Polar phonon mixing in magnetoelectric EuTiO 3

Transcription

1 Eur. Phys. J. B (2009) DOI: /epjb/e Regular Article THE EUROPEAN PHYSICAL JOURNAL B Polar phonon mixing in magnetoelectric EuTiO 3 V. Goian 1,S.Kamba 1,a, J. Hlinka 1,P.Vaněk 1, A.A. Belik 2,T.Kolodiazhnyi 3, and J. Petzelt 1 1 Institute of Physics, ASCR, v.v.i. Na Slovance 2, Prague 8, Czech Republic 2 International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki, Japan 3 Optronic Materials Center (OMC), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki, Japan Received 27 February 2009 / Received in final form 30 April 2009 Published online 16 June 2009 c EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009 Abstract. Infrared reflectivity spectra of antiferromagnetic incipient ferroelectric EuTiO 3 were investigated up to 600 K. Three polar phonons typical for the cubic perovskite Pm 3m structure were observed. Analysis of phonon plasma frequencies showed that the lowest-energy TO1 phonon corresponds predominantly to the Slater mode describing vibration of Ti cations against the oxygen octahedra and the TO2 phonon expresses vibrations of the Eu cation against the TiO 6 octahedra. The highest frequency TO4 phonon represents O-octahedra bending. Incipient ferroelectric behavior of the permittivity is caused by pronounced softening of the TO1 phonon, which is coupled to the TO2 mode. Although the Eu cations are not involved in the TO1 mode, the spin ordering of the 4f electrons at Eu cations has influence on the frequency of the TO1 mode due to Eu-O-Eu super-exchange interaction. This is probably responsible for the 7% change of the permittivity induced by the magnetic field in the antiferromagnetic phase, as reported by Katsufuji and Takagi [Phys. Rev. B 64, (2001)]. PACS j Infrared and Raman spectra d Dielectric properties of solids and liquids q Magnetomechanical and magnetoelectric effects, magnetostriction 1 Introduction The coupling between static electrical and magnetic properties observed in magnetoelectric materials is an interesting effect both from the view-point of fundamental physics as well as for potential application in multistatememory elements [1,2] Unfortunately, most of the magnetoelectrics exhibit small magnetoelectric effect, which cannot be used in applications. Nevertheless, recently new multiferroics with giant magnetoelectric effect were discovered (e.g. TbMnO 3,TbMn 2 O 5 )[3 5], allowing a rotation of polarization with the external magnetic field B, because the ferroelectric polarization in these materials is induced by incommensurate spin spiral ordering and therefore the polarization is strongly coupled with magnetization. Such effect was successfully explained by antisymmetric Dzyaloshinskii-Moriya interaction [2]. Change of polarization is closely related to change of permittivity ε with magnetic field (magnetocapacitive effect), which reaches up to several hundreds percents in such materials [3,4]. In classical multiferroics, where the ferroelectric order is not induced by Dzyaloshinskii-Moriya interaction, the magnetocapacitive effect is usually very small, not exceeding 1%. Higher magnetocapacitive effect was oba kamba@fzu.cz served only in slightly conducting materials, where the combination of Maxwell-Wagner polarization and magnetoresistence is responsible for the change of measured extrinsic ε with B [6,7]. Unusually high 7%-change of ε with B was observed also in EuTiO 3 crystal, which is not multiferroic neither conducting below 80 K [8]. It is an incipient ferroelectric with a G-type antiferromagnetic (AFM) structure below 5.3 K [9]. It crystallizes in the cubic perovskite structure with Pm 3m space group [10 12], which does not change down to the lowest measured temperature of 2 K. Its ε increases on cooling and saturates below 30 K [8]. Below T N =5.3 K,ε drops down, but its value remarkably increases with applied B and at B > 1 T acquires values even higher than in the paramagnetic phase [8,13]. Far-infrared (FIR) reflectivity studies of EuTiO 3 ceramics (not fully dense) explained the temperature dependence of ε in the paramagnetic phase by a drop of the lowest TO1 phonon frequency on cooling [13] (ferroelectric soft mode SM) which saturates below 30 K due to quantum fluctuations. How is the measured quasistatic ε related to the IR spectra? The jth polar phonon contributes additively to the static permittivity by Δε j so that the static permittivity is ε(0) = Δε j + ε,whereε denotes the high frequency permittivity resulting from electronic absorption processes. Moreover, a general summation rule for phonon

2 2 The European Physical Journal B Fig. 1. (Color online) Eigen-displacements (normal coordinates) of (a) Slater, (b) Last and (c) Axe zone-centre polar modes in cubic perovskites. Gray, blue and red balls mark perovskite A-site ions, B-site ions and oxygens, respectively (after Ref. [15]). plasma frequencies Ω Pj = Δε j ω TOj holds (here ω TOj marks transverse phonon frequency of the jth phonon), requiring the sum of Ω 2 Pj to be temperature independent and in the case of uncoupled phonons even each Ω Pj should be temperature independent. It means that each change of phonon frequency ω TOj should be accompanied by a change of Δε j and hence ε(0). IR studies in reference [13] really confirmed, that the observed temperature dependence of quasistatic permittivity is due to softening of the lowest frequency phonon on cooling. If the temperature and magnetic field dependence of ε in the AFM phase of EuTiO 3 is fully due to a change of SM frequency, one could expect a decrease of the SM frequency by 7 cm 1 with the applied B [14]. Unfortunately, our recent FIR studies with magnetic field were not able to see it due to high signal losses in the magnetic cryostat [13]. It is well known that three polar phonons of F 1u symmetry are infrared (IR) active in Pm 3m perovskite structure [15]. Their eigenvectors are schematically shown in Figure 1. So called Slater mode describes vibration of Ti 4+ cations against the oxygen octahedra, so called Last mode expresses a vibration of Eu 2+ cations against the TiO 6 octahedra and the highest-frequency Axe phonon represents bending of the O-octahedra [15]. What is the eigenvector of the SM in EuTiO 3? IR spectrum and dielectric properties of EuTiO 3 are similar to the classical incipient ferroelectric SrTiO 3, in which the SM corresponds very well to the Slater mode [15]. On other hand, in lead-based perovskites (like PbTiO 3 ) the displacement of lead is mainly responsible for the ferroelectric polarization, i.e. SM is the Last vibration [15]. What about EuTiO 3? Does the SM include mainly Eu vibrations (Last mode) which could allow us to understand the sensitivity of SM to the orientation of localized spins in the 4f levels of Eu 2+ cations, or does the SM eigenvector consist mainly of Ti vibrations (Slater mode) which would be more responsible for the incipient ferroelectric properties? The answer to these questions will be the subject of this paper. 2 Experiment The EuTiO 3 powder (its preparation was described elsewhere [13]) was loaded into Au capsules and sintered in a belt-type high-temperature high-pressure furnace at Fig. 2. (Color online) IR reflectivity spectra of EuTiO 3 ceramics at selected temperatures. (1 cm 1 =30GHz). 900 C under pressure of 6 GPa for 30 min. Room temperature X-ray diffraction confirmed the resulting cubic perovskite phase with less than 3% of pyrochlore Eu 2 Ti 2 O 7 phase. Density of the ceramics was more than 95%. The unpolarized IR reflectance spectra were taken using a Bruker IFS 113v FTIR spectrometer at temperatures between 10 and 600 K with the resolution of 2 cm 1. An Optistat Oxford Instruments continuous-flow helium cryostat equipped with polyethylene windows was used for cooling the sample down to 10 K, while a commercial high-temperature cell Specac P/N 5850 was used for heating it up to 600 K (the sample start to decompose above 600 K). A helium-cooled Si bolometer operating at 1.6 K wasusedasadetectorforlow-temperature measurements, while a pyroelectric DTGS detector was used above room temperature. 3 Results and discussion Previous low-temperature IR reflectivity studies [13] were performed on low-density (91%) ceramics with 5% of pyrochlore phase. The porosity caused parasitic diffuse scattering of the reflected IR beam (rising with frequency), which deteriorated the reflectance above 200 cm 1.Therefore it was not possible to evaluate accurately the parameters of higher-frequency phonons. Hence we repeated the FIR measurements with our new high dense sample and extended the studied temperature range up to 600 K. In Figure 2 the corresponding IR spectra are shown at selected temperatures. Increase of reflectivity on cooling can be seen due to a decreasing phonon damping as well as a shift of the edge of the first reflectivity band (SM) to lower frequencies. The three broad reflection bands correspond to 3F 1u modes permitted in the Pm 3m cubic structure of EuTiO 3. Additional reflection band near 430 cm 1 seen at low temperatures could be a trace of the pyrochlore phase. The complex permittivity ε (ω) =ε (ω) iε (ω) is related to reflectivity R by the well-known formula 2 ε (ω) 1 R(ω) =. (1) ε (ω)+1

3 V. Goian et al.: Polar phonon mixing in magnetoelectric EuTiO 3 3 Fig. 4. (Color online) Temperature dependences of the two lowest-frequency phonon frequencies. Temperature dependence of the previously published [13] SM frequency in less dense ceramics is added for comparison. Fig. 3. (Color online) Real (a) and imaginary, (b) components of the complex dielectric function calculated from the IR spectra fits at different temperatures. Inset (c) shows the temperature dependence of static permittivity obtained from the phonon contributions to ε. For the fit of reflectivity, we used a generalizedoscillator model with the factorized form of the complex permittivity ε (ω) =ε j ω 2 LOj ω2 + iωγ LOj ω 2 TOj ω2 + iωγ TOj (2) where ω TOj and ω LOj is the transverse and longitudinal frequency of the jth polar phonon, respectively, and γ TOj and γ LOj is their respective damping constant. Complex permittivity obtained from the reflectivity fit is shown in Figure 3. The maxima in ε (ω) roughly correspond to ω TOj. They are numbered in Figure 3 and TO3 is missing, because it is (in analogy with other simple cubic perovskites) the silent mode. It can be seen from Figure 3b that mainly the lowest-frequency TO1 phonon softens on cooling. Dielectric contribution Δε j of the jth mode to static permittivity can be calculated by Δε j = ε (ωlok 2 ω2 TOj ) k ωtoj 2 (ωtok 2 (3) ω2 TOj ). k j Static ε (T ) obtained from the IR reflectivity fits shows a clear incipient ferroelectric behavior in the whole temperature range up to 600 K (see inset of Fig. 3). Unfortunately, ε (T ) cannot be properly measured at low frequencies (below 1 MHz) above 80 K due to partial conductivity arising possibly from oxygen defects and small concentration of Eu 3+ from the secondary pyrochlore phase. Nevertheless, the low-temperature value of ε is only slightly lower than that measured on a single crystal [8]. This can be caused by the 5% porosity of our ceramics. Note that twice lower value of ε was reported for the 80% dense ceramics [13]. Temperature dependences of the soft TO1 and TO2 mode frequencies are plotted in Figure 4. One can see that the SM frequencies in ceramics of two different densities are the same within the accuracy limits of our measurements. The SM should obey the Cochran law ω SM (T )= A(T T c ) (4) in the classical paraelectric state [16]. Our fit gives the following parameters: A =(27.06 ± 0.8) cm 2 K 1 and T c =( ± 15.4) K. The latter parameter is the extrapolated critical temperature T c whichitisinourcase negative. At low temperatures the quantum fluctuations prevent the phonon softening and therefore the SM frequency saturates (as well as ε (T )) and the Cochran law is no more satisfied below 100 K. In this case it is more appropriate to use the Barrett formula [17] T 1 ω SM (T )= A [( ) ( ) ] T1 T1 coth T 0. (5) 2 2T marks the temperature below which quantum fluctuations become important and critical temperature T 0 has the same meaning as T c in the Cochran law. Our fit in Figure 5 gives the following parameters: A = (27.45 ± 1.3) cm 2 K 1, T 1 = (154.6 ± 9.8) K and T 0 = ( 170±29.3) K. One can see that T 0 is very close to T c.it is also important to note that the SM frequency increases on heating and reaches nearly the TO2 mode frequency near 600 K, therefore one could expect a coupling of both modesasdiscussedbelow. In the following part we will determine which atom vibration takes part in each polar mode. For this purpose we calculated the mode-plasma frequencies Ω Pj for all the modes and plotted their temperature dependence

4 4 The European Physical Journal B Fig. 5. (Color online) Temperature dependence of modeplasma frequencies of the soft Slater type TO1 mode (black squares), the Last type TO2 mode (red stars) and the Axe TO4 mode (green triangles) obtained from the IR reflectivity fits of EuTiO 3 ceramics. in Figure 5. The plasma frequencies are proportional to the mode effective charges which quantify the macroscopic electric response of a crystal to displacements of its atoms. Note that each Ω Pj should be temperature independent in the case of temperature independent phonon eigenvectors. Comparison with mode plasma frequencies observed in other similar perovskites [15] indicates that the phonon eigenvectors in EuTiO 3 are analogical to those of SrTiO 3. There is a close agreement between the plasma frequencies (619 cm 1 in EuTiO 3, 680 cm 1 in SrTiO 3 )oftheto4 Axe mode, which is known to be associated with a bending of oxygen octahedra. This correspondence indicates similar anisotropy of the oxygen Born effective charge tensors in the two compounds. It is well known that the Born effective charge of B-site cation in ABO 3 perovskite is the highest [18]. With this is related the fact that the Slater mode has the highest mode-plasma frequency [15]. The considerable value of mode-plasma frequency of the soft TO1 mode (1550 cm 1 at 10 K) proves that its eigenvector is primarily due to the Ti vs. O vibrations, as for example in SrTiO 3 or BaTiO 3. In other words, our analysis confirms that the SM in EuTiO 3 is the Slater-type mode, in agreement with the prediction from first-principles [14]. It follows from the previous analysis, that the TO2 mode near 150 cm 1 must be so called Last mode describing the vibration of the Eu cations against the TiO 6 octahedra. Figure 5 shows that Ω P 4 is temperature independent, which indicates that the eigenvector of this mode is basically temperature independent. However, the plasma frequency Ω P 1 of the SM is decreasing on heating while the Ω P 2 of the Last mode increases. It gives evidence about a strong coupling of both modes as well as about the mixed character of both eigenvectors at high temperature, where their frequencies approach to anti-crossing. Let us note that in the early paper by Katsufuji and Takagi [8], it was assumed that the TO1 soft mode is of the Last type, i.e. vibration of Eu vs. TiO 6.Indeed,itmay appear that the involvement of the Eu vibrations in the TO1 mode could favor the sensitivity of the SM frequency to the spin orientation of 4f electrons of Eu cations in the AFM phase. However, our analysis clearly shows that the Eu vibration is not responsible for the TO1 mode. Instead, the soft TO1 mode is found to be essentially of a Slater type, i.e. mainly the Ti O 6 vibrations are involved. Our findings are thus in agreement with the first principles calculations by Fennie and Rabe [14], showing that the spin order of Eu cations have direct influence on Slater vibrations of Ti O 6. We are thus wondering if the mechanism of the magnetocapacative effect could be understood as the impact of Eu O Eu superexchange interaction on the electrons involved in the covalent Ti O 6 bonding. We have also tried to measure directly the change of TO1 phonon frequency with magnetic field in antiferromagnetic phase [13]. Unfortunately, the expected SM frequency change was not revealed due to insufficient sensitivity of the experiment [13]. But our very recent IR measurements on compressively strained EuTiO 3 thin film were able to reveal a 2 cm 1 shift of the SM frequency with magnetic field [19]. The observed shift is smaller in thin film than expected for the bulk sample (7 cm 1 )since the SM frequency is stiffened by the stress from the substrate (as in compressively strained SrTiO 3 films) [20] and consequently also the static permittivity and magnetocapacative effect are lower. The small frequency shift could be revealed because the SM reflection band in a compressively strained thin film is very narrow and sharp (unlike in bulk reflectivity) and therefore its measurements is more accurate and more sensitive. 4Conclusion We have shown that the incipient-ferroelectric-like temperature dependence of ε observed in the paramagnetic phase of EuTiO 3 is due to TO1 phonon softening. From its high plasma frequency we found that the TO1 phonon is the Slater mode, i.e. it includes Ti vibrations against the O 6 -octahedra. The TO2 Last mode observed near 150 cm 1 involves the Eu vibration against the TiO 6 octahedra. Analysis of the temperature dependences of modeplasma frequencies clearly shows that both TO1 and TO2 modes are coupled, because the plasma frequency transfers from TO1 to TO2 mode above 200 K. Regardless of this coupling we suppose that the Eu spin order in the AFM phase influences the TO1 phonon frequency predominantly due to Eu O Eu superexchange interaction. This is probably responsible for the previously reported large magnetocapacitive effect in EuTiO 3. The authors acknowledge the support of the Czech Science Foundation (project No. 202/09/0682), AVOZ and WPI Initiative on Materials Nanoarchitectonics (MEXT, Japan).

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