Inversion symmetry breaking by oxygen octahedral rotations in Ruddlesden-Popper NaRTiO₄ family Akamatsu, K. Fujita, T. Kuge, A. S. Gupta, A. Togo, S. Lei, F. Xue, G. Stone, J. M. Rondinelli, L. Q. Chen, I. Tanaka, V. Gopalan, K. Tanaka, Phys. Rev. Lett. 112, 187602 (2014).

Rotations of oxygen octahedra are ubiquitous, but they cannot break inversion symmetry in simple perovskites. However, in a layered oxide structure, this is possible, as we demonstrate here in $A$-site ordered Ruddlesden-Popper $\mathrm{Na}R{\mathrm{TiO}}_4$ ($R$ denotes rare-earth metal), previously believed to be centric. By revisiting this series via synchrotron x-ray diffraction, optical second-harmonic generation, piezoresponse force microscopy, and first-principles phonon calculations, we find that the low-temperature phase belongs to the acentric space group $P\bar{4}{\mathrm{2\_}}_{1}m$, which is piezoelectric and nonpolar. The mechanism underlying this large new family of acentric layered oxides is prevalent, and could lead to many more families of acentric oxides.

Improper Inversion symmetry breaking in Ruddlesden-Popper n=1 phase with a combination of cation ordering and oxygen octahedral rotations.  The “x” symbols represent inversion centers, which disappear in the rightmost schematic which becomes noncentrosymmetric. This mechanism was experimentally proven for B=Ti and A=La, Nd, Sm, Eu, Gd, Dy, Y, and Ho (panel below).

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Hybrid Improper Ferroelectricity in (Sr,Ca)₃Sn₂O₇ and Beyond: Universal Relationship between Ferroelectric Transition Temperature and Tolerance Factor in n = 2 Ruddlesden−Popper Phases, Suguru Yoshida, Hirofumi Akamatsu, Ryosuke Tsuji, Olivier Hernandez, Haricharan Padmanabhan, Arnab Sen Gupta, Alexandra S. Gibbs, Ko Mibu, Shunsuke Murai, James M. Rondinelli, Venkatraman Gopalan, Katsuhisa Tanaka, and Koji Fujita, Journal of the Am. Chem. Soc. 140, 15690−15700 (2018).

Hybrid improper ferroelectricity, which utilizes nonpolar but ubiquitous rotational distortions to create polarization, offers an attractive route to the discovery of new ferroelectric and multiferroic materials because its activity derives from geometric rather than electronic origins. Design approaches based on group theory and first principles can be utilized to explore the crystal symmetries of ferroelectric states, but do not make accurate predictions for some important parameters of ferroelectrics, such as Curie temperature (T_C). Here, we establish a predictive and quantitative relationship between T_C and the Goldschmidt tolerance factor, t, by employing n = 2 Ruddlesden-Popper (RP) A₃B₂O₇ as a prototypical example of hybrid improper ferroelectrics. The focus is placed on an RP system, (Sr_1−xCa_x)₃Sn₂O₇ (x = 0, 0.1, and 0.2), which allows for the investigation of the purely geometric (ionic-size) effect on ferroelectric transitions, due to the absence of the second-order Jahn–Teller active (d⁰ and 6s²) cations that often lead to ferroelectric distortions through electronic mechanisms. We observe a ferroelectric-to-paraelectric transition with T_C = 410 K for Sr₃Sn₂O₇. We also find that the T_C increases linearly up to 800 K with increasing the Ca²⁺ content, i.e., with decreasing the value of t. Remarkably, this linear relationship is applicable to the suite of all known A₃B₂O₇ ferroelectrics, indicating that T_C correlates with the simple crystal-chemistry descriptor, t, based on the ionic-size mismatch. This study provides a predictive guideline for estimating T_C of a given material, which would complement the group-theoretical design approach.

Universal linear relation between Curie temperature and tolerance factor: Curie temperatures (T_C) of n = 2 RP ferroelectrics against the tolerance factor (t) of their perovskite unit. The result of linear fitting is depicted by an orange line with the critical t value, t₀. Blue triangles represent the data for (Sr_1−xCa_x)₃Sn₂O₇ (x = 0, 0.1, 0.2) obtained in this work. The black circles show the data previously reported for Ca₃Ti₂O₇, Sr₃Zr₂O₇, and Ca₃Mn₂O₇. The squares indicate the reported data for solid-solution systems, (Ca,Sr)₃Ti₂O₇ and Ca₃(Ti,Mn)₂O₇.

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Ferroelectric Sr₃Zr₂O₇: Competition between Hybrid Improper Ferroelectric and Antiferroelectric Mechanisms, Suguru Yoshida, Koji Fujita, Hirofumi Akamatsu, Olivier Hernandez, Arnab Sen Gupta, Forrest G. Brown, Haricharan Padmanabhan, Alexandra S. Gibbs, Toshihiro Kuge, Ryosuke Tsuji, Shunsuke Murai, James M. Rondinelli, Venkatraman Gopalan, and Katsuhisa Tanaka, Advanced Funct. Mater. (2018), 28, 1801856,

In contrast to polar cation displacements driving oxides into noncentrosymmetric and ferroelectric states, inversion-preserving oxide anion displacements, such as rotations or tilts of oxygen octahedra about cation coordination centers, are exceedingly common. More than one nonpolar rotational mode in layered perovskites can lift inversion symmetry and combine to induce an electric polarization through a hybrid improper ferroelectric (HIF) mechanism. This form of ferroelectricity expands the compositional palette to new ferroelectric oxides because its activity derives from geometric rather than electronic origins. Here, we report the new Ruddlesden-Popper HIF Sr₃Zr₂O₇, which is the first ternary lead-free zirconate ferroelectric, and demonstrates room-temperature polarization switching. This compound undergoes a first-order ferroelectric-to-paraelectric transition, involving an unusual change in the ‘sense’ of octahedral rotation while the octahedral tilt remains unchanged. Our first-principles calculations show that the paraelectric polymorph competes with the polar phase and emerges from a trilinear coupling of rotation and tilt modes interacting with an antipolar mode. This form of hybrid improper ‘antiferroelectricity’ was recently predicted theoretically but has remained undetected. Our work establishes the importance of understanding anharmonic interactions among lattice degrees of freedom, which is important for the discovery of new ferroelectrics and likely to influence the design of next-generation thermoelectrics.

Hybrid Improper Ferroelectric Sr3Zr2O7: Temperature dependence of SHG intensity upon heating (orange line) and cooling (blue line). (b) P(E) hysteresis loops at room temperature for a bulk Sr₃Zr₂O₇ sample. The electric field was applied at frequency of 50 Hz.

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Emergent room temperature phase in CaTiO₃ nanoparticles and single crystals, Mariola O Ramirez, Tom TA Lummen, Irene Carrasco, Eftihia Barnes, Ulrich Aschauer, Dagmara Stefanska, Arnab Sen Gupta, Carmen de las Heras, Hirofumi Akamatsu, Martin Holt, Pablo Molina, Andrew Barnes, Ryan C Haislmaier, Przemyslaw J Deren, Carlos Prieto, Luisa E Bausá, Nicola A Spaldin, Venkatraman Gopalan, APL Materials, 7, 011103 (2019).

Polar instabilities are well known to be suppressed on scaling materials down to the nanoscale, when electrostatic energy increase at surfaces exceeds lowering of bulk polarization energy. Surprisingly, here we report an emergent low symmetry polar phase arising in nanoscale powders of CaTiO₃, the original mineral named perovskite discovered in 1839, and considered nominally nonpolar at any finite temperature in the bulk. Using nonlinear optics and spectroscopy, X-ray diffraction and microscopy studies, we discover a well-defined polar to non-polar transition at a T_C = 350 K in these powders. The same polar phase is also seen as a surface layer in bulk CaTiO₃ single crystals, forming striking domains with in-plane polarization orientations. Density Functional Theory reveals that oxygen octahedral distortions in the surface layer leads to the stabilization of the observed monoclinic polar phase.  These results reveal new ways of overcoming the scaling limits to polarization in perovskites.

Emergent ferroelectricity in bulk CaTiO3: (left panels a, c, d)  a) Raman mapping of a (110)_O CaTiO₃ bulk single crystal surface, with the white bar being 8 m The direction of the fundamental input light (E^w0) and generated output light (E^w0-Dw) are shown together with the x-y lab axes on the bottom left. (c) Schematic of the domain structure at the surface of the single crystal sample. The different domain variants are shown on the right along with the a, b, and c orthorhombic axes. (d) SHG microscopy images of the same region shown in (a). The polarization directions of the fundamental (E^w) and second harmonic (E^2w) are shown on the bottom right, and the white bar being 8 mm. DFT theory  is shown in the right panels (a, b, c, d): Structural model of CaTiO₃ with the middle section frozen to the bulk lattice parameter values, and the structure relaxed along the z-direction.  The lab axes are shown above and the orthorhombic lattice parameter orientation are shown below.  The Ca atoms are green and the TiO₆ octahedra are blue. (b) Layer-resolved polarization computed using nominal ionic charges.  (c) Layer-averaged displacements along the in-plane directions, and (d) angle changes, with the center of the frozen layer being 0.

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