Appl Phys A (2009) 96: 893–898 DOI 10.1007/s00339-009-5315-y

Terahertz spectroscopy of central and soft phonon modes in LuFe2 O4 S.Z. Li · S.J. Luo · R. Fu · B.B. Jin · K.F. Wang · J.-M. Liu · J.F. Ding · X.G. Li

Received: 17 March 2009 / Accepted: 18 June 2009 / Published online: 9 July 2009 © Springer-Verlag 2009

Abstract The terahertz dielectric response of LuFe2 O4 is investigated by terahertz time-domain spectroscopy over a temperature range of 6–290 K. It is revealed that besides the central mode associated with the charge-ordered state, a soft TO1 mode at below ∼240 K is identified indicating the existence of displacing ferroelectricity, in addition to the chargeordering-induced ferroelectricity at below 320 K. The anomaly of the soft mode at ∼180 K reflects the magnetoelectric correlation between the soft TO1 mode and the spin/charge fluctuations revealed recently. Finally, the magnetic property at below ∼240 K is discussed. PACS 75.80.+q · 77.55.+f 1 Introduction In recent years, enormous progress in the field of multiferroicity has been made. The invention of new magnetoelectric (ME) materials, which simultaneously possess at least S.Z. Li · S.J. Luo · K.F. Wang · J.-M. Liu () Nanjing National Laboratory of Microstructure, Nanjing University, Nanjing 210093, China e-mail: [email protected] S.Z. Li · S.J. Luo · K.F. Wang · J.-M. Liu International Center for Materials Physics, Chinese Academy of Sciences, Shenyang, China R. Fu · B.B. Jin Department of Electric Science and Engineering, Nanjing University, Nanjing 210093, China J.F. Ding · X.G. Li Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei 230026, China

two orders among ferroelectric (FE), ferromagnetic (FM) (or antiferromagnetic [AFM]), and ferroelastic order parameters, has provoked this field [1, 2]. The potential applications include multiple-state memories, magnetic sensing, and electric field controlled FM resonance with magnetically modulated piezoelectricity [3, 4]. LuFe2 O4 (LFO), a candidate with high-temperature multiferroicity, has a hexagonal layered structure in which Fe sites are crystallographically equivalent [5]. It undergoes a three-dimensional charge ordering (CO) at below 320 K, and the Fe2+ /Fe3+ superstructure due to the charge ordering ensues resulting in the typical disorder-order (OD) type ferroelectricity [6]. LFO also has a two-dimensional ferrimagnetic (FIM) order at below 250 K, as revealed by neutron scattering and Mössbauer spectroscopy [6–8], which is accompanied with a significant spin/charge fluctuations at T ≈ 175 K [9]. The stacking faults of Fe–O layers results in the deviation of local magnetic order from the FIM state. However, no more spin structure fluctuation at T < 175 K is observed. The correlation between the anomalous dielectric and CO behaviors of LFO was also comprehensively investigated. Yet the nature of the CO sequence remains controversy, it is generally believed that the CO state is accompanied with lattice distortions [10]. By analogy with the robust long-range order of Ising spin in a triangular lattice antiferromagnet, a model CO structure in which the two triangular sheets of a W layer (i.e., a Fe2 O4 layer) do not have the same number of Fe2+ and Fe3+ ions, i.e., [Fe2+ ]:[Fe3+ ] = 1:2 in one triangular sheet, and √ 2:1√in another triangular sheet, was proposed [7]. The 3 × 3 superstructure of this CO model is compatible with experimental observation [7]. However, a different approach to the CO structure in which one triangular sheet of W layer has only Fe2+ ions and the other triangular sheet has only Fe3+ ions, was claimed, too [11]. First-

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principle calculations revealed almost equal stability for the two different types of CO structures, referring to the Fe2 O4 layers in LFO [12]. Furthermore, for ferroelectricity generation, the calculated spontaneous polarization along the caxis is 52.7 µC/cm2 , while measured polarization at below ∼320 K is ∼20 µC/cm2 and jumps up to ∼25 µC/cm2 at ∼240 K [7]. Although the OD-type ferroelectricity has been well recognized on one side, no reproducible data have been reported in other experiment so far. Therefore, it seems that the nature of ferroelectricity in LFO is still under debate. The issue to be addressed is that the ferroelectricity in LFO does exist or not. Furthermore, we know little about the origin of polarization jump at ∼240 K and possible ME effect between electric polarization and spin configuration if any. To go ahead, it is of interest to measure the dielectric spectroscopy, i.e., the response of the low-frequency phonon modes by terahertz time-domain spectroscopy (THz-TDS), in order to reveal the possible soft TO1 mode (SM) and central mode (CM). The THz-TDS has been employed to investigate multiferrroics, such as TbMnO3 , Eu1−x Yx MnO3 , and BiFeO3 , as well as ME coupling inside them [13–15]. It was also applied to study the phonon modes of SrTiO3 and BaTiO3 and other materials [16–18]. Since LFO is a relevant ME compound without rare earth magnetism, while the FIM ordering occurs at ∼240 K (TFIM ), the polarization jumps occur also near TFIM suggesting a possible ME coupling [6]. However, a microscopic understanding of this coupling is insufficient, while the THz-TDS may provide useful clue to the origin of ferroelectricity and ME coupling in LFO. In this work, we report our THz-TDS measurement on the dielectric property of LFO. In particular, we reveal the existence of the lowest TO1 mode over a broad T -range, which allows us a comprehensive understanding of the ferroelectricity origin and possible ME coupling.

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with magnetic field. The sample for measurement is a disk of 0.4 mm in thickness and 1.0 cm in diameter. In order to understand the ME coupling, we also evaluated the magnetism using superconducting quantum interference device system (SQUID, Quantum Design Inc.).

3 Results and discussions 3.1 Structural and transport characterization Figure 1 shows a unit cell structure of LuFe2 O4 , clearly illustrating the layers of Fe2 O4 alternating with layers of Lu3+ ions. There are three Fe2 O4 layers (W layer) per unit cell. As shown in Fig. 2a, the XRD spectrum indicates that LFO sample is rhombohedral with space group R-3m, without any impurity phase. The evaluated lattice parameters are a = 3.43 Å and c = 25.27 Å, consistent with earlier reports [19]. Figure 2b shows the room temperature selectedarea electron diffraction patterns obtained along the [120] zone axis. The space group R-3m assignment is confirmed by the bright fundamental diffraction spots satisfying the reflection condition: −h + k + l = 3n (n is an integer). As indicated by the arrows, the clean satellite reflections are visible and confirm the three-dimensional (3D) charge-order pattern which does exist at room temperature, and is further affirmed by the dark-field image displaying clearly the stripe-like lamella domains, as shown in Fig. 2c. Because the charge ordering is the origin of ferroelectricity [20], these stripe domains are also ferroelectric [5, 19, 21]. The charge-ordering transition at ∼320 K can be further confirmed by the measured ρ–T data within T = 200– 400 K, shown in Fig. 2d. While a semiconductor-like behavior (dρ/dT < 0) is observed over the whole T -range, the Fig. 1 A hexagonal unit cell structural model of LuFe2 O4

2 Experimental details Polycrystalline LuFe2 O4 pellets were prepared by thoroughly mixing high-purity Lu2 O3 (99.9%), Fe2 O3 (99.99%), and Fe metal powder (Alfa, 99.99%) in a stoichiometric ratio. The pelletized samples were sintered in an evacuated quartz tube at 1100◦ C for 48 h. Here the reactive sintering was employed to obtain densely sintered pellets [8]. The sample crystallinity was confirmed by the θ –2θ X-ray diffraction and transmission electron microscopy (TEM). The TEM investigations were performed on a JEM4000 electric microscope, and the samples were prepared by mechanical polishing and Ar ion milling at room temperature. The T dependent resistivity ρ was probed by the physical property measurement system (PPMS, Quantum Design Inc.). The dielectric property was measured by a home-made THzTDS covering 6–300 K, but unfortunately not facilitated

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Fig. 2 (a) an XRD θ –2θ scan, (b) [120] zone-axis selected-area electrons diffraction pattern, and (c) dark-field image of LuFe2 O4 at room temperature. The superlattice reflection spots in (c) are indicated by arrows. (d) Measured ρ–T curve

high-T data (T = 320–400 K) and low-T data (T = 220– 320 K) allow different activation energies, due to the charge ordering at ∼320 K. The charge-ordered state has reasonably higher activation energy for electron transport than the charge-disordered state. Nevertheless, no significant change of the transport behavior across the 2D FIM transition at T ≈ 240 K is observed [22]. 3.2 THz-TDS It is well known that the pulsed nature of the THz radiation allows one to probe short-life carriers in order to examine the corresponding temporal evolution of the conductivity and to study the dielectric constant through the refractive index. Figure 3a shows the THz pulse waves before and after inserting the sample at various temperatures. A monocycle electromagnetic pulse is observed at around t = 0 before the sample insertion. The THz pulse wave, after the sample insertion at around t ≈ 3 ps, is the first pulse that passes directly through the sample. The amplitude decreases and the phase changes due to the reflection and absorption by the sample. The pulse shape becomes sharp with decreasing temperature until T ≈ 180 K, beyond which the amplitude

increases with decreasing T . At low T , the second and third pulses due to the internal reflection are clearly observed at around 12 and 18 ps. With the THz-TDS data, we can evaluate the conductivity of LFO from the Drude model and its generalizations. The Drude model treats the conduction electrons as free charges to move under an electric field but subject to a collisional damping force. However, this model can be modified in an analogy with the ‘Cole–Cole’ (CC) model or ‘Cole–Davidson’ (CD) one for liquids, upon the symmetric and asymmetric distributions of relaxation times. Here, we employ the single-component Drude conductivity which is expressed as σ (ω) = ε0 · ωp2 /(τ −1 − iω), where ωp is the plasma frequency defined as ωp = Nc e2 /ε0 m∗ and Nc is the number density of carriers, e is the electron charge, m∗ is the effective carrier, mass and τ is the average collision time. The Drude model shows a free-carrier absorption, which can not fit the conductivity data of LFO. In fact, the real part of conductivity σ increases with frequency, as shown in Fig. 3b, which does not coincide with the Drude model. These inconsistencies together with the structural and transport data allow us to argue that LFO may be a ferroelectric

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Fig. 4 Frequency dependence of (a) real part ε  and (b) imaginary part ε  of the dielectric constant of LuFe2 O4 at various T by THz-TDS

Fig. 3 (a) Measured THz pulse waveforms before and after the sample insertion at various temperatures, (b) real part of conductivity σ (ω) at different temperatures

material, although more data, such as optical conductivity, are still required. 3.3 Dielectric spectroscopy To further clarify the origin of ferroelectricity, in particular the origin of polarization jump at ∼240 K, we explore the dielectric response in the THz range. The measured dielectric constants (real part ε  and imaginary part ε  ) as a function of frequency ω at various T are presented in Figs. 4a and 4b, respectively. These data are evaluated from the TDS data using the standard procedure [23, 24]. It is shown that over the whole T -range, ε  (ω) in the low-ω regions shows linear but steep increase with reducing ω. This behavior remains nearly T -independent. In the high-ω region, a broad ε  (ω) peak is observed at low T , whose shape and position are strongly T -dependent. Correspondingly, ε  (ω) at various T also exhibit two peaks in the two regions.

Clearly, the two features have different sources which may be associated with ferroelectric mode dispersions. Usually, ferroelectric transitions can be classified into either the OD type or displacing type. Far away from the transition point, some phonon softening appears and then ceases when the transition point is approached. Meanwhile, additional relaxation appears and usually contributes substantially to the permittivity maximal. Such a relaxation is often called the CM in analogy to inelastic scattering experiments. In this case, the ferroelectric transition is usually referred as a crossover transition from the displacing type to the OD type [25]. For the OD type, the phonon frequency, defined by the ε  (ω) peak location in the low-ω region, is only weakly T -dependent corresponding to an excitation of the relaxation type, i.e., the CM [18], characterized by the steep increasing ε  (ω) with reducing ω. For the displacing type, a soft TO1 mode with the phonon frequency decreasing rapidly (i.e., redshift) at T → TC , the FE transition point, would be observed, which is a signature of the SM. This corresponds to the ε  (ω) peak in the high-ω region, which is strongly T -dependent. The THz data in Fig. 3 show the coexistence of both CM and SM in LuFe2 O4 at low T . In fact, such coexistence was identified in a number of ferroelectrics [18, 25]. This coexistence in LuFe2 O4 allows us to argue that the ferroelectricity has contributions not only from the charge ordering initiating at ∼320 K but also from the displacing mechanism (SM softening) initiating at ∼240 K. The charge-order-induced polarization was already recognized in early work [6, 20], and the corresponding CM remains active at below ∼320 K, as revealed in Fig. 3. No strong T -dependence and anomaly of this mode were observed. We then focus on the SM dynamics over the whole T -range and its relevance with the magnetic orderings. First, upon increasing T from the low-T side, the TO1 mode shows a significant softening (redshift) and nearly disappears at T ∼ 240 K, the point at which the measured po-

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larization jumps. This suggests a displacing-type ferroelectric transition at T ≈ 240 K, contributing to the polarization jump. This argument will be further evidenced below. Second, at T < 240 K, the ε(ω) profile of the TO1 mode shows a distinct Lorentzian behavior. A combination of the ε  (ω) and ε  (ω) data allows a highly reliable fitting of the dispersion. As it is well known [26], the TO1 mode can be described by the soft-phonon frequency ωTO , damping factor γTO , and dielectric strength ε1 , following the classical damped oscillator dispersion model: ε  (ω) = ε(∞) + ε1 ε  (ω) = ε1

2 (ω2 − ω2 ) ωTO TO 2 − ω2 )2 + ω2 γ 2 (ωTO TO

2 ωγTO ωTO 2 − ω2 )2 + ω2 γ 2 (ωTO TO

where ε(∞) is the high-frequency permittivity. The fitted ωTO and γTO as functions of T , respectively, are plotted in Fig. 5a. If the peak anomalies of these parameters are ignored, to be discussed below, one sees that damping factor γTO decreases slowly with increasing T , indicating the gradual softening of the TO1 mode upon T close to T ≈ 240 K. This softening is evidenced by the decreasing characteristic frequency ωTO with increasing T until T ≈ 240 K at which the mode peak becomes disappeared. It should be mentioned that the measured ωTO does not truly go to zero (ωTO → 0) before the peak disappears, due to the frequency limit and uncertainty background of our THz-TDS. Therefore, the displacing-type ferroelectric transition does occur at T ≈ 240 K. Now, we explore the origin of peak anomalies of ωTO and γTO at T ≈ 180 K. Recent work on LuFe2 O4 revealed that the spin structure exhibits significant fluctuations due to the stacking faults of Fe–O layers at ∼180 K [9, 27, 28]. This stacking fault sequence also matches with the charge fluctuations. The anomalies of ωTO and γTO at T ≈ 180 K seem to be attributed to the ME coupling between the soft TO1 mode and the spin/charge fluctuations in the FIM configuration. On the one hand, we understand that the dielectric anomaly is associated with the spin fluctuations because the dielectric response has an essential contribution from the spin–phonon coupling, which, for example, can be expressed as a linear term proportional to Si · Sj  where Si is the spin moment at site i and Sj is its neighbor [29]. On the other hand, the TO1 soft mode is mainly attributed to the vibration of combined Fe and O ions in the lattice, thus it is natural to expect the variations of ωTO and γTO in response to the charge/spin fluctuations in the lattice at T ≈ 180 K. 3.4 Magnetic behaviors Finally, we came to investigate the magnetic behavior of LuFe2 O4 and Fig. 5b shows the measured magnetization

Fig. 5 (a) T -dependences of ωTO and γTO with uncertainty bars for the TO1 soft mode, and (b) magnetization M under the FC and ZFC conditions for LuFe2 O4 . The inset in (b) shows the dM/dT data of the ZFC curve

(M) under zero-field cooled (ZFC) and field cooling (FC) conditions. The measuring field is 1000 Oe. For the ZFC case, M is small at low T and increases steadily with increasing T up to 200 K, beyond which is a sharp transition peak at ∼230 K. Afterwards M falls rapidly down to almost zero. The transition point determined by the dM/dT curve is T ≈ 230 K, as shown in the inset of Fig. 5b. This behavior is roughly consistent with the FIM transition from the paramagnetic charge-order state at TFIM ∼ 240 K. In contrast, the measured M under the FC condition begins to increase at TFIM and then increase linearly with decreasing T . It is interesting to note that the FC curve does not separate from the ZFC curve until ∼230 K, below which the ZFC curve goes down to nearly zero at low T , while the FC curve goes up linearly. Therefore, at low T , LuFe2 O4 seems to exhibit a spin-glass like behavior. Although the separation between the FC and ZFC curves at low T would not be a unique hallmark of a spin-glass state, there should exist some short-

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ranged magnetic clusters consistent with earlier identification of a spin-glass-like 2D magnetic ordering at ∼240 K [30]. It should be reminded that the FIM transition (∼240 K) is consistent with the point at which the TO1 mode disappears implying the ME coupling between the spin order and the displacing-type ferroelectric order in LuFe2 O4 . This issue is worthy of further investigations.

4 Conclusion In summary, we have performed the THz-TDS investigation of the phonon modes in LuFe2 O4 . The free-carrier conduction cannot be fitted by the Drude model. It has been revealed that besides the central mode associated with the charge-ordered state, a TO1 soft mode appears at below ∼240 K, which is argued to be responsible for the polarization jump at ∼240 K in addition to the charge-orderinginduced polarization at ∼320 K. This soft mode has an abnormal response to the spin/charge fluctuations at ∼180 K. We have discussed several aspects of the ME coupling in LuFe2 O4 by presenting the one-to-one correspondence between the dynamics of the soft mode and the magnetic behaviors. Acknowledgements The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (50832002 and 50832007), the National Key Program for Basic Researches of China (2009CB929501 and 2009CB623303), the Program for New Century Excellent Talents in University (2007CB310404), and the Jiangsu Natural Science Foundation of China (BK2008024).

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