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Spectroscopic studies of the ferroelectric and magnetic phase transitions in multiferroic Sr1−x Ba x MnO3
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 28 (2016) 175901 (7pp)
doi:10.1088/0953-8984/28/17/175901
Spectroscopic studies of the ferroelectric and magnetic phase transitions in multiferroic Sr1−xBaxMnO3 V Goian1, F Kadlec1, C Kadlec1, B Dabrowski2, S Kolesnik2, O Chmaissem2, D Nuzhnyy1, M Kempa1, V Bovtun1, M Savinov1, J Hejtmánek1, J Prokleška3 and S Kamba1 1
Institute of Physics, The Czech Academy of Sciences, Na Slovance 2,182 21 Prague, Czech Republic Department of Physics, Northern Illinois University, DeKalb, IL, USA 3 Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 12116 Prague 2, Czech Republic 2
E-mail:
[email protected] Received 11 January 2016 Accepted for publication 29 February 2016 Published 29 March 2016 Abstract
Dielectric response of perovskite Sr1−xBaxMnO3 (x = 0.43 and 0.45) ceramics was investigated using microwave, THz and infrared spectroscopic techniques in order to study the ferroelectric and antiferromagnetic phase transitions with critical temperatures TC ≈ 350 K and TN ≈ 200 K, respectively. The two lowest-frequency polar phonons are overdamped above TN and they exhibit pronounced softening on heating towards TC. Nevertheless, permittivity ε′ in the THz range shows only a small anomaly at TC because the phonon contribution to ε′ is rather small. The phonons are coupled with a central mode which provides the main contribution to the dielectric anomaly at TC. Thus, the ferroelectric phase transition has characteristics of a crossover from displacive to order–disorder type. At the same time, the intrinsic THz central peak is partially screened by conductivity and related Maxwell–Wagner relaxation, which dominates the microwave and lower-frequency spectra. Below TN, the ferroelectric distortion markedly decreases, which has an influence on the frequencies of both the central and soft modes. Therefore, ε′ in the THz range increases at TN on cooling. In spite of the strong spin–phonon coupling near TN, surprisingly no magnetodielectric effect was observed in the THz spectra upon applying magnetic field of up to 7 T, which is in contradiction with the theoretically expected huge magnetoelectric coupling. We explain this fact as due to the insensitivity of TN to magnetic field. Keywords: multiferroics, soft and central modes, phonons, magnetoelectric effect, spin-phonon effect S Online supplementary data available from stacks.iop.org/JPhysCM/28/175901/mmedia (Some figures may appear in colour only in the online journal)
1. Introduction
are very promising candidates for advanced applications in electric-field controlled magnetic memories, spintronics and magnonics [1]. Unfortunately, multiferroics are rather rare in nature, and their magnetoelectric coupling is frequently found to be weak. The scarcity of multiferroics is usually explained by the fact that the transition-metal d electrons, which are
The search for new multiferroics with large room-temper ature magnetoelectric coupling is at the forefront of material scientists’ and physicists’ interests, because compounds that exhibit simultaneous ferroelectric and magnetic ordering 0953-8984/16/175901+7$33.00
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(IR) spectroscopy and inelastic x-ray scattering; they published spectra obtained upon cooling below room temperature. These showed phonon anomalies near TN due to spin-phonon coupling, and revealed a pronounced softening of the lowestfrequency phonon with increasing Ba concentration. Based on this fact, the authors assigned the ferroelectric phase transition to the displacive type. The main aim of this paper is to extend the existing knowledge about the lattice dynamics of Sr1−xBaxMnO3 by studying ferroelectric compounds (x > 0.4) as a function of temperature, including temperatures around TC ≈ 350 K, and by applying external magnetic field; to our knowledge, such studies have not been reported yet. As for the ferroelectric properties, we show that the materials exhibit a crossover character with features of both displacive and order-disorder phase-transition types, because, as TC is approached, a central mode (CM) contributes more to low-frequency permittivity ε′ than phonons. Concerning the magnetoelectric behavior, we demonstrate that the THz dielectric spectra are independent of external magnetic field of up to 7 T; we explain this by the insensitivity of TN with respect to magnetic field.
essential for magnetism, reduce the tendency to an off-center ferroelectric distortion [2]. For this reason, type-I multiferroics like BiFeO3 or YMnO3 contain ferroelectrically active cations (Bi, Y, etc) that are different from the magnetically active ones (Fe, Mn, etc) and, therefore, their magnetoelectric coupling is quite small [3]. A strong magnetoelectric coupling occurs mainly in type-II multiferroics, where the ferroelectric polarization is induced by special spin ordering. At the same time, in contrast to most of the type-I materials, their critical temper atures are frequently lower than 100 K and the values of their spontaneous ferroelectric polarization are two to four orders of magnitude smaller than in canonical ferroelectrics [4]. In the last few years, several theoretical papers suggested that a large ferroelectric polarization can occur in perovskitestructured AMnO3 compounds (A = Ba, Sr, Ca) owing to offcentering of magnetic Mn4+ ions stabilized via a charge-lattice coupling of the Peierls type [5–7]. Consequently, the magnetoelectric coupling should be strong; however, to date, such a behavior has not yet been demonstrated; this has various reasons. As for non-mixed bulk crystals, BaMnO3 with perovskite structure is unstable at ambient conditions in which only the non-ferroelectric hexagonal phase can be synthesized. Perovskite SrMnO3 and CaMnO3 are paraelectric and antiferromagnetic at low temperatures, respectively; for them, it was theoretically predicted that ferroelectricity should occur only under epitaxial strains [5, 7]. Owing to strong spin-phonon coupling confirmed in these materials [8, 9], strained AMnO3 thin films should become simultaneously ferromagnetic and ferroelectric at temperatures above 100 K and they should display a giant magnetoelectric coupling [5, 7]. However, the required epitaxial strain is rather high (more than 3–5%), which is probably the reason why strain-induced ferroelectricity and ferromagnetism have not been confirmed in AMnO3 thin films to date. Only very recently, a report was published about breaking of space center symmetry in a SrMnO3 thin film induced by a tensile strain of 1.7% (the polar structure was revealed only using second harmonic generation, which does not provide the possibility to detect polarization switching), but the work did not deal with its magnetic or magnetoelectric properties [10]. Another promising possibility of creating lattice strain is offered by mixed compounds. Sakai et al [11] studied Sr1−xBaxMnO3 crystals with 0.45 ⩽ x ⩽ 0.50 where substitution of Sr ions by larger Ba induces a negative chemical pres sure; they observed ferroelectricity below 410 K. According to their results, the ferroelectric phase has a tetragonal crystal structure (space group P4mm) with quite a large tetragonal distortion (c/a = 1.013) near 300 K. X-ray diffraction revealed the broken spatial symmetry to be due to displacements of the Mn4+ cations, in agreement with the theoretical predictions. Near TN = 200 K, the system undergoes a phase transition to a G-type antiferromagnetic phase and the tetragonal distortion together with the ferroelectric polarization drastically reduce by ~70%. For this reason, a giant magnetoelectric coupling is expected [11] in Sr1−xBaxMnO3; nevertheless, its measurements were not reported up to now, probably due to leakage conductivity in this system. Sakai et al [11, 12] also investigated phonons in non-ferroelectric Sr1−xBaxMnO3 (0 ⩽ x ⩽ 0.4) crystals using infrared
2. Experimental details Polycrystalline samples of perovskite Sr1−xBaxMnO3 (x = 0.43 and 0.45) were synthesized using a two-step solidstate method [11, 13, 14], which is required to avoid the more stable hexagonal polymorph and to remain in the pseudocubic arrangement where the ferroelectric order exists. First, hexagonal precursor materials were synthesized in flowing H2/Ar gas at temperatures near 1300 °C to obtain singlephase oxygen-reduced perovskite samples. Then, these were annealed in oxygen at 350 °C, resulting in the oxygen stoichiometry of 3.00 ± 0.002, as verified by precise thermogravimetric measurements. The sample density was higher than 95%. Sr1−xBaxMnO3 samples with x = 0.43 and 0.45 exhibit ferroelectric properties with a tetragonal noncentrosymmetric P4mm crystal structure at room temperature. Since the oxygen stoichiometry will somewhat change during high-temperature THz and IR measurements (performed in vacuum), the samples were first investigated below room temperature and only then measured on heating above 300 K. Dielectric measurements in the high-frequency range (1 MHz–1.8 GHz) were performed using a computer-controlled dielectric spectrometer equipped with a HP 4291B impedance analyzer, a Novocontrol BDS 2100 coaxial sample cell, and a Sigma System M18 temperature chamber. Time-domain THz spectroscopic experiments were performed by measuring the complex sample transmission using two custom-made spectrometers utilizing Ti:sapphire femtosecond lasers [15]; one with an Oxford Instruments Optistat cryostat used for measurements without magnetic fields, and another with an Oxford Instruments Spectromag cryostat enabling measurements with external magnetic field Hext ⩽ 7 T. Here, the Voigt configuration was used with the electric component of the THz radiation ETHz set perpendicularly to Hext where a stronger effect is expected. Additionally, 2
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a control measurement with ETHz||Hext was performed at 170 K. Reference measurements with an empty aperture, enabling a reliable determination of the transmittance, were performed systematically at each value of the applied magnetic field. The detection was based on electro-optic sampling with a 1 mm thick [1 1 0] ZnTe crystal as a sensor which allowed us to measure the time profiles of the electric field of the transmitted THz pulses [15]. A plane-parallel sample plate with a diameter of 6 mm and thickness of 38 μm was used for the measurements. Since the room-temperature THz spectra changed slightly after high-temperature measurements in vacuum, the sample was annealed in an oxygen atmosphere (575 K, 10 h) before the low-temperature THz studies with external magnetic field were performed. Near-normal-incidence IR reflectivity spectra were measured using a Fourier-transform IR spectrometer Bruker IFS 113v. An Oxford Instruments Optistat optical cryostat was used for measurements between 10 and 300 K. The frequency range of the low-temperature IR measurements was limited by the transparency of the used polyethylene windows (up to 650 cm−1), whereas the measurements above room temper ature were performed up to 3000 cm−1. At high temperatures, two deuterated triglycine sulfate detectors were used. At low temperatures, a liquid-He-cooled Si bolometer operating at 1.6 K served as a far-IR detector. Figure 1. Temperature dependence of the dielectric permittivity and conductivity of Sr1−xBaxMnO3 (x = 0.45) plotted at selected frequencies between 1 MHz and 1.8 GHz. The tiny anomaly near 320 K is an instrumental artifact.
3. Results and discussion 3.1. Temperature-dependent broadband spectroscopy
temperatures, the reflection bands become undulated due to the lowering of crystal symmetry and phonon splitting. The IR reflectivity and THz complex permittivity spectra ε*(ω) were simultaneously fit assuming the factorized form of the dielectric function based on a generalized dampedharmonic-oscillator model:
In the MHz region, high values of the dielectric-permittivity ε′ of the Sr1−xBaxMnO3 (x = 0.45) sample were obtained with a strong frequency dependence (see figure 1) due to a relatively high conductivity and the resulting Maxwell–Wagner (M–W) polarization [16]. Qualitatively the same behavior was observed for the x = 0.40 and 0.43 samples. According to the phase diagram published in [11, 14], the ferroelectric phase transition should occur between 300 and 400 K; nevertheless, no significant anomaly related to this transition was observed. The expected dielectric anomaly at TC is probably screened by the M–W relaxation. The low-frequency (100 Hz–1 MHz) conductivity strongly decreases on cooling below 100 K and reaches values of 10−9–10−7 Scm−1 at 20 K but the M–W relaxation still remarkably contributes to ε′ (see figures S1 and S4 in supplemental material (stacks.iop.org/ JPhysCM/28/175901/mmedia))4. Consequently, the influence of the M–W relaxation decreases on cooling and, below 50 K, an almost temperature independent ε′(T ) ≈ 350 is observed at 1 MHz (figure S1). In contrast, ε′(T ) at lower frequencies remains temperature dependent (figures S1 and S2). The influence of conductivity on the dielectric permittivity strongly decreases with increasing frequency [8]. Taking advantage of this observation, we have performed THz and IR spectroscopic measurements. IR reflectivity spectra show three broad and asymmetric bands (see figure 2). At lower
n ω 2 − ω 2 + iωγ LOj LOj ε∗(ω ) = ε∞ ∏ 2 , (1) 2 ω − ω + ωγ i j = 1 TOj TOj
where ωTOj and ωLOj are the frequencies of the jth transverse optical and longitudinal optical phonons, γTOj and γLOj are the corresponding damping constants, and ε∞ denotes the highfrequency (electronic) contribution to the permittivity determined from the room-temperature frequency-independent reflectivity above the phonon frequencies. The reflectivity R(ω) is related to the complex dielectric function ε*(ω) by: 2
ε*(ω ) − 1 R(ω ) = . (2) ε*(ω ) + 1
The temperature dependence of phonon frequencies is plotted in figure 3. Spectra of ε*(ω) calculated using the fit parameters are shown in figure 4 together with the exper imental THz data. Phonon modes below 150 cm−1 have damping constants γTOj higher than the frequencies ωTOj, i.e. they are overdamped (see all phonon parameters in table S1— suppl. materials)4. In this situation, precise ωTOj values cannot
4
See supplemental material at stacks.iop.org/JPhysCM/28/175901/mmedia for additional experimental details and figures. 3
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Figure 3. Temperature dependence of the phonon frequencies in Sr0.55Ba0.45MnO3 ceramics obtained from the fits of IR and THz spectra. The area corresponding to the ferroelectric phase transition (TC) interval is hatched, and the vertical dashed line denotes the Néel temperature TN. Note the two changes in the frequency scale. The mode below 10 cm−1 is the CM.
Figure 2. Solid lines: IR reflectivity spectra of Sr0.55Ba0.45MnO3
ceramics taken at selected temperatures. Symbols: reflectivity calculated from the spectra of the complex refractive index in the THz range. Dashed lines: spectra obtained from the fits.
be unambiguously determined and only the relaxation frequencies ω R =
ω2TOj γTOj
mentioned above. Thus, our results extend the previous studies by Sakai et al [11, 12] who, based on their observations of the soft mode, assumed that the ferroelectric phase transition in Sr1−xBaxMnO3 crystals was a displacive one. It should be noted that Sakai et al did not report IR spectra of ferroelectric compounds (i.e. x > 0.4); their conclusions were based only on observations of phonon softening with increasing Ba concentration in paraelectric Sr1−xBaxMnO3 (i.e. x ⩽ 0.3) below room temperature. In a sample with x = 0.3, Sakai et al observed overdamping of the soft mode above TN, so it is natural that our samples with x ⩾ 0.4 exhibit an overdamped soft mode in a broader temperature region. Let us also note that the values of ε′ at TC are rather low for displacive phase transitions. One could argue that the low-frequency ε′(T ) can attain much higher values due to the existence of a CM below the THz region, but at the frequency of 1.8 GHz, despite the fact that ε′(T ) remains significantly influenced by the conductivity, it exhibits values of at most 600, see figure 1. Surprisingly, there is no distinct maximum in ε′ at TC, although the behavior of the soft and CMs is reminiscent of the canonical ferroelectric BaTiO3 where the soft optical mode frequency exhibits only a shallow minimum at TC and a strong low-frequency dielectric anomaly is caused by a soft CM [20]. The smaller dielectric anomaly in Sr1−xBaxMnO3 could be caused by electronic polarization, as predicted in [21, 22], while the anomalies in canonical insulating ferroelectrics arise mainly from cationic displacements.
, corresponding to the optical conductivity
maxima, are physically meaningful [17]. A single soft optical mode is resolved in the paraelectric phase above 375 K. The phonon softens on cooling towards TC (ca. 350–375 K) and splits in two at TC. Both these modes harden down to TN and then a dramatic change occurs: below TN, the lower-frequency component drops sharply and becomes underdamped, while the higher-frequency one stiffens by almost 80 cm−1. On further cooling, the lower-frequency soft mode continues to harden. Note the existence of an overdamped mode below 10 cm−1 (see figures 3 and 4). A similar mode is known in many ferroelectrics [17–19] as the CM and it reveals the dynamical disorder of the crystal lattice. CMs are usually seen close to ferroelectric phase transitions where a crossover from displacive to order-disorder phase transition type occurs. In our case, the CM is seen at all temperatures. We suppose that above TC, the CM expresses a dynamical disorder of the Mn cations among eight equivalent positions whereas below TC, it is a manifestation of vibrations of the ferroelectric domain walls. Its dielectric strength and damping decrease on cooling, which is clearly seen in the ε*(ω) spectra, figure 4. Above room temperature, the CM makes a major contribution to the static permittivity, which is also in agreement with the order-disorder character of the ferroelectric phase transition. The behavior of the soft and CMs gives evidence of the crossover from displacive to order-disorder phase type transition 4
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Figure 5. Temperature dependences of THz permittivity in Sr1−xBaxMnO3, x = 0.43 and 0.45 taken at selected frequencies. Note 1 THz = 33.4 cm−1.
seven IR-active modes (3 A1 and 4 E symmetries) are allowed [23]. Indeed, we observe two new modes activating below TC and one additional mode appears below TN, bringing the total number of the observed phonons at low temperatures to seven. Thus, we can conclude that the number of observed polar phonons corresponds to the cubic Fm3 m structure in the paraelectric phase and to the tetragonal P4mm symmetry in the ferroelectric phase. In contrast to the spectra of ε*(ω) in the MHz and GHz range shown in figure 1, the IR and THz spectra of Sr1−xBaxMnO3 are very little influenced by the conductivity. Consequently, intrinsic low-frequency values of ε′ can be determined from the sum of the phonon and CM contributions to ε′. In figure 5, we present ε′(T ) measured at frequencies of 10 and 15 cm−1. In both studied samples, ε′ steps up near TN due to spinphonon coupling and then it remains nearly constant down to 10 K. This jump in ε′ cannot be due to the sample conductivity which decreases on cooling. Instead, it is completely caused by softening of the lowest-frequency phonon near TN (see figure 3). Above room temperature, ε′(T) exhibits a weak and broad peak near 400 K, which is apparently linked to the ferroelectric phase transition. Unfortunately, the conductivity increases with temperature, which may partially influence the shape of the ε′(T ) maximum and the actual value of TC is probably somewhat lower than the position of the peak in ε′(T ). The shape of ε′(T ) is similar for Sr1−xBaxMnO3 ceramics with both x = 0.43 and 0.45. The positions of the peaks below 400 K differ slightly, which is in agreement with the value of TC being slightly lower for x = 0.43 than for x = 0.45, as shown by the phase diagram published in [11, 14]. We also measured x-ray diffraction in our ceramics using synchrotron radiation which has revealed lattice anomalies near TC and TN (see figure S6). The values of ε′ at TC are rather low for displacive phase transitions. Comparable increases in ε′(T ) are seen near TN and TC as shown in figure 5. It is known from theoretical calculations that the force driving the ferroelectric distortion comes from the tendency of empty Mn eg states to establish a stronger covalency with the surrounding O p orbitals [6]. By contrast,
Figure 4. Complex dielectric permittivity spectra (lines) calculated using parameters obtained from the fits of IR reflectivity and THz permittivity spectra. Experimental THz data are marked by symbols.
One could assume that our IR and THz data can be influenced by porosity or conductivity of the studied ceramics. Nevertheless, our samples are highly dense (more than 95%) and our calculation of phonon parameters using the effective medium approximation (Bruggeman model) did not reveal any significant influence of a porosity of up to 10% on the phonon parameters (see table S1 in supplemental mat erial)4. Also the conductivity has a negligible influence on the THz and IR spectra, since only a small increase in the THz permittivity and far IR reflectivity was observed on heating. Nevertheless, we observed an increase in the room-temper ature THz permittivity and in losses after heating in vacuum to 475 K and subsequent cooling to 300 K (see figure S7). This was most probably caused by creation of oxygen vacancies in ceramics, enhancement of conductivity and the related M–W relaxation, which enhances the contribution to the intrinsic CM. The influence of M–W relaxation disappeared after a subsequent sample annealing in an oxygen atmosphere (573 K, 10 h), following which the sample became stoichiometric again. Next, let us discuss the number of observed polar phonons in our spectra. In the cubic paraelectric phase, the Pm3 m and Fm3 m crystal structures allow three and four polar phonons with the F1u symmetry, respectively [23]. We observed four modes above TC, which supports the Fm3 m crystal structure due to local chemical ordering of Sr and Ba cations. Below TC, in the ferroelectric tetragonal phase (P4mm space group), 5
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Figure 7. Temperature dependence of the magnetic susceptibility measured at two values of magnetic field. The inset shows the temperature derivatives of susceptibility; the peak corresponds to the Néel temperature TN. The low-field data are noisier; nevertheless, they show that TN does not depend on the magnetic field.
effects gives evidence that the G-type AFM structure of Sr1−xBaxMnO3 and its Néel transition temperature are independent of the external magnetic field up to at least 7 T. This is a surprising result because a huge magnetoelectric effect was predicted as a consequence of the large change in the ferroelectric distortion at TN and based on the assumption that both magnetization and polarization originate from the same Mn cations. Direct magnetic susceptibility measurements (see figure 7) confirm these results indicating the robustness of the G-type AFM structure in magnetic field. One can speculate that the magnetoelectric effect is absent, because the real magnetic structure of ferroelectric Sr1−xBaxMnO3 is antiferromagnetic while the theory [7] predicted a huge magnetoelectric coupling in a hypothetical ferroelectric ferromagnet (i.e. tensile strained SrMnO3 films). It seems that a large magnetoelectric effect can be expected mainly in multiferroics whose magnetic structure is highly sensitive to the magnetic field, such as spin-order induced multiferroics [4]. Most of these materials have low critical temperatures, but there are examples of multiferroics exhibiting both ferroelectric and magnetic ordering temperatures above 300 K [24] together with a pronounced room-temperature magnetoelectric effect, as observed in Z-type hexaferrite [25].
Figure 6. THz complex dielectric spectra of Sr0.55Ba0.45MnO3 ceramics measured around TN at 0 T (solid lines) and 7 T (dashed lines). The weak peak between 12 and 15 cm−1 is a feature which appeared after sample annealing.
the half-filled Mn t2g orbitals give rise to magnetic ordering [21, 22] which reduces the ionic off-center displacement and its contribution to the polarization. Consequently, upon cooling below TN, the lowest-frequency phonon softens and therefore ε′ increases. 3.2. THz spectroscopy in external magnetic field
Since ε′ strongly changes at TN due to spin-phonon coupling, a large magnetoelectric and magnetodielectric coupling is expected near TN. Unfortunately, a direct measurement of the magnetoelectric coupling near TN in Sr1−xBaxMnO3 is difficult due to high electric leakage above 100 K. However, this shortcoming could be overcome by measuring the magnetodi ∂ε′ electric effect ∂H in the THz region at TN and in its vicinity. The spectra of ε*(ω) measured at 0 and 7 T are shown in figure 6. Within our experimental accuracy, no changes in ε*(ω) with the applied magnetic field were observed at and near TN in either of the variants of the Voigt geometry. Influence of the magnetic field on the behavior of ε′(T ) at 1 kHz could only be investigated below 100 K because, above this temperature, the low-frequency ε′ exhibits giant values due to M–W relaxation. Changes in ε′ of less than 1% were detected (see figure S5) but these are caused mainly by magnetoresistance which influences the electrical conductivity and the low-frequency ε′(T) even below 50 K. The absence of intrinsic magnetodielectric
( )
4. Conclusions In conclusion, the ferroelectric phase transition in Sr1−xBaxMnO3 displays a crossover from the displacive type to the order-disorder one. The optical soft mode softens on heating towards TC but its dielectric strength is quite small, so the observed dielectric anomaly in the THz region is rather low. The CM in the microwave region is the main mechanism 6
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[7] Lee J H and Rabe K M 2010 Phys. Rev. Lett. 104 207204 [8] Kamba S et al 2014 Phys. Rev. B 89 064308 [9] Goian V, Kamba S, Borodavka F, Nuzhnyy D, Savinov M and Belik A A 2015 J. Appl. Phys. 117 164103 [10] Becher C et al 2015 Nat. Nanotechnol. 10 661 [11] Sakai H et al 2011 Phys. Rev. Lett. 107 137601 [12] Sakai H, Fujioka J, Fukuda T, Bahramy M S, Okuyama D, Arita R, Arima T, Baron A Q R, Taguchi Y and Tokura Y 2012 Phys. Rev. B 86 104407 [13] Dabrowski B, Chmaissem O, Mais J, Kolesnik S, Jorgensen J D and Short S 2003 J. Solid State Chem. 170 154 [14] Pratt D K, Lynn J W, Mais J, Chmaissem O, Brown D E, Kolesnik S and Dabrowski B 2014 Phys. Rev. B 90 140401 [15] Kužel P, Němec H, Kadlec F and Kadlec C 2010 Opt. Express 18 15338 [16] Lunkenheimer P, Krohns S, Riegg S, Ebbinghaus S G, Reller A and Loidl A 2010 Eur. Phys. J. Spec. Top. 180 61 [17] Petzelt J, Kozlov G V and Volkov A A 1987 Ferroelectrics 73 101 [18] Buixaderas E, Kamba S and Petzelt J 2004 Ferroelectrics 308 131 [19] Goian V, Kamba S, Orloff N, Birol T, Lee C H, Nuzhnyy D, Booth J C, Bernhagen M, Uecker R and Schlom D G 2014 Phys. Rev. B 90 174105 [20] Nuzhnyy D, Petzelt J, Savinov M, Ostapchuk T, Bovtun V, Kempa M, Hlinka J, Buscaglia V, Buscaglia M T and Nanni P 2012 Phys. Rev. B 86 014106 [21] Giovannetti G, Kumar S, Ortix C, Capone M and van den Brink J 2012 Phys. Rev. Lett. 109 107601 [22] Nourafkan R, Kotliar G and Tremblay A M S 2014 Phys. Rev. B 90 220405 [23] Hlinka J, Petzelt J, Kamba S, Noujni D and Ostapchuk T 2006 Phase Trans. 79 41 [24] Kimura T 2012 Annu. Rev. Condens. Matter Phys. 3 93 [25] Chun S H et al 2012 Phys. Rev. Lett. 108 177201
driving the phase transition near TC. Below TN, THz-range ε′(T) markedly increases upon cooling due to reduced ferroelectric distortion and related softening of the lowestfrequency phonon. No changes in the THz ε*(ω) spectra with magnetic field of up to 7 T were observed. This is in contradiction to the expected huge magnetoelectric effect in these compounds. We explain this by a high stability of the magn etic structure and the Néel temperature against the external magnetic field. Therefore, we consider the search for a strong magnetoelectric effect as promising in spin-order induced ferroelectrics whose magnetic structure is highly sensitive to magnetic field. Acknowledgments This work was supported within the program of Czech Research Infrastructures, Project LM2011025, by the Czech Science Foundation, Projects 14—14122P, 15—08389S and by KONTAKT II project LH 15122. References [1] Matsukura F, Tokura Y, and Ohno H 2015 Nat. Nanotechnol. 10 209 [2] Hill N 2000 J. Phys. Chem. B 104 6694 [3] Khomskii D 2009 Physics 2 20 [4] Tokura Y, Seki S and Nagaosa N 2014 Rep. Prog. Phys. 77 076501 [5] Bhattacharjee S, Bousquet E and Ghosez P 2009 Phys. Rev. Lett. 102 117602 [6] Rondinelli J M, Eidelson A S, and Spaldin N A 2009 Phys. Rev. B 79 205119
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