Ferroelectric transition and soft-phonon dynamics associated with off-center displacement of magnetic ions in perovskite Sr 1– x Ba x MnO 3 Materials Science : Electronic & Magnetic Properties 64 Since ferroelectricity was discovered in perovskite BaTiO 3 in 1940s, a variety of ferroelectric oxides have been extensively studied in terms of electronic device engineering as well as academic interest. Most of the perovskite ferroelectrics AB O 3 so far identified, however, consist of non-magnetic B (transition metal) site with no d -orbital electrons (Fig. 1(a)). Typical examples include Pb(Zr,Ti)O 3 and KNbO 3 . The requirement of the d 0 electronic configuration in the off-center transition metal ions can be interpreted in terms of the covalent bonding [1]. Since electrons can virtually hop from the filled 2 p orbital in oxygen to the empty d shells in the transition metal ions, the d 0 states are energetically stabilized by forming a covalent bond (Fig. 1(b)). This empirical rule for the ferroelectric perovskites, however, has been a severe restriction in designing new multiferroic materials where magnetism and ferroelectricity coexist. Since magnetic ordering in contrast requires the partial occupation of the d shell of the transition metal ions, mutually exclusive conditions are necessary for the emergence of both ferroelectricity and magnetism [2]. Against this empirical rule, a few multiferroic perovskites have been investigated, as exemplified by TbMnO 3 with the spiral magnetic order [3] and BiFeO 3 with an off-center Bi ( A site) ion [4]. However, they show only small polarization or otherwise weak magnetoelectric coupling. Recently, several first- principles calculations have pointed out the possible ferroelectric ground state with large polarization (tens of μ C/cm 2 ) for A MnO 3 ( A =Ca, Sr, and Ba), accompanied by the Mn 4+ ion displacement due to strong Mn-O bond covalency [5]. In reality, cubic SrMnO 3 is a typical Mott insulator with G-type (staggered in all three directions) antiferromagnetism and to be paraelectric down to the lowest temperature. Although the ferroelectric instability was predicted to be promoted with increasing the ionic radius of the A site ions, no ferroelectric transition was experimentally observed up to 20% Ba substitution for Sr. For a larger radius of the A site ion, the hexagonal polymorph becomes so stable that the cubic perovskite structure cannot be synthesized by the conventional solid-state reaction. To overcome this problem, we have developed a two-step crystal growth technique, consisting of a floating-zone method and high-pressure oxygen annealing (~6 GPa) [6]. This enabled the synthesis of single crystals with the perovskite structure up to 50% Ba substitution. Figure 2(a) shows the dependence of lattice constant a on Ba concentration ( x ) for Sr 1− x Ba x MnO 3 (0≤ x ≤ 0.5). As x increases from 0 to 0.4, the lattice constant at 300 K monotonically increases from 3.807 to 3.856 Å with keeping the cubic symmetry. Around x = 0.45, the crystal structure changes from cubic to tetragonal, indicating ferroelectric distortion with an elongation of the c -axis. Figure 2(b) shows a magnetoelectric phase diagram for Sr 1− x Ba x MnO 3 as a function of x . The ferroelectric transition temperatures T C were determined as the temperatures where the tetragonal distortion vanishes (Fig. 2(d)). The G-type antiferromagnetic phase is stable for the entire doping range (0≤ x ≤ 0.5), although the transition temperature T N gradually decreases from 230 K ( x =0) to 185 K ( x = 0.5). For x ≥ 0.45, a novel multiferroic phase thus appears below T N (< T C ), associated with the antiferromagnetic ordering of off-center Mn 4+ ions. Spontaneous electric polarization, P S , along the c -axis was clearly observed in the P - E hysteresis curve, as shown in Fig. 2(c). The measured P S value at 2 K is ~4.5 μ C/cm 2 in a specimen with heavily-twinned tetragonal domains, suggesting the intrinsic P S value of 13.5 μ C/cm 2 for a single domain. The values of P S and T C for x =0.5 are almost comparable with those for BaTiO 3 ( P S =26 μ C/cm 2 and T C =406 K). Since there are no lone pairs in Sr 2+ /Ba 2+ ions, the observed ferroelectricity is attributed to the displacement of the magnetic Mn 4+ ion with d 3 configuration. The long-range ordering of Mn 4+ spins has strikingly large effects on the spontaneous polarization and lattice distortion, as shown in Fig. 2(d). The c / a value, which reaches 1.012 around room temperature, begins to decrease with decreasing temperature around 225 K (> T N ) probably due to the antiferromagnetic fluctuation, and then steeply drops at T N . Below 150 K, the c / a value is almost constant (~1.0035), (a) (b) A site (Ba 2+ , Pb 2+ , K + , ...) O B site c a (Ti 4+ , Zr 4+ , Nb 5+ , ...) Mn 4+ ? Transition Metal 3 d Oxygen 2 p Fig. 1. (a) Crystal structure of perovskite oxides. For most proper ferroelectrics, the transition metal ions in the B sites are nonmagnetic. (b) Energy diagram of covalent bonding between transition metal 3 d and oxygen 2 p orbitals. Partially occupied 3 d states in transition metal ions are energetically unfavorable in forming a covalent bond. ( d 0 -ness rule) 65 at approximately 30% of the maximum deviation from the cubic value ( c / a =1). Based on a simple relation ( c / a − 1) ∝ P S 2 , the P S value above T N is estimated to be about 1.9 times as large as that below T N : ~25 μ C/cm 2 . The antiferromagnetic ordering thus can produce huge variation in P S of the order of μ C/cm 2 . The ferroelectric transition in Sr 1− x Ba x MnO 3 is governed by a soft phonon, reflecting the displacement- type ferroelectricity. Figure 3 shows the phonon dispersion along the [110] direction for x = 0–0.4, revealed by the inelastic X-ray scattering experiments at BL35XU . The measurements were performed on single crystals with a typical dimension of ~1 × 1 × 1 mm 3 . The dispersion of the transverse optical (TO1) mode markedly varies with x , whereas those of the acoustic mode (TA) and TO2 do not change notably. In particular, the energy of TO1 mode around the zone center decreases toward zero as the doping level approaches the ferroelectric phase, showing typical soft-mode behavior. More interestingly, strong coupling between soft phonon mode and magnetism was observed. Detailed temperature dependence of inelastic X-ray scattering for x=0.3 has revealed that the soft-mode energy hardens by as much as ~50% upon the magnetic order. From Lyddane-Sachs-Teller relation, this corresponds to 60% drop in dielectric constant at T N , suggesting significant magnetodielectric effects in paraelectric systems as well [6]. Our results confirm the violation of the empirical “ d 0 -ness” rule for ferroelectric perovskites and open up a promising class of new multiferroic materials with large electric polarization and huge magnetoelectric coupling. Future studies may seek a ferromagnetic ground state in further Ba-substituted compounds, which may realize switching of magnetization (polarization) with electric (magnetic) fields feasible for novel spintronics devices. 3.8 3.85 3.9 a, c (Å) a a c 0 0.1 0.2 0.3 0.4 0.5 0 100 200 300 400 G-type AFM MF FE Temperature (K) x (Ba) (a) (b) 300 K PM PE –100 –50 0 50 100 –5 0 100 200 300 400 1 1.005 1.01 E (kV/cm) T C T (K) x =0.5 (d) 0 5 P r ( μ μ C/cm 2 ) 2 K, 0 T 1 kHz x =0.5 (c) T N Sr1- x Ba x MnO 3 T C T N c/a 0.5 0.4 0.3 0.2 0.1 0.0 30 25 20 15 10 5 0 0.5 0.4 0.3 0.2 0.1 0.0 0.5 0.4 0.3 0.2 0.1 0.0 0.5 0.4 0.3 0.2 0.1 0.0 x=0.3 x=0.2 x=0 x=0.4 TO2 TO1 TA ξ //(001) 300 K Sr1- x Ba x MnO 3 q in ( q q 0) q in ( q q 0) q in ( q q 0) q in ( q q 0) E (meV) Fig. 2. (a) Lattice constant and (b) phase diagram for Sr 1- x Ba x MnO 3 as a function of Ba concentration ( x ). PM, AFM, PE, FE, and MF denote paramagnetic, antiferromagnetic, paraelectric, ferroelectric and multiferroic phases, respectively. (c) Remnant P-E hysteresis curve for x = 0.5 along [001] and (d) temperature profile of ferroelectric distortion ( c / a ) for x = 0.5 measured by powder X-ray diffraction. Fig. 3. Plots of the inelastic-X-ray- scattering intensity at 300 K in the energy-wave-vector ( ω - q ) plane in the [110] ( Γ -M) direction for x = 0–0.4. The measurements were performed around the 005 Bragg reflection to detect the phonons with polarization vector ξ parallel to [001]. The closed symbols denote the phonon frequency ω q , obtained by the fitting based on the damped harmonic oscillators. The points at q = 0 were determined from the optical spectra. [6] Hideaki Sakai a,†, *, Yasujiro Taguchi a and Yoshinori Tokura a,b,c a RIKEN Advanced Science Institute (Wako) b Dept. of Applied Physics, The University of Tokyo c ERATO Multiferroics Project, JST *E-mail: hs36@st-andrews.ac.uk † Present address: School of Physics and Astronomy, University of St. Andrews, UK References [1] R.E. Cohen: Nature 358 (1992) 136. [2] N.A. Hill: J. Phys. Chem. B 104 (2000) 6694. [3] T. Kimura et al .: Nature 426 (2003) 55. [4] For a review, G. Catalan and J.F. Scott: Adv. Mat. 21 (2009) 2463. [5] S. Bhattacharjee et al .: Phys. Rev. Lett. 102 (2009) 117602; J.M. Rondinelli et al .: Phys. Rev. B 79 (2009) 205119; J.H. Lee et al .: Phys. Rev. Lett. 104 (2010) 207204. [6] H. Sakai, J. Fujioka, T. Fukuda, D. Okuyama, D. Hashizume, F. Kagawa, H. Nakao, Y. Murakami, T. Arima, A.Q.R. Baron, Y. Taguchi and Y. Tokura: Phys. Rev. Lett. 107 (2011) 137601.
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