp–d interaction between confined carriers and magnetic ions was described in the self-consistent mean-field approximation, which leads to the coupled nonlinear Schrödinger equations for the electron and the hole. The local response to the effective field was modeled by the experimental high-field magnetization curve in the bulk material. The electron–hole Coulomb interaction was taken into account. An exact numerical solution of the three coupled equations was used to calculate the equilibrium polaron size, the binding energy Ep, and the spin Sp. The results of calculations for Cd1 – xMnxTe nanocrystals at x = 0.11 are presented in Fig. 10. The binding energy Ep decreases with an increase in the quantum dot radius a and Ep ∝ a–3 at T ≥ 30 K. In small dots (a ≤ 2 nm), the binding energy Ep decreases slowly as the temperature T increases. In large dots (a ≥ 4 nm), the binding energy Ep(T) decreases rapidly. A similar temperature dependence was obtained for the spin Sp (Fig. 11). It is of interest that the polaron binding energy as a function of the magnetic field strength decreases and tends to the same value irrespective of the temperature (Fig. 12). Figure 11 also illustrates the dependence of the polaron spin Sp on the polaron size a. Therefore, as the polaron size increases, the polaron spin increases and the polaron binding energy decreases. As a consequence, the dependence of the magnetization of the system on the polaron size exhibits a maximum whose position depends on the temperature (Fig. 13). Quasi-zero-dimensional magnetic polarons in single Cd0.93Mn0.07Te/Cd0.6Mg0.4Te quantum dots were experimentally studied by photoluminescence spectroscopy [121]. In order to provide a high spatial resolution required for measuring single quantum dots, an aluminum mask with an aperture less than 150 nm in diameter was produced by electron-beam and lift-off lithography. The photoluminescence spectra of these small-sized regions are usually consist of individual lines (10–20) of quantum dots in a spectral range of 100 meV. The photoluminescence spectra of single quantum dots with well-resolved lines were analyzed in detail. By comparing the experimental data with model calculations, the energy (approximately 10 meV), the internal magnetic field (3.5 T), and the radius (3 nm) of the magnetic polarons were obtained. Increase in the Lifetime of Magnetic Polarons Due to Spatial Separation of Carriers The analysis of results of magnetostatic investigations into the boundaries of glass formation regions for chalcogenide systems containing transition metals demonstrates that glass formation regions in these systems either are absent at all (crystalline microphases are

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS Ep, meV 35

Sp 140

a = 5.0 nm

a = 5.0 nm

120

575

30 1.8 K

100

25

80 60

20 4.2 K

40

15

20

10

a = 1.5 nm 0 10

20

30

40

50 T, K

5

Fig. 11. Temperature dependences of the polaron spin magnetic moment in zero field for Cd0.89Mn0.11Te quantum dots of different sizes a [101].

10 K

0

1

3

2

4

5

6

7

8

9

10 H, T

Fig. 12. Dependences of the polaron binding energy on the magnetic field strength at different temperatures [101].

formed at transition metal contents of lower than 0.05 at %) or are very small [122]. Under these conditions of crystalline phase formation when the concentration of structural units forming a phase is low and the cooling rate of a viscous melt is relatively high (quenching in air or into water), diffusion processes are suppressed and the precipitated crystalline phase has a high degree of dispersion. Moreover, even in the case when the glass matrix does not involve microcrystals of the transition metal compound, the metal distribution over the glass volume is characterized by pronounced concentration fluctuations [122]. The above factors have given impetus to the development of the model of pseudoimpurity conductivity in chalcogenide glasses [123]. A contact potential difference arises at a “microcrystal–glass matrix” interface. According to estimates of different authors, the screening length in chalcogenide glasses is equal to hundreds and even thousands of angstroms. Chalcogenide compounds of transition metals, as a rule, possess a metallic conductivity or are degenerate semiconductors. Moreover, it should be taken into account that their microcrystals precipitate from an alloys of a complex chemical composition and, hence, have a high impurity concentration. Consequently, unlike chalcogenide glasses, these microcrystals have a considerably shorter screening length. As a result, the space-charge region covers only a part of the microcrystal and does not exhaust completely its supply of free carriers. This can be judged from the inequality

contact potential difference is of the order of one-fourth of the band gap of the chalcogenide glass (U > 0.5 eV), ε > 10, r > 10–8 m, and Nk > 1020 cm–3, we find that the inequality holds true. In this case, the radius of the space-charge region in the glass can be estimated from the relationship 3εU R =  1 + ----------------- r,  4πeN C

(2)

where NC is the density of charged states in the spacecharge region in the glass. It turns out that the volume R 12 11

CdMnTe 1.8 K

10 9 8 7 6 5

4.2 K

4 3

(1)

5 a, nm

where Nk is the free-carrier density in the microcrystal, r is the microcrystal radius, ε is the permittivity, and U is the contact potential difference. By assuming that the

Fig. 13. Dependences of the light-induced magnetization enhancement factor R on the size of Cd0.89Mn0.11Te quantum dots [101].

2

2

2

2πe N k r ----------------------- > 1, εU

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

3

4

576

TVER’YANOVICH et al.

fraction of space-charge regions is 1.5 orders of magnitude larger than the volume fraction of microcrystals. Consequently, in order to form an infinite cluster that is composed of space-charge regions and provides through transfer in the macroscopic sample, it is sufficient to introduce fractions of atomic percent of the transition metal into the glass composition. As is known, the band structure of the semiconductor is bent in the space-charge region. In the case of intrinsic semiconductors, this leads to an increase in the electrical conductivity and a decrease in the activation energy of electrical conduction. Therefore, the microcrystal is a “collective” impurity that injects its carriers into the glass matrix. An increase in the temperature results in a decrease in the radius of the space-charge region due to the thermal activation of carriers. At a critical temperature, the infinite cluster of space-charge regions is broken and charge transfer occurs over the glass matrix with undistorted band structure. Aa a consequence, the dependence of the logarithm of the electrical conductivity on the reciprocal of the temperature exhibits a kink characteristic of the impurity conductivity in semiconductors. Now, we return to the problem under consideration. Let us assume that the band gap of the glass matrix is larger than the band gap of the crystalline inclusion. In this case, pump radiation at a certain wavelength should be absorbed in the p–n junction region. The junction field spatially separates generated charge carriers of opposite sign, increases the density of majority carriers in both phases, and, correspondingly, enhances the ferromagnetism of the crystalline inclusion. Note that the spatial separation of electrons and holes leads to a decrease in their recombination probability. In order to confirm experimentally the formation of p–n junctions at the interface between the vitreous matrix and crystalline inclusions, it is possible to use the effect of a sharp increase in the permittivity of semiconductor glasses when there arise microcrystals of transition metal compounds in their bulk. This effect was theoretically justified and experimentally confirmed in [124, 125]. The main idea is as follows. For a two-phase system formed by the high-conductivity inclusions and the low-conductivity matrix without insulating interlayers in between, an increase in the permittivity of the matrix (due to the formation of inclusions) is proportional to their volume fraction, which is considerably less than unity. If the p–n junction is formed, its central region has a conductivity lower than those of both phases and can be treated as an insulator. The appearance of the insulating interlayer leads to the formation of capacitors whose high capacitance is due to the small thickness of the insulating layer. This is responsible for the increase in the permittivity of the composite material. Now, we consider the (0.3CuSe · 0.7AsSe)1 – x(MnSe)x system [122]. By using EPR spectroscopy and magne-

tochemical measurements, it was established that crystalline inclusions containing the transition metal are formed beginning with 1 at % Mn. It is at this Mn content that the permittivity of the material starts to increase rapidly and rises severalfold. Similar results were obtained for alloys containing Co and Cr [122, 124, 125]. The (0.2CuSe · 0.8AsSe)1 – x(Cr2Se3)x system, in which CuCr2Se4 ferromagnetic spinel precipitates in the form of the crystalline phase, is of special interest for our study. PUBLISHED RESULTS OF INVESTIGATIONS INTO THE INFLUENCE OF LIGHT ON FUNCTIONAL PROPERTIES OF MAGNETIC SEMICONDUCTORS The investigation performed by Shamoto et al. [126] clearly demonstrated the possibility of observing the photoinduced ferromagnetism. The temperature dependence of the dc resistivity for the Lu2V2O7 compound without laser irradiation can be adequately described by an exponential function with an activation energy of 0.2 eV [126]. Under exposure of the compound to continuous green radiation (λ = 514.5 nm), the temperature dependence of the dc resistivity drastically changes and becomes almost metallic in character with I = 1 and 10 mA at 80 and 110 K, respectively (Fig. 14). Since the resistivity is high even in the metallic range at 50 K (4.2 kΩ cm at 1 mA, 1.4 kΩ cm at 10 mA), it is assumed that only the surface of the sample exposed to light becomes metallic. In this experiment, the number of photons incident on the sample is equal to 2.4 × 1017 photons/s. By assuming that an efficiently irradiated region of the sample has the shape of a cylinder 1.5 mm in radius and 0.1 mm in thickness, i.e., 7.0 × 10–4 mm3 in volume, we find that the number of photons per vanadium atom is approximately equal to 20 photons/s. According to [126], the lifetime τ of excited carriers in the given sample is equal 100 s at temperatures below 100 K. If the local efficiency of electron excitation from the lower Hubbard band to the upper Hubbard band is higher than 0.05%, all electrons of the lower Hubbard band transfer to the upper Hubbard band, resulting in the local metallic state. A change in the lifetime τ can be associated with the local ferromagnetic order, because the scattering rates of conduction electrons in ferromagnetic clusters decrease, as is the case with the Tl2Mn2O7 compound [127]. A similar anomalous behavior of the resistivity was observed in the form of a persistent photoconductivity in semiconductors, such as AlxGa1 – xAs [128]. It was assumed that the mechanism of this phenomenon is associated with the defect formation under laser irradiation. This explains the long lifetime of excited carriers. For the Lu2V2O7 compound (Fig. 14), the long lifetime is more likely due to the transition from the lower Hubbard band to the upper Hubbard band (this transition is

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS 200

100

Resistivity, Ω cm 10000

T, K 50 Unexposed to radiation (I = 1 mA)

102

577

8000

E = 2.54 eV

Resistivity

Unexposed to radiation (I = 10 mA)

6000 514.5 nm (I = 1 mA)

101

4000

E = 2.41 eV

2000

514.5 nm (I = 10 mA)

100 0

5

10

15 20 25 1000/T, K–1

30

35

0

5.0 × 1016 1.5 × 1017 2.5 × 1017 1 × 1017 2 × 1017 Number of photons

Fig. 14. Temperature dependences of the dc resistivity for the Lu2V2O7 compound exposed and unexposed to green laser radiation (E = 2.41 eV) [126].

Fig. 15. Dependences of the resistivity on the number of photons for two types of radiation (E = 2.41, 2.54 eV) at T = 70 K [127].

originally forbidden by the selection rules), even though the existence of lattice defects cannot be ruled out. As can be seen from Fig. 15, the efficiency of decreasing the resistivity under exposure to photons with the energy E = 2.41 eV is 1.5 times higher than that with the energy E = 2.54 eV. The low efficiency is explained by the mixing of the transition from the O 2p orbital to the upper Hubbard band and the transition from the lower Hubbard band to the upper Hubbard band. Furthermore, the higher the photon energy, the larger the expected number of lattice defects. According to Lang and Logan [128], the difference between the efficiencies serves as an additional proof that the above anomaly is caused by the carriers excited from the lower Hubbard band to the upper Hubbard band in ferromagnetic clusters. In this respect, it should be emphasized that the photoinduced transitions are observed at temperatures slightly higher than the Curie temperature TC = 73 K for the Lu2V2O7 compound. However, the authors did not study the influence of laser radiation on the magnetic properties of the material.

of band electrons with magnetic ions. The exchange interaction leads to the formation of magnetic polarons and excitons. The magneto-optical properties of diluted magnetic semiconductors beginning from quasi-twodimensional to zero-dimensional nanostructures were investigated in [129]. Two-dimensional quantum wells, quantum wires, and quantum dots were produced by molecular-beam epitaxy and electron-beam lithography. Special attention was focused on the formation of exciton magnetic polarons and their dynamics. These processes proceed during flip of spins of neighboring magnetic ions, which are optically induced by excitons owing to the exchange interaction. The role of the exciton localization in the formation of exciton magnetic polarons in the CdMnTe semiconductor was discussed in [131, 132]. Recent investigations revealed that exciton magnetic polarons can exist in a free state [133]. The formation of free and localized exciton magnetic polarons is discussed in [129].1

Oka et al. [129] studied the exciton dynamics in quantum wells, quantum dots, and quantum wires of diluted magnetic semiconductors by time-resolved photoluminescence spectroscopy. The exciton photoluminescence data upon resonance excitation of Cd1 – xMnxTe/ZnTe (x = 0.1) quantum wells indicate that magnetic polarons are formed in these objects.

This work was supported by the Russian Foundation for Basic Research, project no. 04-03-33049a.

Diluted magnetic semiconductors are compound semiconductors that involve magnetic ions in cation sites. These materials possess magneto-optical properties, such as the Zeeman effect and Faraday rotation [130]. These properties are associated with the exchange interactions GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

ACKNOWLEDGMENTS

REFERENCES 1. Wolf, S.A., Awschalom, D.D., Buhrman, R.A., Daughton, J.M., von Molnár, S., Roukes, M.L., Chtchelkanova, A.Y., and Treger, D.M., Spintronics: A SpinBased Electronics Vision for the Future, Science (Washington, D.C., 1883–), 2001, vol. 294, pp. 1488–1495. 1 Free

and localized exciton magnetic polarons differ in the lifetime and binding energy.

2005

578

TVER’YANOVICH et al.

2. Semiconductor Spintronics and Quantum Computation, Awschalom, D.D., Loss, D., and Samarth, N., Eds., Berlin: Springer-Verlag, 2002. 3. Ball, P., Meet the Spin Doctors, Nature (London), 2000, vol. 404, p. 918. 4. Awschalom, D.D. and Kikkawa, J. M., Electron Spin and Optical Coherence in Semiconductors, Phys. Today, 1999, vol. 52, no. 6, pp. 33–38. 5. Molnar, S. and Read, D., Magneto-Transport in Magnetic Compound Semiconductors and Metals, J. Magn. Magn. Mater., 2002, vols. 242–245, p. 13. 6. Pearton, S.J., Abernathy, C.R., and Norton, D.P., Hebard, A.F., Park, Y.D., Boatner, L.A., and Budai, J.D., Advances in Wide Band Gap Materials for Semiconductor Spintronics, Mater. Sci. Eng., 2003, vol. 40, p. 137. 7. Pearton, S.J., Abernathy, C.R., Overberg, M.E., Thaler, G.T., Norton, D.P., Theodorpoulou, N., Hebard, A.F., Park, Y.D., Ren, F., Kim, J., and Boatner, L.A., Wide Band Gap Ferromagnetic Semiconductors and Oxides, J. Appl. Phys., 2003, vol. 93, p. 1. 8. Baibich, M.N., Broto, J.M., Fert, A., Nguyen F. Van Dau, and Petroff, F., Giant Magnetoresistance of (00l)Fe/(001)Cr Magnetic Superlattices, Phys. Rev. Lett., 1988, vol. 61, p. 2472. 9. Barnas, J., Fuss, A., Camley, R., Grunberg, P., and Zinn, W., Novel Magnetoresistance Effect in Layered Magnetic Structures: Theory and Experiment, Phys. Rev. B: Condens. Matter., 1990, vol. 42, p. 8110. 10. Datta, S., Das B. Electronic Analog of the Electro-Optic Modulator, Appl. Phys. Lett., 1990, vol. 56, p. 665. 11. Burkard, G., Loss, D., and DiVincenzo, D.P., Coupled Quantum Dots on Quantum Gates, Phys. Rev. B: Condens. Matter., 1999, vol. 59, p. 2070. 12. Semiconductors and Semimetals, vol. 25 of Dilute Magnetic Semiconductors, Furdyna, J.K. and Kossut, J., Eds., Boston: Academic, 1988. 13. Furdyna, J.K., Diluted Magnetic Semiconductors, J. Appl. Phys., 1988, vol. 64, p. 29. 14. Munekata, H., Ohno, H., Von Molnar, S., Segmuller, A., and Chang, L.L., and Esaki, L., Diluted Magnetic III–V Semiconductors, Phys. Rev. Lett., 1989, vol. 63, p. 1849. 15. Ohno, H., Shen, A., Matsukura, F., Oiwa, A., Endo, A., and Iye Y., (Ga,Mn)As: A New Diluted Magnetic Semiconductor Based on GaAs, Appl. Phys. Lett., 1996, vol. 69, p. 363. 16. Ohno, H., Making Nonmagnetic Semiconductors Ferromagnetic, Science (Washington, D.C., 1883–), 1988, vol. 281, p. 951. 17. Ohno, Y., Young, D.K., Beschoten, B., Matsukura, F., Ohno, H., and Awschalom, D.D., Electrical Spin Injection in a Ferromagnetic Semiconductor Heterostructure, Nature (London), 1999, vol. 402, p. 790. 18. Beschoten, B., Crowell, P.A., Malajovich, I., Awschalom, D.D., Matsukura, F., Shen, A., and Ohno, H., Magnetic Circular Dichroism Studies of Carrier-Induced Ferromagnetism in (Ga1 – xMnx)As, Phys. Rev. Lett., 1999, vol. 83, p. 3073. 19. Ohno, H., Chiba, D., Matsukura, F., Omiya, T., Abe, E., Dietl, T., Ohno Y., and Ohtani, K., Electric-Field Con-

trol of Ferromagnetism, Nature (London), 2000, vol. 408. 20. Das Sarma, S., Hwang, E.H., and Kaminski, A., How to Make Semiconductors Ferromagnetic: A First Course on Spintronics, Solid State Commun., 2003, vol. 127, p. 99. 21. Nagaev, E.L., Fizika magnitnykh poluprovodnikov (Physics of Magnetic Semiconductors), Moscow: Nauka, 1979. 22. Nagaev, E.L., Self-Localization of Carriers in Magnetic Semiconductors, Zh. Eksp. Teor. Fiz., 1968, vol. 54, pp. 228–235. 23. Rho, H., Snow, C.S., Cooper, S.L., Fisk, Z., Comment, A., and Ansermet, J.-Ph., Evolution of Magnetic Polarons and Spin–Carrier Interactions through the Metal–Insulator Transition in Eu1 – xGdxO, Phys. Rev. Lett., 2002, vol. 88, no. 12, p. 127401. 24. Torrance, J.B., Shafer, M.W., and McGuire, T.R., Bound Magnetic Polarons and the Insulator–Metal Transition in EuO, Phys. Rev. Lett., 1972, vol. 29, p. 1168. 25. Snow, C.S., Cooper, S.L., Young, D.P., Fisk, Z., Comment, A., and Ansermet, J.-P., Magnetic Polarons and the Metal–Semiconductor Transitions in (Eu,La)B6 and EuO: Raman Scattering Studies, Phys. Rev. B: Condens. Matter., 2001, vol. 64, p. 174 412. 26. Dietl, T., Spin Order Manipulations in Nanostructures of II–VI Ferromagnetic Semiconductors, J. Magn. Magn. Mater., 2004, vols. 272–276, p. 1969. 27. Haury, A., Wasiela, A., Arnoult, A., Cibert, J., Tatarenko, S., Dietl, T., and Merle d’Aubigne, Y., Observation of a Ferromagnetic Transition Induced by Two-Dimensional Hole Gas in Modulation-Doped CdMnTe Quantum Wells, Phys. Rev. Lett., 1997, vol. 79, p. 511. 28. Boukari, H., Kossacki, P., Bertolini, M., Ferrand, D., Cibert, J., Tatarenko, S., Wasiela, A., Gaj, J.A., and Dietl, T., Light and Electric Field Control of Ferromagnetism in Magnetic Quantum Structures, Phys. Rev. Lett., 2002, vol. 88. 29. Kimura, S., Sato, Y., Suzuki, T., and Ikezawa, M., Deep Magnetic Polaron State in Gd2S3, Physica B (Amsterdam), 1995, vols. 206–207, pp. 786–788. 30. Kasuya, T., Mechanism of Anomalies in High TC CuO2 Systems through Magnetic Polaron Condensation, Physica A (Amsterdam), 1999, vol. 312, pp. 239–246. 31. Bednorz, J.G. and Muller, K.A., Possible High T Superconductivity in the Ba–La–Cu–O System, Z. Phys. B: Condens. Matter, 1986, vol. 64, p. 189. 32. Kasuya, T., Bose Condensation and High-TC Superconductivity in La2 – xSrxCuO4, Physica C (Amsterdam), 1994, vol. 223, p. 233. 33. Kasuya, T., Double Layer Effect on Superconductivity in YBa2Cu3O6 + x, Physica C (Amsterdam), 1994, vol. 224, p. 191. 34. Kasuya, T., Physics in Low Carrier Strongly Correlated Systems: Kondo Insulator Magnetic Polaron and High TC, Physica B (Amsterdam), 1995, vol. 215, p. 88. 35. Keimer, B., Belk, N., Birgeneau, R.J., Cassanho, A., Chen, C.Y., Greven, M., and Kastner, M.A., Magnetic Excitations in Pure, Lightly Doped, and Weakly Metal-

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS lic La2CuO4, Phys. Rev. B: Condens. Matter., 1992, vol. 46, p. 14 034. 36. Kasuya, T., Condensation of Magnetic Polarons, J. Phys. Soc. Jpn. Suppl. B, 1996, vol. 65, pp. 78–82. 37. Kohgi, M., Osakabe, T., Kakurai, K., Suzuki, T., Haga, Y., and Kasuya, T., Evidence for a MagneticPolaron State in the Low-Carrier System CeP, Phys. Rev. B: Condens. Matter., 1994, vol. 49, pp. 7068–7073. 38. Tranquada, J.M., Sternlieb, B.J., Axe, J.D., Nakamura, Y., and Uchida, S., Evidence for Stripe Correlations of Spins and Holes in Copper Oxide Superconductors, Nature (London), 1995, vol. 375, pp. 561–563. 39. Norman, M.R., Ding, H., Randeria, M., Campuzano, J.C., Yokoya, T., Takeuchi, T., Takahashi, T., Mochiku, T., Kadowaki, K., Guptasarma, P., and Hinks, D.G., Destruction of the Fermi Surface in Underdoped High-T/Sub C/Superconductors, Nature (London), 1998, vol. 392. 40. Sato, K., Dederichs, P.H., Katayama-Yoshida, H., and Kudrnovsky, J., Magnetic Impurities and Materials Design for Semiconductor Spintronics, Physica B (Amsterdam), vols. 340–342, pp. 863–869. 41. Matsukura, F., Ohno, H., Shen, A., and Sugawara, Y., Transport Properties and Origin of Ferromagnetism in (Ga,Mn)As, Phys. Rev. B: Condens. Matter., 1998, vol. 57, p. 2037. 42. Bertolini, M., Maslana, W., Boukari, H., Gilles, B., Cibert, J., Ferrand, D., Tatarenko, S., Kossacki, P., and Gaj, J.A., New Structures for Carrier-Controlled Ferromagnetism in Cd1 – xMnxTe Quantum Wells, J. Cryst. Growth, 2003, vol. 251, pp. 342–346. 43. Boukari, H., Bertolini, M., Cibert, J., Ferrand, D., Genuist, Y., Tatarenko, S., Kossacki, S., Gaj, J.A., and Dietl, T., Light and Electric Field Control of Ferromagnetism in CdMnTe Based Quantum Wells, Phys. Status Solidi, 2002, vol. 229, p. 737. 44. Boukari, H., Kossacki, P., Bertolini, M., Ferrand, D., Cibert, J., Tatarenko, S., Wasiela, A., Gaj, J.A., and Dietl, T., Light and Electric Field Control of Ferromagnetism in Magnetic Quantum Structures, Phys. Rev. Lett., 2002, vol. 88. 45. Matsukura, F., Chiba, D., Omiya T., Abe, E., Dietl, T., Ohno, Y., Ohtani, K., and Ohno, H., Control of Ferromagnetism in Field-Effect Transistor of a Magnetic Semiconductor, Physica E (Amsterdam), 2002, vol. 12, pp. 351–355. 46. Wolff, P.A., Semiconductors and Semimetals, Diluted Magnetic Semiconductors, New York: Academic, 1988, vol. 25, p. 413. 47. Benoit a la Guillaume, C., Semenov, Y., and Combescot, M., Free Magnetic Polaron: A Nonlinear Hamiltonian Approach, Phys. Rev. B: Condens. Matter., 1995, vol. 51, p. 14124. 48. Takeyama, S., Adachi, S., Takagi, Y., Karczewski, G., Wojtowicz, T., Kossut J., and Karasawa, T., PhotoInduced Magnetic Polarons in Low-Dimensional Dilute Magnetic Semiconductors, Mater. Sci. Eng., B., 1999, vol. 63, pp. 111–118. 49. Yakovlev, D.R., Uraltsev, I.N., Ossau, W., Landwehr, G., Bicknell-Tassius, R.N., Waag, A., and Schmeusser, S., Two-Dimensional Exciton Magnetic GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

579

Polaron in Semimagnetic Quantum Wells, Surf. Sci., 1992, vol. 263, p. 485. 50. Stirner, T., Harrison, P., Hagston, W.E., and Goodwin, J.P., Theoretical Investigation of Observed MagneticPolaron Energies in Quantum Wells, Phys. Rev. B: Condens. Matter., 1994, vol. 50, p. 5713. 51. Kavokin, A.V. and Kavokin, K.V., Theory of TwoDimensional Magnetic Polarons in an External Magnetic Field, Semicond. Sci. Technol., 1993, vol. 8, p. 191. 52. Karpenko, B.V. and Berdyshev, A.A., Exchange Interaction via Current Carriers in Ordered Semiconducting Magnets, Sov. Phys. Solid State, 1964, vol. 5, p. 2494. 53. Nagaev, E.L., Ferromagnetic and Antiferromagnetic Semiconductors, Sov. Phys. Usp, 1975, vol. 18, pp. 863–919. 54. Afanas’ev, M.M., Kompman, M.E., and Merkulov, I.A., Pis’ma Zh. Tekh. Fiz., 1976, vol. 2, pp. 228–233. 55. Lakhno, V.D. and Nagaev, E.L., Nondissipative Photoferromagnetism in Magnetic Semiconductors, Z. Eksp. Teor. Fiz, 1978, vol. 74, pp. 2123–2130. 56. Gopalan, S. and Cottam, M.G., Theory of Surface and Bulk Excitations in Ferromagnetic Semiconductors, Phys. Rev. B: Condens. Matter., 1990, vol. 42, pp. 10 311–10 316. 57. Haas, C., Ferromagnetic Properties of Spinels, Crit. Rev. Solid State Sci., 1970, vol. 1, pp. 47–78. 58. Suski T., Igalson, J., and Story, T., Ferromagnetism of (Pb,Sn,Mn)Te under High Pressure, J. Magn. Magn. Mater., 1987, vol. 66, p. 325. 59. Haury, A., Wasiela, A., Arnoult, A., Cibert, J., Tatarenko, S., Dietl, T., and Merle d’Aubigne, Y., Observation of a Ferromagnetic Transition Induced by Two-Dimensional Hole Gas in Modulation-Doped CdMnTe Quantum Wells, Phys. Rev. Lett., 1997, vol. 79, p. 511. 60. Kossacki, P., Ferrand, D., Arnoult, A., Cibert, J., Tatarenko, S., Wasiela, A., Merle d’Aubigne, Y., Staihli, J.-L., Ganiere, J.-D., Bardyszewski, W., Swiatek, K., Sawicki, M., Wrobel, J., and Dietl, T., Ordered Magnetic Phase in Cd1 – xMnxTe/Cd1 – y – zMgyZnzTe : N Heterostructures: Magnetooptical Studies, Physica E (Amsterdam), 2000, vol. 6, p. 709. 61. Sato, K., Medvedkin, G.A., Nishi, T., Hasegawa, Y., Misawa, R., Hirose, K., and Ishibashi, T., Ferromagnetic Phenomenon Revealed in the Chalcopyrite Semiconductor CdGeP2 : Mn, J. Appl. Phys., 2001, vol. 89, p. 7027. 62. Overberg, M.E., Gila, B.P., Thaler, G.T., Abernathy, C.R., Pearton, S.J., Theodoropoulou, N.A., McCarthy, K.T., Arnason, S.B., Hebard, A.F., Chu, S.N.G., Wilson, R.G., Zavada, J.M., and Park, Y.D., Room Temperature Magnetism in GaMnP Produced by Both Ion Implantation and Molecular-Beam Epitaxy, J. Vac. Technol., B: Microelectron. Nanometer Struct.-Process., Meas., Phenom., 2002, vol. 20, p. 969. 63. Dietl, T., Ohno, H., Matsukura, F., Cubert, J., and Ferrand, D., Zener Model Description of Ferromagnetism in Zinc-Blende Magnetic Semiconductors, Science (Washington, D.C., 1883–), 2000, vol. 287, p. 1019. 64. Dietl, T., Haury, A., and Merle d’Aubigne, Y., Free Carrier-Induced Ferromagnetism in Structures of Diluted 2005

580

TVER’YANOVICH et al.

Magnetic Semiconductors, Phys. Rev. B: Condens. Matter., 1997, vol. 55, p. 3347. 65. Reed, M.L., El-Masry, N.A., Stadelmaier, H., Ritums, M.E., Reed, N.J., Parker, C.A., Roberts, J.C., and Bedair, S.M., Room Temperature Ferromagnetic Properties of (Ga,Mn)N, Appl. Phys. Lett, 2001, vol. 79, p. 3473. 66. Theodoropoulou, N., Hebard, A.F., Overberg, M.E., Abernathy, C.R., Pearton, S.J., Chu, S.N.G., and Wilson, R.G., Magnetic and Structural Properties of MnImplanted GaN, Appl. Phys. Lett, 2001, vol. 78, p. 3475. 67. Sonoda, S., Shimizu, S., Sasaki, T., Yamamoto, Y., and Hori, H., Molecular Beam Epitaxy of Wurtzite (Ga,Mn)N Films on Sapphire(0001) Showing the Ferromagnetic Behaviour at Room Temperature, J. Cryst. Growth, 2002, vols. 237–239, p. 1358. 68. Sasaki, T., Sonoda, S., Yamamoto, Y., Suga, K., Shimizu, S., Kindo, K., and Hori, H., Magnetic and Transport Characteristics on High Curie Temperature Ferromagnet of Mn-Doped GaN, J. Appl. Phys., 2002, vol. 91, p. 7911. 69. Thaler, G.T., Overberg, M.E., Gila, B., Frazier, R., Abernathy, C.R., Pearton, S.J., Lee, J.S., Lee, S.Y., Park, Y.D., Khim, Z.G., Kim, J., and Ren, F., Magnetic Properties of n-GaMnN Thin Films, Appl. Phys. Lett., 2002, vol. 80, p. 3964. 70. Park, H.-J., Lee, Y.C., Cho, S.-Y., Jeong, C.R., and Cho, S., Room-Temperature Ferromagnetism in CrDoped GaN Single Crystals, Appl. Phys. Lett., 2002, vol. 80, p. 4187. 71. Hashimoto, M., Zhou, Y.-K., Kanamura, M., and Asahi, H., High Temperature (>400 K) Ferromagnetism in III–V-Based Diluted Magnetic Semiconductor GaCrN Grown by ECR Molecular-Beam Epitaxy, Solid State Commun., 2002, vol. 122, p. 37. 72. Overberg, M.E., Abernathy, C.R., Pearton, S.J., Theodoropoulou, N.A., McCarthy, K.T., and Hebard, A.F., Indication of Ferromagnetism in Molecular-Beam-Epitaxy-Derived n-Type GaMnN, Appl. Phys. Lett., 2001, vol. 79, p. 1312. 73. Kim, K.H., Lee, K.J., Kim, D.J., Kim, H.J., Ihm, Y.E., Djayaprawira, D., Takahashi, M., Kim, C.S., Kim, C.G., and Yoo, S.H., Magnetotransport of p-Type GaMnN Assisted by Highly Conductive Precipitates, Appl. Phys. Lett., 2003, vol. 82, p. 1775. 74. Dhar, S., Brandt, O., Trampert, A., Daweriz, L., Friendland, K.J., Ploog, K.H., Keller, J., Beschoten B., and Guntherodt, G., Origin of High-Temperature Ferromagnetism in (Ga,Mn)N Layers Grown on 4H–SiC(0001) by Reactive Molecular-Beam Epitaxy, Appl. Phys. Lett., 2003, vol. 82, p. 2077. 75. Katayama-Yoshida, H. and Sato, K., Spin and Charge Control Method of Ternary II–VI and III–V Magnetic Semiconductors for Spintronics: Theory vs. Experiment, J. Phys. Chem. Solids, 2003, vol. 64, pp. 1447– 1452. 76. Warczewski, J. and Krok-Kowalski, J., Magnetic, Electrical, and Structural Properties of Some Ternary and Quaternary Spinels with Chromium, J. Phys. Chem. Solids, 2003, vol. 64, pp. 1609–1614.

77. Lotgering, F.K., Coordination of Cr and Magnetic Properties, in Proceedings of the International Conference on Magnetism, Nottingham, 1964, pp. 533–539. 78. Lotgering, F.K., On the Antiferromagnetism of ZnCr2Se4, Solid State Commun., 1965, vol. 3, p. 347. 79. Kubiak, S., Zarek, W., Drzazga, Z., Krok, J., and Chejkowski, A., Magnetic Properties of the Chalcogenide Spinels CdCr2S4, CdCr2Se4, HgCr2S4, HgCr2Se4, Acta Phys. Pol., A, 1974, vol. 5, p. 819. 80. Krok, J., Spalek, J., Juszczyk, S., and Warczewski, J., Effect of Double Exchange on Magnetic Properties of CuxZn1 – xCr2Se4, Phys. Rev. B: Condens. Matter., 1983, vol. 28, p. 6499. 81. Warczewski, J., Krok-Kowalski, J., Koroleva, L.I., Mydlarz, T., Gilewski, A., and Pacyna, A., Double Exchange Magnetic Interaction and Giant Negative Magnetoresistivity in the Spin Glass State of the New Compound CuCr1.6Sb0.4S4, J. Alloys Compd., 2001, vol. 319, p. 7. 82. Krok-Kowalski, J., Warczewski, J., Gusin, P., Liszkowski, P., Krajewski, K., Koroleva, L.I., Pacyna, A., Mydlarz, T., and Matyjasik, S., Influence of the Sb Concentration onto the Spin Glass State in the Spinel Compounds CuCr2 – xSbxS4, J. Magn. Magn. Mater., 2002, vols. 242–245, pp. 921–923. 83. Krok-Kowalski, J., Warczewski, J., and Nikiforov, K., Correlations of the Magnetic and Electrical Properties with the Ionic Radii of Cations and Anions for the Series of Ternary and Quaternary Spinel-Type Chromium Compounds, J. Alloys Compd., 2001, vol. 315, pp. 62–67. 84. Shannon, R.D., Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides, Acta Crystallogr., Sect. A: Found. Crystallogr., 1976, vol. 32, p. 751. 85. Tang, J.K., Li, L., Saxena, S.S., Puri, A., Falster, A.U., and Simons, W.B., The Effects of Arsenic Doping on the Magnetic Properties of CuCr2Se4, IEEE Trans. Magn., 1994, vol. 30, p. 4972. 86. Baran, M., Szymczak, R., Szymczak, H., and Tsurkan, V., Spin Glass Like Behavior of Magnetization in Anion Substituted CuCr2Se4 Magnetic Semiconductor, J. Magn. Magn. Mater., 1995, vols. 140–144, p. 2043. 87. Krupicka, S. and Novak, P., Oxide Spinels, in Ferromagnetic Materials, Amsterdam: North-Holland, 1982, pp. 189–304. 88. Van Stapele, R.P., Sulphospinel, in Ferromagnetic Materials, Amsterdam: North-Holland, 1982, pp. 603– 745. 89. Okonska-Kozlowska, I., Kopyczok, J., Lutz, H.D., and Stingl, T., Single-Crystal Structure Refinement of Spinel-Type CuCr2Se4, Acta Crystallogr., Sect. C: Struct. Commun., 1993, vol. 49, p. 1448. 90. Colominas, C., Neutron-Diffraction Investigation of CuCr2Se4 and CuCr2Te4, Phys. Rev., 1967, vol. 153, p. 558. 91. Robbins, M., Lehmann, H.W., and White, J.G., Neutron Diffraction and Electrical Transport Properties of CuCr2Se4, J. Phys. Chem. Solids, 1967, vol. 28, p. 897. 92. Kanomata, T., Ido, H., and Kaneko, T., Effect of Pressure on Curie Temperature of Chalcogenide Spinels

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005

EFFECT OF LIGHT ON THE MAGNETIC PROPERTIES OF SEMICONDUCTORS CuCr2X4 (X = S, Se, and Te), J. Phys. Soc. Jpn., 1970, vol. 29, pp. 332. 93. Nakatani, L., Nose, H., and Masumoto, K.H., J. Jpn. Inst. Metal., 1977, vol. 41, p. 939. 94. Okonska-Kozlowska, I., Krok, J., and Anorg, Z., Formation of Crystalline Solid Solution in System Zn1 − xCuxCr2Se4, Z. Anorg. Allg. Chem., 1978, vol. 447, p. 235. 95. Goodenough, J.B., Tetrahedral-Site Copper in Chalcogenide Spinels, Solid State Commun., 1967, vol. 5, p. 577. 96. Lotgering, F.K. and van Stapele, R.P., Magnetic Properties and Electrical Conduction of Copper-Containing Sulfo- and Selenospinels, J. Appl. Phys., 1968, vol. 39, p. 417. 97. Ogata, F., Hamajima, T., Kambara, T., and Gondara, K., The Spin-Polarised Electronic Band Structure of Chromium Spinels: II. CuCr2Se4 and CuCr2Te4, J. Phys. C: Solid State Phys., 1982, vol. 15, p. 3483. 98. Winiarski, A., Okonska-Kozlowska, I., Heimann, J., and Neumann, M., Investigation of CuxGayCrzSe4 Single Crystals, J. Alloys Comp., 1996, vol. 232, p. 63. 99. Belov, K.P., Koroleva, L.I., Shalimova, M.A., and Batorova, S.D., Some Peculiarities of Electric and Magnetic Properties of Cd1 – xCuxCr2Se4, Sov. Phys. Solid State, 1975, vol. 17, p. 197. 100. Rodic, D., Antic, B., Tellgren, R., Rundlof, H., and Blanusa, J., A Change of Magnetic Moment of Cr Ion with the Magnetic Phase Transition in CuCr2Se4, J. Magn. Magn. Mater., 1998, vol. 187, pp. 88–92. 101. Bhattacharjee, A.K. and Benoit a La Guillaume, C., Exciton Magnetic Polaron in Semimagnetic Semiconductor Nanocrystals, Phys. Rev. B: Condens. Matter., 1997, vol. 55, no. 16, p. 10613. 102. Wang, Y. and Herron, N., Nanometer-Sized Semiconductor Clusters: Materials Synthesis, Quantum Size Effects, and Photophysical, J. Phys. Chem., 1991, vol. 95, p. 525. 103. Murray, C.B., Norris, D.J., and Bawendi, M.G., Synthesis and Characterization of Nearly Monodisperse CdE (E = S, Se,Te) Semiconductor, J. Am. Chem. Soc., 1993, vol. 115, p. 8706. 104. Norris, D.J., Sacra, A., Murray, C.B., and Bawendi, M.G., Measurement of the Size Dependent Hole Spectrum in CdSe Quantum Dots, Phys. Rev. Lett., 1994, vol. 72, p. 1994. 105. Benoit a la Guillaume, C., Exciton Magnetic Polaron in Semimagnetic Semiconductor Nanocrystals, in Proceedings of the XXII International Conference on Physics of Semiconductors, Vancouver, 1994, p. 2585. 106. Golnik, A., Ginter, J., and Gaj, J.A., Magnetic Polarons in Exciton Luminescence of Cd1 – xMnxTe, J. Phys. C: Solid State Phys., 1983, vol. 16, p. 6073. 107. Akinaga, H., Takita, K., Sasaki, S., Takeyama, S., Miura, N., Nakayama, T., Minami, F., and Inoue, K., Optical Properties and Dynamical Behavior of Localized and Bound Excitons in Cd1 – xMnxTe (x = 0.04) Grown by Molecular-Beam Epitaxy, Phys. Rev. B: Condens. Matter., 1992, vol. 46, p. 13 136. 108. Mackh, G., Ossau, W., Yakovlev, D.R., Waag, A., Landwehr, G., Hellmann, R., and Gobel, E.O., Localized GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

581

Exciton Magnetic Polarons in Cd1 – xMnxTe, Phys. Rev. B: Condens. Matter., 1994, vol. 49, p. 10 248. 109. Yakovlev, D.R., Ossau, W., Landwehr, G., BicknellTassius, R.N., Waag, A., Schmeusser, S., and Uraltsev, I.N., Two Dimensional Exciton Magnetic Polaron in Cd1 – xMnxTe Quantum Well Structures, Solid State Commun., 1992, vol. 82, p. 29. 110. Mackh, G., Ossau, W., Yakovlev, D.R., Hellmann, R., Gobel, E.O., Wojtowicz, T., Karczewski, G., Kossut, J., and Landwehr, G., Two Dimensional Exciton Magnetic Polaron in CdTe/Cd1 – xMnxTe Quantum Well Structures, in Proceedings of the International Conference on Semiconductor Heteroepitaxy, Montpellier, 1995, p. 210. 111. Nhung Tran Hong and Planel, R., Quantitative Measurements of Magnetic Polaron Binding on Acceptors in CdMnTe Alloys, Physica A (Amsterdam), 1983, vols. 117–118, p. 488. 112. Bhattacharjee, A.K., Planel, R., and Benoit a la Guillaume, C., Nanocrystals of Diluted Magnetic Semiconductors, in Proceedings of the XVII International Conference on Physics of Semiconductors, San Francisco, 1984, p. 1431. 113. Nhung Tran Hong, Planel, R., Benoit a la Guillaume, C., and Bhattacharjee, A.K., Acceptor-Bound Magnetic Polaron in Cd1 – xMnxTe Semimagnetic Semiconductors, Phys. Rev. B: Condens. Matter., 1985, vol. 31, p. 2388. 114. Warnock, J. and Wolff, P.A., Spherical Model of Acceptor-Associated Bound Magnetic Polarons, Phys. Rev. B: Condens. Matter., 1985, vol. 31, p. 6579. 115. Heiman, D., Warnock, J., Wolff, P.A., Kershaw, R., Ridgley, D., Dwight, K., and Wold, A., Polarized Photoluminescence from Bound Magnetic Polarons in (Cd,Mn) Se, Solid State Commun., 1984, vol. 52, p. 909. 116. Scalbert, D., Nawrocki, M., Benoit a la Guillaume, C., and Cernogora, J., Anisotropy of Magnetic Polarons Bound to Acceptors in Sd1 – xMnxSe, Phys. Rev. B: Condens. Matter., 1986, vol. 33, p. 4418. 117. Bhattacharjee, A.K., Crystal-Field Model for AcceptorAssociated Bound Magnetic Polarons in Wurtzite Semiconductors, Phys. Rev. A: Condens. Matter., 1987, vol. 35, p. 9108. 118. Wang, Y., Herron, N., Moller, K., and Bein, T., ThreeDimensionally Confined Diluted Magnetic Semiconductor Clusters: Zn1 – xMnxS, Solid State Commun., 1991, vol. 77, p. 33. 119. Bhargava, R.N., Gallagher, D., Hong, X., and Nurmikko, A., Optical Properties of Manganese-Doped Nanocrystals of ZnS, Phys. Rev. Lett., 1994, vol. 72, p. 416. 120. Yanata, K., Suzuki, K., and Oka, Y., Magneto-Optical Studies on Cd1 – xMnxSe Quantum Dots, Jpn. J. Appl. Phys., Suppl., 1995, vol. 34-1, p. 164. 121. Maksimov, A.A., Bacher, G., McDonald, A., Kulakovskii, V.D., and Forchel, A., Magnetic Polarons in a Single Diluted Magnetic Semiconductor Quantum Dot, Phys. Rev. B: Condens. Matter., 2000, vol. 62, p. 7767. 122. Tver’yanovich, Yu.S. and Gutenev, M.S., Magnetokhimiya stekloobraznykh poluprovodnikov (Magne2005

582

TVER’YANOVICH et al. tochemistry of Vitreous Semiconductors), St. Petersburg: St. Petersburg Gos. Univ., 1997.

123. Tver’yanovich, Y.S. and Borisova, Z.U., On the Doping of Chalcogenide Glassy Semiconductors, J. Non-Cryst. Solids, 1987, vol. 90, nos. 1–3, pp. 405–412. 124. Gutenev, M.S., Tver’yanovich, Yu.S., Krasil’nikova, A.P., and Kochemirovskii, V.A., Dielectric Spectroscopy of Chalcogenide Glasses Doped with Transition Metals, Fiz. Khim. Stekla, 1989, vol. 15, no. 1, pp. 84–90. 125. Tver’yanovich, Yu.S., Gutenev, M.S., and Borisova, Z.U., Microinhomogeneity of Sb19Ge22Se59 Glass Doped with Cobalt, Neorg. Mater., 1987, vol. 23, no. 10, pp. 1749–1750. 126. Shamoto, S., Tazawa, H., Ono, Y., Nakano, T., Nozue, Y., and Kajitani, T., Light-Induced Metal–Insulator Transition in Lu2V2O7, J. Phys. Chem. Solids, 2001, vol. 62, pp. 325–329. 127. Shimakawa, Y., Kubo, Y., and Manako, T., Giant Magnetoresistance in Tl2Mn2O7 with the Pyrochlore Structure, Nature (London), 1996, vol. 379, p. 53.

128. Lang, D.V. and Logan, R.A., Large-Lattice-Relaxation Model for Persistent Photoconductivity in Compound Semiconductors, Phys. Rev. Lett., 1977, vol. 39, p. 635. 129. Oka, Y., Shen, J., Takabayashi, K., Takahashi, N., Mitsu, H., Souma, I., and Pittini, R., Dynamics of Excitonic Magnetic Polarons in Nanostructure Diluted Magnetic Semiconductors, J. Lumin., 1999, vols. 83–84, pp. 83–89. 130. Furdyna, J.K. and Kossut, J., Semiconductors and Semimetals, in Diluted Magnetic Semiconductors, New York: Academic, 1988, vol. 25. 131. Mackh, G., Ossau, W., Yakovlev, D.R., Waag, A., Landwehr, G., Hellmann, R., and Gobel, E.O., Localized Exciton Magnetic Polarons in Cd1 – xMnxTe, Phys. Rev. B: Condens. Matter, 1994, vol. 49, p. 10248. 132. Mackh, G., Ossau, W., Yakovlev, D.R., Waag, A., Litz, T., and Landwehr, G., Exciton Magnetic Polarons in Semimagnetic Quantum Wells with Nonmagnetic and Semimagnetic Barriers, Solid State Commun., 1993, vol. 88, p. 221. 133. Miao, J., Stirner, T., and Hagston W.E., Magnetic Localization of Free Exciton Magnetic Polarons in Diluted Magnetic Semiconductors, J. Appl. Phys., 1997, vol. 81, p. 6297.

GLASS PHYSICS AND CHEMISTRY

Vol. 31

No. 5

2005