Ferroelectric Soft Mode Research Articles

Phonon Inverse Faraday Effect from Electron-Phonon Coupling.

The phonon inverse Faraday effect describes the emergence of a dc magnetization due to circularly polarized phonons. In this work we present a microscopic formalism for the phonon inverse Faraday effect. The formalism is based on time-dependent second order perturbation theory and electron phonon coupling. While our final equation is general and material independent, we provide estimates for the effective magnetic field expected for the ferroelectric soft mode in the oxide perovskite SrTiO_{3}. Our estimates are consistent with recent experiments showing a huge magnetization after a coherent excitation of circularly polarized phonons with THz laser light. Hence, the theoretical approach presented here is promising for shedding light into the microscopic mechanism of angular momentum transfer between ionic and electronic angular momentum, which is expected to play a central role in the phononic manipulation of magnetism.

Soft Mode Behavior in Transition Metal Doped SrTiO3 Thin Films on MgO Substrates

The ferroelectric soft mode in polycrystalline pristine SrTiO3 and weakly doped SrTiO3 : M (M = 2 at% Fe, Ni, Mn, Co) thin films on (001) MgO substrates has been studied using time-domain terahertz spectroscopy. Spectra of real and imaginary parts of film permittivity were determined in the frequency range of 5–100 cm–1 at temperatures between 5 and 300 K. Central frequency and dielectric contribution of the ferroelectric soft mode show Barrett-like temperature dependencies similar to crystalline SrTiO3. Large negative values of Curie temperature and enhanced positive values of Barrett quantum temperatures are discovered indicating that doped SrTiO3 thin films are farther from ferroelectric phase transition than SrTiO3 crystals.

Light-Induced Complete Reversal of Ferroelectric Polarization in Sliding Ferroelectrics.

Previous experiments have provided evidence of sliding ferroelectricity and photoexcited interlayer shear displacement in two-dimensional materials, respectively. Herein, we find that a complete reversal of vertical ferroelectric polarization can be achieved within an astonishing 0.5ps in h-BN bilayer by laser illumination. Comprehensive analysis suggests that ferroelectric polarization switching originates from laser-induced interlayer sliding triggered by selective excitation of multiple phonons. The interlayer electron excitation from the p_{z} orbitals of the upper layer N atoms to the p_{z} orbitals of the lower layer B atoms produces desirable and directional interlayer forces activating the in-plane optical TO-1 and LO-1 phonon modes. The atomic motions driven by the coupling of TO-1 and LO-1 modes are coherent with ferroelectric soft mode, thus modulating the dynamical potential energy surface and resulting in ultrafast ferroelectric polarization reversal. Our work provides a novel microscopic insight into ultrafast polarization switching in sliding ferroelectrics.

Revealing the phase transition scenario in antiferroelectric thin films by x-ray diffuse scattering

There is no consensus among researchers regarding how phase transitions occur in antiferroelectric (AFE) epitaxial heterostructures, in particular, in heterostructures based on model AFE lead zirconate. The questions about the number of phase transitions in such films and by what mechanism they occur remain controversial. This paper presents a look at the phase transition scenario in two types of epitaxial heterostructures: PbZrO3/Ba[La–Sn]O3/MgO (001) thin films with thicknesses from 25 to 1000 nm and PbZrO3/SrRuO3/SrTiO3 (001) thin film 100 nm thick using the diffuse x-ray scattering in the grazing incidence setup. We register the characteristic butterfly-shaped diffuse scattering (DS) intensity distribution in the HK pseudocubic planes, which corresponds to the anisotropic ferroelectric soft mode. No incommensurate soft mode was observed in the cuts of reciprocal space parallel to the film surface by diffuse scattering. We reproduce the shape of DS distribution at different temperatures by the model based on the dielectric stiffness and the electric polarization correlation tensor in the cubic approximation. Such modeling allows not only to characterize the DS parameters from the challengingly low signal-to-background data set, but also to extract experimentally the sensitivity of the materials with respect to inhomogeneous polarization. While the observed temperature evolution of DS is consistent with the dielectric measurements, the correlation between the DS and the phase transition sequence observed by superstructure reflections is yet to be understood better.

Intrinsic-strain-induced ferroelectric order and ultrafine nanodomains in SrTiO3

Nano ferroelectrics holds the potential application promise in information storage, electro-mechanical transformation, and novel catalysts but encounters a huge challenge of size limitation and manufacture complexity on the creation of long-range ferroelectric ordering. Herein, as an incipient ferroelectric, nanosized SrTiO3 was indued with polarized ordering at room temperature from the nonpolar cubic structure, driven by the intrinsic three-dimensional (3D) tensile strain. The ferroelectric behavior can be confirmed by piezoelectric force microscopy and the ferroelectric TO1 soft mode was verified with the temperature stability to 500 K. Its structural origin comes from the off-center shift of Ti atom to oxygen octahedron and forms the ultrafine head-to-tail connected 90° nanodomains about 2 to 3 nm, resulting in an overall spontaneous polarization toward the short edges of nanoparticles. According to the density functional theory calculations and phase-field simulations, the 3D strain-related dipole displacement transformed from [001] to [111] and segmentation effect on the ferroelectric domain were further proved. The topological ferroelectric order induced by intrinsic 3D tensile strain shows a unique approach to get over the nanosized limitation in nanodevices and construct the strong strain-polarization coupling, paving the way for the design of high-performance and free-assembled ferroelectric devices.

Terahertz ferroelectric soft mode in weakly doped SrTiO3: M thin films (M=Mn, Ni, Fe, Co)

Systematic study of the terahertz soft-mode in SrTiO3: M thin (150 nm) films doped (2 at%) with transition metals M = Mn, Fe, Ni, Co is performed at frequencies 7–1000 cm−1 and temperatures 5–300 K. The soft mode dielectric strength and frequency follow the Barrett-like temperature behaviours with unusually high quantum temperatures and large in magnitude negative Curie temperatures, indicating strong destabilization of the ferroelectric state due to a combined effect of quantum fluctuations, dead layers at the boundaries of crystallites, misfit strains within crystallites and disorder induced by doping. Dopant-dependent variation in the asymmetry of the Fano resonance describing coupling of the TO2 phonon and continuum states of polarization fluctuations is observed suggesting presence of polar nanoregions in the films. Clear correlation between the asymmetry parameter and the Barrett quantum temperature is observed that highlights the complex character of the local structure-dielectric properties relationships in the films.

Nature of Dielectric Relaxation in SrTiO<sub>3</sub>:Mn Single Crystals

Dielectric spectra of SrTiO3and SrTiO3:Mn single crystals have been studied in the frequency range of 10‒3000 cm–1and in the temperature range of 5–297 K using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy. A comparative analysis of the experimental results made it possible to detect a significant broadening of the absorption lines corresponding to the Slater and Last phonon modes, while the parameters of the Axe mode when replacing Ti with Mn (2 at %) stay invariant. This effect is associated with an enhance in structural disorder in the cation subsystem (B-sublattice) of the SrTiO3crystal. It has been established that doping with Mn ions reduces the antiferrodistortive phase transition temperature by about 20 K, but hardly affects the character of the temperature dependence of the parameters of a ferroelectric soft mode at temperatures of about 60–297K. It has been found that an additional excitation with the frequency below the frequency of the ferroelectric soft mode should be taken into account for an appropriate model description of the dispersion of the permittivity of SrTiO3:Mn in the terahertz frequency range. The results obtained in this work indicate that dielectric relaxation in the SrTiO3:Mn crystal is due to thermally activated hops of Mn atoms between displaced (noncentral) crystallographic sites; i.e., the mechanism of radiofrequency relaxation in SrTiO3:Mn is hopping rather than polaronic, which is also actively discussed in the literature.

Tuning the Multiferroic Properties of BiFeO_{3} under Uniaxial Strain.

More than twenty years ago, multiferroic compounds combining in particular magnetism and ferroelectricity were rediscovered. Since then, BiFeO_{3} has emerged as the most outstanding multiferroic by combining at room temperature almost all the fundamental or applicative properties that may be desired: electroactive spin wave excitations called electromagnons, conductive domain walls, or a low band gap of interest for magnonic devices. All these properties have so far only been discontinuously strain engineered in thin films according to the lattice parameter imposed by the substrate. Here we explore the ferroelectricity and the dynamic magnetic response of BiFeO_{3} bulk under continuously tunable uniaxial strain. Using elasto-Raman spectroscopy, we show that the ferroelectric soft mode is strongly enhanced under tensile strain and driven by the volume preserving deformation at low strain. The magnonic response is entirely modified with low energy magnon modes being suppressed for tensile strain above pointing out a transition from a cycloid to an homogeneous magnetic state. Effective Hamiltonian calculations show that the ferroelectric and the antiferrodistortive modes compete in the tensile regime. In addition, the homogeneous antiferromagnetic state becomes more stable compared to the cycloidal state above a +2% tensile strain close to the experimental value. Finally, we reveal the ferroelectric and magnetic orders of BiFeO_{3} under uniaxial strain and how the tensile strain allows us to unlock and to modify in a differentiated way the polarization and the magnetic structure.

Resonant Excitation of the Ferroelectric Soft Mode by a Narrow-Band THz Pulse.

This study investigates the impact of narrow-band terahertz pulses on the ferroelectric order parameter in Ba0.8Sr0.2TiO3 films on various substrates. THz radiation in the range of 1-2 THz with the pulse width of about 0.15 THz was separated from a broadband pulse with the interference technique. The 375 nm thick BST film on a MgO (001) substrate exhibits enhanced THz-induced second harmonic generation when excited by THz pulses with a central frequency of 1.6 THz, due to the resonant excitation of the soft phonon mode. Conversely, the BST film on a Si (001) substrate shows no enhancement, due to its polycrystalline state. The 800 nm thick BST film on a MgO (111) substrate demonstrates the maximum of a second harmonic generation signal when excited by THz pulses at 1.8 THz, which is close to the soft mode frequency for the (111) orientation. Notably, the frequency spectrum of the BST/MgO (111) film reveals peaks at both the fundamental and doubled frequencies, and their intensities depend, respectively, linearly and quadratically on the THz pulse electric field strength.

Temperature‐Dependent Anharmonic Phonons in Quantum Paraelectric KTaO3 by First Principles and Machine‐Learned Force Fields

AbstractUnderstanding collective phenomena in quantum materials from first principles is a promising route toward engineering materials properties and designing new functionalities. This work examines the quantum paraelectric state, an elusive state of matter characterized by the smooth saturation of the ferroelectric instability at low temperature due to quantum fluctuations associated with anharmonic phonon effects. The temperature‐dependent evolution of the soft ferroelectric phonon mode in the quantum paraelectric KTaO3 in the range 0–300 K is modeled by combining density functional theory (DFT) calculations with the stochastic self‐consistent harmonic approximation assisted by an on‐the‐fly machine‐learned force field. The calculated data show that including anharmonic terms is essential to stabilize the spurious imaginary ferroelectric phonon predicted by DFT in the harmonic approximation, in agreement with experiments. Augmenting the DFT workflow with machine‐learned force fields allows for efficient stochastic sampling of the configuration space using large supercells in a wide temperature range, inaccessible to conventional ab initio protocols. This work proposes a robust computational workflow capable of accounting for collective behaviors involving different degrees of freedom and occurring at large time/length scales, paving the way for precise modeling and control of quantum effects in materials.

Can the ferroelectric soft mode trigger an antiferromagnetic phase transition?

Type-II multiferroics, where spin interactions induce a ferroelectric polarization, are interesting for new device functionalities due to large magnetoelectric coupling. We report on a new type of multiferroicity in the quadruple-perovskite BiMn3Cr4O12, where an antiferromagnetic phase is induced by the structural change at the ferroelectric phase transition. The displacive nature of the ferroelectric phase transition at 125 K, with a crossover to an order-disorder mechanism, is evidenced by a polar soft phonon in the THz range and a central mode. Dielectric and pyroelectric studies show that the ferroelectric critical temperature corresponds to the previously reported Néel temperature of the Cr3+ spins. An increase in ferroelectric polarization is observed below 48 K, coinciding with the Néel temperature of the Mn3+ spins. This increase in polarization is attributed to an enhanced magnetoelectric coupling, as no change in the crystal symmetry below 48 K is detected from infrared and Raman spectra.

Anisotropic Rashba coupling to polar modes in KTaO3

Motivated by the discovery of superconductivity in KTaO3-based heterostructures, we study a pairing mechanism based on spin-orbit assisted coupling between the conduction electrons and the ferroelectric (FE) modes present in the material. We use ab initio frozen-phonon computations to show a linear-in-momentum Rashba-like coupling with a strong angular dependence in momentum for the lower manifold, deviating from the conventional isotropic Rashba model. This implies the Rashba-like interaction with the polar modes has substantial L = 3 cubic harmonic corrections, which we quantify for each electronic band. The strong anisotropy of the Rashba interaction is captured by a microscopic toy model for the electrons. We find its origin to be the angular dependence in electronic momentum imposed by the kinetic term on the degenerate manifold. A comparison between the toy model and ab initio results indicates that additional symmetry allowed terms beyond odd-parity spin-conserving inter-orbital hopping processes are needed to describe the Rashba-like polar interaction between the electrons and the soft FE mode.

Terahertz time-domain spectroscopic ellipsometry of metallic strontium titanate

The coexistence of the polar instability and metallic conduction has attracted much attention. Ferroelectric soft optic modes and carrier electrons were investigated in A- and B-site heterovalent doped strontium titanate SrTiO3 crystals by the terahertz time-domain spectroscopic ellipsometry. The observed real and imaginary parts of a complex dielectric constant were fitted by the damped harmonic oscillator model for the ferroelectric soft optic mode and the Drude-Smith model for carrier electrons. The observed soft mode frequency increases as the La and Nb content increases. It is found that the square of the ferroelectric soft mode frequency linearly changes to the carrier electron concentration. This fact indicates that the carrier electrons suppress the ferroelectric instability and the ferroelectric soft mode frequency increases as the carrier concentration increases.

Lattice dynamics and Raman spectrum of supertetragonal PbVO3

Lead vanadate PbVO3 is a polar crystal with a P4mm space group under ambient conditions. PbVO3 is isostructural with the model soft mode-driven ferroelectric PbTiO3, but it differs due to the so-called “supertetragonal” elongation of its unit cell. In this study, we investigated the lattice dynamics of PbVO3 based on Raman spectroscopy at room temperature and first-principle calculations. All zone-center transverse optical phonon modes were identified by polarized, angle-dependent Raman spectroscopy and assigned as follows: E modes at 136, 269, 374, and 508 cm−1; A1 modes at 188, 429, and 874 cm−1, and B1 mode at 319 cm−1. The calculations confirmed the experimental symmetry assignment and allowed us to obtain the longitudinal optical phonon wavenumbers. In addition, we analyzed the mode eigenvectors in detail in order to identify the atomic displacements associated with each mode and compare them with PbTiO3. Despite differences in chemistry and strain, the phonon eigenvectors were found to be highly comparable in both compounds. We investigated the position of the ferroelectric soft mode in PbVO3 compared with PbTiO3. Sizeable splitting of the B1+E modes appeared as a characteristic feature of supertetragonal phases. The peculiarity of the vanadyl V–O bond frequency in PbVO3 was also addressed.

Dielectric properties of ammonium iron sulphate-dodecahydrate alum crystal

The statistical Green function theory and extended two sublattice pseudospin coupled-mode model Hamiltonian. The modified model summing with phonon anharmonic couplings, extra spin-lattice couplings, direct spin-spin coupling together with an applied electric field has been used to explain the dielectric properties of ammonium iron alum crystal. The expressions for energy shift, linewidth, ferroelectric soft mode frequency, dielectric permittivity, and dielectric loss tangent are derived. By fitted the model values of different parameters in the above theoretical expressions. The temperature dependence of soft mode frequency, dielectric permittivity, and dielectric loss properties have been numerically calculated. Our theoretical obtained results compared well agreement with experimental results reported by others.

Partial breakdown of translation symmetry at a structural quantum critical point associated with a ferroelectric soft mode

We report that complete suppression of a phonon-driven structural phase transition causes partial breakdown of a three-dimensional translation symmetry in a well-defined sublattice. This state is revealed for a dielectric compound, ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$, that comprises an ${\mathrm{AlO}}_{4}$ network incorporated into a hexagonal Ba(Sr) sublattice. Pair distribution function analyses and inelastic neutron scattering experiments provide clear-cut evidence of the ${\mathrm{AlO}}_{4}$ network forming a continuum of Al-O short-range correlations similar to glasses, whereas the Ba(Sr) sublattice preserves the original translational symmetry. This glassy network significantly dampens the phonon spectrum and transforms it into the broad one resembling those typically observed in glass materials.

Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics

Experimental evidence suggests that superconductivity in ${\mathrm{SrTiO}}_{3}$ is mediated by a soft transverse ferroelectric mode which, according to conventional theories, has negligible coupling with electrons. A phenomenological Rashba-type coupling has been proposed on symmetry arguments but a microscopic derivation is lacking. Here, we fill this gap and obtain a linear coupling directly from a minimal microscopic model of the electronic structure. We find that the effective electron-electron pairing interaction has a strong momentum dependence. This yields an unusual situation in which the leading $s$-wave channel is followed by a subleading $p$-wave state which shows a stronger pairing instability than the $d$-wave state. The bare Rashba coupling constant is estimated for the lowest band of doped ${\mathrm{SrTiO}}_{3}$ with the aid of first-principles computations. Extrapolating the estimation to the multiband regime we show that it can explain bulk superconductivity. For densities where the Meissner effect has not been observed an extra softening due to inhomogeneities is needed to explain the zero resistance state.

Isotope tuning of the superconducting dome of strontium titanate

Doped strontium titanate SrTiO$_3$ (STO) is one of the most dilute superconductors known today. The fact that superconductivity occurs at very low carrier concentrations is one of the two reasons that the pairing mechanism is not yet understood, the other is the role played by the proximity to a ferroelectric instability. In undoped STO, ferroelectric order can in fact be stabilized by substituting $^{16}$O with its heavier isotope $^{18}$O. Here we explore the superconducting properties of doped and isotope-substituted SrTi$(^{18}$O$_{y}^{16}$O$_{1-y})_{3-\delta}$ for $0\le y \le 0.81$ and carrier concentrations between $6\times 10^{17}$ and $2\times 10^{20}$ cm$^{-3}$ ($\delta<0.02$). We show that the superconducting $T_c$ increases when the $^{18}$O concentration is increased. For carrier concentrations around $5\times 10^{19}$~cm$^{-3}$ this $T_c$ increase amounts to almost a factor $3$, with $T_c$ as high as 580~mK for $y=0.74$. When approaching SrTi$^{18}$O$_3$ the maximum $T_c$ occurs at a much smaller carrier densities than for pure SrTi$^{16}$O$_3$. Our observations agree qualitatively with a scenario where superconducting pairing is mediated by fluctuations of the ferroelectric soft mode.

Quantum paraelectric phase of SrTiO3 from first principles

We demonstrate how the quantum paraelectric ground state of ${\mathrm{SrTiO}}_{3}$ can be accessed via a microscopic ab initio approach based on density functional theory. At low temperature the quantum fluctuations are strong enough to stabilize the paraelectric phase even though a classical description would predict a ferroelectric phase. We find that accounting for quantum fluctuations of the lattice and for the strong coupling between the ferroelectric soft mode and lattice elongation is necessary to achieve quantitative agreement with experimental frequency of the ferroelectric soft mode. The temperature dependent properties in ${\mathrm{SrTiO}}_{3}$ are also well captured by the present microscopic framework.

Lattice instability of B-site substituted SrTiO3 crystals studied by terahertz time-domain spectroscopic ellipsometry

The B-site substituted quantum paraelectric strontium titanate, SrTiO3 (STO), crystals with the perovskite structure were studied regarding their dielectric properties in the terahertz frequency range. When Ti4+ ions at the B-site are substituted by heterovalent Nb5+ ions, free electrons are introduced and the conductivity increases. The complex dielectric constants were accurately determined by the terahertz time-domain spectroscopic ellipsometry. The dielectric spectra were analyzed by the damped harmonic oscillator model for a ferroelectric soft mode and the Drude-Smith model for free electrons. The soft mode frequency and the plasma frequency increased with the increasing Nb content. The square of the plasma frequency is proportional to the concentration of free electrons. It was found that the change in the ferroelectric soft mode frequency is approximately proportional to the concentration of free electrons. This fact suggests that the increase in the free electrons by donor-doping suppresses the ferroelectric instability.