Session L32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Mechanisms of Ferroelectricity

General Theory for the Ferroelectric Polarization Induced by Spin-Spiral Order

Multiferroics display magnetic, polar and elastic order parameters simultaneously and hence present fascinating fundamental physics and potentially promising applications. The multiferroic phenomenon has been explained by several different models. However, none of them can correctly describe the ferroelectric polarization of triangular-lattice antiferromagnets induced by helical spin-spiral order. To resolve this problem, we develop a general theory for the ferroelectric polarization induced by spin-spiral order on the basis of symmetry considerations and then evaluate the coefficients needed to specify the general theory on the basis of density functional calculations. Our theory not only explains the ferroelectricity of triangular-lattice antiferromagnets driven by helical spin-spiral order, but also incorporates all known models of magnetic-order-driven ferroelectricity as special cases.   

Modeling functional piezoelectricity in perovskite superlattices with competing instabilities

Multi-component Perovskite Superlattices (SLs) of the form ABO$_{3}$, provide a very promising avenue for the design of materials with multifunctional properties. Furthermore the interfaces of such multi-component SLs are home to competing anti-ferrodistortive and ferroelectric instabilities which can produce unexpected functionalities. However, at present first principles calculations exceeding more than 10 units cells, are particularly costly as they scale with the valence electrons as $N^{3}$. We present a first-principles modeling technique that allows us to accurately model the piezoelectric strains of paraelectric/ferroelectric SLs, BaTiO$_{3}$/CaTiO$_{3}$ and PbTiO$_{3}$/SrTiO$_{3}$, under a fixed displacement field. The model is based on a maximally localized wannier center layer polarization technique, as well as a truncated cluster expansion, that makes use of the fact that such PE/FE SLs have been shown to have highly localized ionic and electronic interface effects. The prediction of the piezoelectricity for a SL of an arbitrary stacking sequence will be demonstrated. We also use our model to conduct a systemic study of the interface effects on piezoelectric response in the above SLs paying special attention to a strong non-linear effect observed in Bulk SrTiO$_{3}$.   

Competing (anti-)ferrodistortive and ferroelectric instabilities in SrTiO$_{3}$ and layered La$_{2}$Ti$_{2}$O$_{7}$

We present first-principles calculations on the competition between antiferrodistortive (AFD) and ferroelectic instabilities in oxides. High temperature cubic SrTiO$_{3}$ is well known to undergo an AFD transformation at around 105 K. Further reducing the temperature shows a softening of the ferroelectric polar phonons, however the material remains incipient-ferroelectric with an overall paraelectric behavior. This behavior is believed to be linked to a suppression of the polar instability by the AFD one, the mechanism still being debated. Our calculations show that freezing in the AFD indeed reduces the polar instability. At the theoretical equilibrium angle, the material however still retains a polar instability with a double-well depth of $\sim$0.2 meV per SrTiO$_{3}$ unit, inline with the material being incipient-ferroelectric. A change in polar eigenvectors with increasing AFD rotation together with a decomposition of forces into long- and short-range components allows us to propose an underlying mechanism. We will further discuss a similar suppression mechanism observed in layered La$_{2}$Ti$_{2}$O$_{7}$, where conventional ferroelectricity is suppressed by ferrodistortive modes, these modes however still leading to improper ferroelectricity due to the layered structure.   

First Principles Study of Piezoelectricty in Improper Ferroelectrics

Piezoelectric materials are key components of many important technologies, and discovering materials with improved piezoelectric responses is a major goal of materials science. In particular, finding new mechanisms for piezoelectricity which allow for high piezoelectric coefficients, especially in lead-free materials, could have great technological impact. Recently, there has been a renewed interest in improper ferroelectrics, which are materials where a non-zero polarization is induced indirectly by the coupling of the polar distortion to non-polar unstable modes, frequently oxygen octahedral rotations. This mechanism for creating a polarization may also offer the possibility of increased coupling to strain, leading to high piezoelectric coefficients. Here, we use first principles density functional theory to investigate the mechanism of the piezoelectric response of Ca$_3$Ti$_2$O$_7$, an improper ferroelectric which we find to have large piezoelectric coefficients.   

Engineering polar perovskites from centric polyhedra building blocks

Increasing demands for electric field-tunable electromagnetic (EM) materials has renewed interests in ferroelectricity and its coupling to EM properties in perovskite oxides. Using density functional computations combined with group theoretical methods, we detail the crystal-chemistry criteria that enable the rational design of new perovskite oxides displaying octahedral rotation-induced ferroelectricity---electric polarizations ($P$) without second-order Jahn-Teller cations from $B$O$_6$ building blocks. We show that interleaving two bulk perovskites to form an ordered and layered arrangement of $A$-site cations [chemical composition $(A,A^\prime)B_2$O$_6$] produces a new trilinear free energy term coupling $B$O$_6$ rotations to $P$. This symmetry rule combined with an energetic condition, describing the lattice dynamical properties of the bulk materials, enables the routine design of synthetic ferroelectric perovskites. We illustrate these guidelines and achieve sizeable electric polarizations in layered gallate and aluminate perovskites, i.e.\ bulk materials with no tendencies to ferroelectricity. Finally, we argue that this strategy could be exploited for the design of ferroelectricity in a variety of crystal classes exhibiting flexible cation--anion polyhedral frameworks.   

Crossover between hybrid improper ferroelectricity and proper ferroelectricity in layered perovskites

Recent progress in designing materials with unconventional mechanisms of ferroelectricity has shown that nominally non-polar octahedral rotations can induce an electrical polarization in certain layered perovskites, e.g., the n=2 Ruddlesden-Popper Ca$_3$Mn$_2$O$_7$, and certain A-site ordered AA'B$_2$O$_6$ double perovskites. In these (what have recently been termed) hybrid improper ferroelectrics, two unstable octahedral rotations of different symmetries couple trilinearly with the polarization. A key question that is still unclear is what the consequences of this coupling are in determining whether these materials exhibit conventional proper ferroelectricity, as in SrBi$_2$Ta$_2$O$_9$, or something resembling improper ferroelectricity. In this talk we discuss this question of proper vs improper in A$_3$B$_2$O$_7$ layered perovskites. First we develop simple criteria for realizing this novel form of ferroelectricity based solely on the properties of the ABO$_3$ parent perovskites. Then we explore how composition and epitaxial strain lead to different ferroelectric behaviors arising from the same rotation-polarization coupling. Finally we show how strain can tune a single material between rotation-driven hybrid improper ferroelectricity and conventional proper ferroelectricity.   

Competition and cooperation between octahedral rotations and ferroelectricity in simple and layered ABX$_3$ perovskites

Researchers have been studying octahedral rotations in perovskites for over half a century. It is now known that such lattice distortions are generally driven by the coordination preferences of the A-site cation. The role of octahedral rotations in modulating the magnetic, electronic and orbital properties of perovskites has been elucidated and a set of empirical rules for rationalizing the structures of known materials and for predicting the structures of as yet unsynthesized materials has been established. Despite this progress, there remains a long-standing problem concerning octahedral rotations and ferroelectricity: there are very few ferroelectric ABX$_3$ perovskites with octahedral rotations. This has lead to the widespread assumption that octahedral rotations compete with and suppress ferroelectricity. In this talk, I will describe our recent work on the interaction between ferroelectricity and octahedral rotations in simple and layered perovskites. Using a combination of Density Functional Theory and simple crystal chemical models, we have shown that in contrast to the common assumption, ferroelectricity and octahedral rotations do not always compete. In particular, I will discuss the manner in which rotations can actually induce ferroelectricity in ABX$_3$ perovskites and present strategies for designing new functional materials based on this mechanism. In a related direction, I will also discuss the role of layering in inducing hybrid improper ferroelectricity in some Ruddlesden-Popper phases and double perovskites. Our approach provides a chemically intuitive picture -- one that combines first-principles lattice dynamics with a local description of bonding -- to explain why particular materials adopt particular structures. Such knowledge is at the foundation of the current materials-by-design effort.   

A Unified Formalism toward Polarization, Magnetization and the $\theta$-term in a Periodic Insulator

The traditional perturbative calculation expands in powers of the gauge potential. This procedure proves problematic when a uniform electric or magnetic field is present. Here we provide a perturbative expansion of the electronic Green's functions directly in powers of the fields. On the other hand, the first order correction to the free energy to an insulator with periodic boundary conditions in the presence of the electric field is actually a Berry's phase. To express the Berry's phase in terms of the Green's functions, one is required to extend the Green's function to one extra dimension. With the trick, one can then calculate the effective action to arbitrary order of the electric and magnetic field. One new result we have obtained is that the $\theta$-term is given by the combination of the Green's functions in the extended momentum space, similar to the Wess-Zumino-Witten term, even without time reversal symmetry.   

Observation and Theory of Intrinsic Ferromagnetism in Ferroelectric Materials

Quantized waves obeying Bose-Einstein statistics will contribute a $T^{3/2}$ term to the specific heat if the dispersion relation goes as q2. We measure the magnetic and electric field dependence of the specific heat on the ferroelectric material tri-glycine sulphate (TGS) over the temperature range 0.05 K $<$ T $<$ 350 K. We detect a $T^{3/2}$ term in the specific heat in the low-temperature limit, which is taken to be the dielectric analog to magnetic spin wave. Near the Curie temperature ($T_{C}$ = 320 K), the shape of the specific-heat anomaly is thermally broadened. However, the anomaly changes to the characteristic sharp lambda-shape expected for a continuous transition with the application of either a magnetic field or electric field, giving the expected entropy change at $T_{C}$ of $R$ln2. These results are explained on the basis that the frequencies of optical dipole oscillations are split by the magnetic field, and the resulting gas of excitations are paramagnetic. Consequently they contribute to the specific heat near $T_{C}$, which increases with magnetic field.   

Dramatic effect of the near-electrode layer configurations on the phase transition characteristics of ferroelectric-paraelectric superstructures

Ferroelectric-paraelectric superstructures have attracted great interest. A few experimental reports have emphasized the effect of individual layer thickness on the transition temperature of these systems. Here, we theoretically show that the phase transition characteristics of these systems are very sensitive to the structural configuration near the electrodes. The phase transition is homogeneous in the system only if the layers contacting the electrodes are paraelectric layers of 1/2 thickness of other individual layers. If the ferroelectric layer contacts the electrode (and the other.electrode is contacted by a paraelectric layer) the phase transition temperature is higher than in the previous structure and the spatial distribution of the polarization at the phase transition is inhomogeneous being maximal near the electrode and disappearing far from it. A striking result is that the transition temperature in one unit bilayer is the same as a system consisting of any number of bilayers. Moreover, the profile of the polarization is unchanged upon addition of new bilayer units to the system. We also discuss general features of the domain structures below the phase transition temperature and transition anomalies.   

The phase diagram of Sr$_{1-x}$Eu$_{x}$TiO$_{3}$: Crossover from displacive to order-disorder dynamics

The phase diagram of Sr$_{1-x}$Eu$_{x}$TiO$_{3}$ is determined experimentally by EPR and resistivity measurements and analyzed theoretically in terms of the self-consistent phonon approximation (SPA) as a function of x (0.0 $\le $ x $\le $ 1.0). It is observed that the oxygen octahedral tilting instability temperature T$_{S}$ increases nonlinearly with x. The theoretical analysis demonstrates that a crossover from displacive to order-disorder dynamics takes place for x$\ge $0.25, signaled by a change in the local double-well potential and the soft mode temperature dependence.   

Electrocaloric effect in ferroelectric alloys from atomistic simulations

Caloric effects, such as magnetocaloric and electrocaloric effects, have attracted a lot of attention recently in the context of increasing interest in energy conversion and renewable energy materials and devices. Here we develop and use accurate first-principles-based simulations to study electrocaloric effect (ECE) from an atomistic point of view. In particular, we develop a computational technique that allows both direct and indirect simulations of ECE within the {\it same} atomistic framework. We then use such a tool to provide first systematic comparison between ECE estimates obtained from direct and indirect approach which will allow us to bridge the macroscopic and atomistic description of ECE. The results of our direct atomistic simulations are then used to explore the intrinsic features of ECE in ferroelectrics with multiple transitions.