We revisit the quantum phase transition from a paraelectric state to a ferroelectric one and in particular the widespread distinction between a longitudinal modes to transverse one. In contrast to transitions at finite temperature, for a quantum phase transition breaking a discrete symmetry the splitting between the modes is irrelevant. We show that an anisotropy in the context of a quantum phase transition leads to a different behavior, compared to a classical transition, and suggest an experiment to observe it. The result is essential for explaining the pairing mechanism in strontium titanate.
Magnetic and dielectric studies of SrCu3Ti4O12 carried out over 5-300K confirm antiferromagnetic (AFM) ordering of Cu-spins at TN =23K. Dielectric constant ε' measured across 1Hz-1MHz signifies quantum paraelectric character, Barrett-fittable almost down to TN. Competition of athermal fluctuations and the literature-reported magneto-phonon-softening near TN manifests a maiden quantum paraelectric glass (QPG) state. Emergent AFM-field tunes the otherwise quantum ordering (at absolute-zero) of the dipoles to finite-temperature kinetic glass transition; spectral dispersion of dielectric constant …
Infrared reflectivity and time-domain terahertz transmission spectra of EuTiO3 ceramics revealed a polar optic phonon at 6 - 300K, whose softening is fully responsible for the recently observed quantum paraelectric behaviour. Even if our EuTiO3 ceramics show lower permittivity than the single crystal due to a reduced density and/or small amount of secondary pyrochlore Eu2Ti2O7 phase, we confirmed the magnetic field dependence of the permittivity, also slightly smaller than in single crystal. Attempt to reveal the soft phonon dependence at 1.8K on the magnetic field up to 13T remained below the…
I show that a nonequilibrium paraelectric to ferroelectric transition can be induced using midinfrared pulses. This relies on a quartic $lQ_{\textrm{l$_z$}}^2Q_{\textrm{h$_x$}}^2$ coupling between the lowest ($Q_{\textrm{l$_z$}}$) and highest ($Q_{\textrm{h$_x$}}$) frequency infrared-active phonon modes of a paraelectric material. Density functional calculations show that the coupling constant $l$ is negative, which causes a softening of the $Q_{\textrm{l$_z$}}$ mode when the $Q_{\textrm{h$_x$}}$ mode is externally pumped. A rectification along the $Q_{\textrm{l$_z$}}$ coordinate that stabiliz…
Spatial correlation between atoms can generate a depletion in the energy dispersion of acoustic phonons. Two well known examples are rotons in superfluid helium and the Kohn anomaly in metals. Here we report on the observation of a large softening of the transverse acoustic mode in quantum paraelectric SrTiO$_3$ by means of inelastic neutron scattering. In contrast to other known cases, this softening occurs at a tiny wave vector implying spatial correlation extending over a distance as long as 40 lattice parameters. We attribute this to the formation of mesoscopic fluctuating domains due to t…
We propose a two-sublattice proton ordering model for the quasione-dimensional CsH$_2$PO$_4$ ferroelectric with hydrogen bonds, which takes into account linear on lattice strains $u_1$, $u_2$, $u_3$ and $u_5$ contribution to the energy of proton subsystem. The model also takes into account the dependence of effective dipole moments of pseudospins on the order parameters, which enables one to agree the effective dipole moments in paraelectric and ferroelectric phases. Within this model in two-particle cluster approximation on short-range interactions and in the mean field approximation on long-…
For CuInP$_2$S$_6$ layered ferrielectric crystal, that is most investigated among wide family of van der Waals ferroics MM$'$P$_2$X$_6$ (M - Cu, Ag; M$'$ - In, Bi, Cr, $\dots$; X - S, Se), by Brillouin spectroscopy the temperature dependence of the longitudinal hypersound velocity was investigated for the acoustic phonons propagated in the plane of crystal layers. Pronounced softening of acoustic phonon branch is observed in the paraelectric phase below $T^{*} \approx 330~$K at cooling to temperature $T_C \approx 312~$K of the first order phase transition into ferrielectric phase. Below $T_C$ …
The temperature dependence of the elastic properties of antiferroelectric PbHfO3 was investigated by Brillouin scattering. The two structural phase transitions of antiferroelectric-antiferroelectric-paraelectric phases were clearly identified by discontinuous changes in the acoustic mode frequencies and the hypersonic damping. The substantial softening of the mode frequency along with the remarkable increase in the acoustic damping observed in the paraelectric phase indicated the formation of precursor noncentrosymmetric (polar) clusters and their coupling to the acoustic waves. This was corro…
We carry out a theoretical investigation to clarify the dynamic property of photo-created nano-sized ferroelectric cluster observed in the paraelectric BaTiO3 as a real time correlation of speckle pattern between two soft X-ray laser pulses, at just above the paraelectric-ferroelectric phase transition temperature. Based on a model with coupled soft X-ray photon and ferroelectric phonon mode, we study the time dependence of scattering probability by using a perturbative expansion approach. The cluster-associated phonon softening as well as central peak effects are well reproduced in the phonon…
Charge transport in doped quantum paralectrics (QPs) presents a number of puzzles, including a pronounced $T^2$ regime in the resistivity. We analyze charge transport in a QP within a model of electrons coupled to a soft transverse optical (TO) mode via a two-phonon mechanism. For $T$ above the soft-mode frequency but below some characteristic scale ($E_0$), the resistivity scales with the occupation number of phonons squared, i.e., as $T^2$. The $T^2$ scattering rate does not depend on the carrier number density and is not affected by a crossover between degenerate and non-degenerate regimes,…
Molecular-dynamics simulations of KNbO$_3$ reveal preformed dynamic chain-like structures, present even in the paraelectric phase, that are related to the softening of phonon branches over large regions of the Brillouin zone. The phase sequence of ferroelectric transitions is correctly reproduced, showing that the first-principles effective Hamiltonian used in the simulations captures the essential behavior of the microscopic fluctuations driving the transitions. Real space chains provide a framework for understanding both the displacive and order-disorder characteristics of these phase transi…
The valence fluctuations which are related to the charge disproportionation of phosphorous ions $P^{4+} + P^{4+}\rightarrow P^{3+} + P^{5+}$ are the origin of ferroelectric and quantum paraelectric states in Sn(Pb)$_2$P$_2$S$_6$ semiconductors. They involve recharging of SnPS$_3$ or PbPS$_3$ structural groups which could be represented as half-filled sites in the crystal lattice. Temperature-pressure phase diagram for Sn$_2$P$_2$S$_6$ compound and temperature-composition phase diagram for (Pb$_y$Sn$_{1-y}$)$_2$P$_2$S$_6$ mixed crystals, which include tricritical points and where a temperature …
Despite important breakthroughs in the last decade, the calculation of temperature dependent properties of solids still remains a challenging task, especially in the vicinity of structural phase transitions. We show that the combination of machine-learning interatomic potentials with quantum self-consistent ab initio lattice dynamics allows to calculate efficiently the temperature dependence of dielectric properties of the quantum paraelectric perovskite KTaO$_3$, with a precision beyond what could be reasonably achieved using plain density functional theory. We first follow the strong anharmo…
Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon soft…
We measured transverse and longitudinal dielectric permittivities of KDP and DKDP in the piezoelectric resonance frequency region under the hydrostatic pressure. The transverse permittivity decreases with pressure in the paraelectric phase and increases in the ferroelectric phase. The pressure dependence of the transverse permittivity of deuterated DKDP is well described by the presented theory. The longitudinal permittivity of a pure KDP exhibits several peaks in the vicinity of the transition point. Upon increasing hydrostatic pressure, the peaks get closer and may merge.
Defects in oxides usually exhibit exotic properties that may be associated with the local lattice dynamics. Here, at atomic spatial resolution, we directly measure phonon modes of an antiphase boundary (APB) in SrTiO3 freestanding membrane and correlate them with the picometer-level structural distortion. We find that the SrTiO3 APB introduces new defect phonon modes that are absent in bulk SrTiO3. These modes are highly sensitive to the subtle structure distortion, i.e., the SrTiO3 APB generates the local electric dipoles forming an antiferroelectric configuration, which significantly softens…
Structural stability of paramagnetic (PM) body-centered cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasi-random structure (SQS) with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N$_4^-$ mode), which corresponds to a bcc-hcp phase transi…
Infrared reflectance spectra of an epitaxial Bi2FeCrO6 thin film prepared by pulsed laser deposition on LaAlO3 substrate were recorded between 10 and 900 K. No evidence for a phase transition to the paraelectric phase was observed, but some phonon anomalies were revealed near 600 K. Most of the polar modes exhibit only a gradual softening, which results in a continuous increase of the static permittivity on heating. It indicates that the ferroelectric phase transition should occur somewhere above 900 K. Magnetic measurements performed up to 1000 K, revealed a possible magnetic phase transition…
Phonon softening phenomena of the $Γ$ point optical modes including the longitudinal optical mode, transverse optical mode and radial breathing mode in "metallic" single wall carbon nanotubes are reviewed from a theoretical point of view. The effect of the curvature-induced mini-energy gap on the phonon softening which depends on the Fermi energy and chirality of the nanotube is the main subject of this article. We adopt an effective-mass model with a deformation-induced gauge field which provides us with a unified way to discuss the curvature effect and the electron-phonon interaction.
We have measured near normal incidence far infrared (FIR) reflectivity spectra of a single crystal of TbMnO3 from 10K to 300K in the spectral range of 50 cm$^{-1}$ to 700 cm$^{-1}$. Fifteen transverse optic (TO) and longitudinal optic (LO) modes are identified in the imaginary part of the dielectric function $ε_2$($ω$) and energy loss function Im(-1/$ε$($ω$)), respectively. Some of the observed phonon modes show anomalous softening below the magnetic transition temperature T$_N$ (~ 46K). We attribute this anomalous softening to the spin-phonon coupling caused by phonon modulation of the super-…
We present an ab initio approach for the calculation of phonon self-energies and their fluctuation diagnostics, which allows us to identify the electronic processes behind phonon anomalies. Application to the transition-metal-dichalcogenide monolayer 1H-TaS$_2$ reveals that coupling between the longitudinal-acoustic phonons and the electrons from an isolated low-energy metallic band is entirely responsible for phonon anomalies such as the mode softening and associated charge-density waves observed in this material. Our analysis allows us to distinguish between different mode-softening mechanis…
We report on the lattice evolution of BiFeO3 as function of temperature using far infrared emissivity, reflectivity, and X-ray absorption local structure. A power law fit to the lowest frequency soft phonon in the magnetic ordered phase yields an exponent β=0.25 as for a tricritical point. At about 200 K below TN~640 K it ceases softening as consequence of BiFeO3 metastability. We identified this temperature as corresponding to a crossover transition to an order-disorder regime. Above ~700 K strong band overlapping, merging, and smearing of modes are consequence of thermal fluctuations and che…
Laser-driven ferroelectricity in $\mathrm{SrTiO_{3}}$ via quantum fluctuation quenching
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Sapienza University of Rome（罗马大学）；Robert Bosch LLC Research and Technology Center（罗伯特博世有限责任公司研究与技术中心）
We report the first principles investigations on the phonons of three polytypes of BaTiO3 (BTO): paraelectric (PE) cubic Pm-3m and two ferroelectric (FE) phases, tetragonal P4mm and rhombohedral R3m. The phonon frequencies calculated using various exchange-correlation functionals, including density functional theory, Hartree-Fock approximation, and their hybrids were reviewed. The pressure-induced interplays between the modes form individual phases were explored by calculating the phonon modes as a function of pressure, P from -15 to 230 GPa. The pressure-sensitive modes of the FE phases showe…
The light-matter interaction can be utilized to qualitatively alter physical properties of materials. Recent theoretical and experimental studies have explored this possibility of controlling matter by light based on driving many-body systems via strong classical electromagnetic radiation, leading to a time-dependent Hamiltonian for electronic or lattice degrees of freedom. To avoid inevitable heating, pump-probe setups with ultrashort laser pulses have so far been used to study transient light-induced modifications in materials. Here, we pursue yet another direction of controlling quantum mat…
We propose a simple and solvable mean-field model of the scattering of transverse optic modes by Polarized Nano Regions (PNR) in the paraelectric phase of relaxor ferroelectrics. The PNR is assumed to be a ferroelectric sphere embedded in the host isotropic medium. The Lagrangian parameters are taken to be the same inside and outside the PNR, with exception of the soft-mode gap temperature dependence. The interaction of the Transverse (TO) with the longitudinal (LO) optic modes is taken into account but the latter is found to be important only at the surface of the PNR. Elementary excitations …
Brillouin scattering studies have been carried out on high quality single crystals of Fe$_3$O$_4$ with [100] and [110] faces in the temperature range of 300 to 30 K. The room temperature spectrum shows a surface Rayleigh wave (SRW) mode at 8 GHz and a longitudinal acoustic (LA) mode at 60 GHz. The SRW mode frequency shows a minimum at the Verwey transition temperature $T_V$ of 123 K. The softening of the SRW mode frequency from about 250 K to $T_V$ can be quantitatively understood as a result of a decrease in the shear elastic constant C$_{44}$, arising from the coupling of shear strain to cha…
