Soft modes in two- and eight-direction order-disorder ferroelectrics

The non-linear relations between polarization strength and electric field strength for ferroelectrics, as well as magnetization strength and magnetic field strength for ferromagnetics, can be achieved by introducing retarded electromagnetic interactions. The electric and magnetic hysteretic loops, as well as polarization and magnetization curves, can be described well based on soft mode theory in the alternating electromagnetic fields of low and medium frequencies. The fundam...

We report an extensive molecular dynamics study of ab-initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to e...

The quantum ferromagnetic transition of itinerant electrons is considered. We give a pedagogical review of recent results which show that zero-temperature soft modes that are commonly neglected, invalidate the standard Landau-Ginzburg-Wilson description of this transition. If these modes are taken into account, then the resulting order parameter field theory is nonlocal in space and time. Nevertheless, for both disordered and clean systems the critical behavior has been exact...

The structural phase transition in hexagonal BaMnO$_3$ occurring at $T_c$=130 K was studied in ceramic samples using electron and X-ray diffraction, second harmonic generation as well as by dielectric and lattice dynamic spectroscopies. The low-temperature phase (space group $P6_{3}cm$) is ferroelectric with a triplicated unit cell. The phase transition is driven by an optical soft mode from the Brillouin-zone boundary [$q = (\frac{1}{3},\frac{1}{3},0)$]; this mode activates ...

We propose a mechanism of stochastic resonance induced by spatial noise (electric random fields) in ferroelectrics. The calculations demonstrate the characteristic of the stochastic resonance: certain random field can increase the susceptibility, the phonon occupancy, and the overcooled temperature. This mechanics of stochastic resonance may be general in other disordered systems.

It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical win...

Hyper-Raman scattering experiments allowed collecting the spectra of the lowest F1u-symmetry mode of PbTiO3 crystal in the paraelectric phase up to 930K as well as down to about 1K above the phase transition. It is realized that this mode is fully responsible for the Curie-Weiss behavior of its dielectric permittivity above Tc. Near the phase transition, this phonon frequency softens down to 17 cm-1 and its spectrum can be well modeled as a response of a single damped harmoni...

A new approach in the investigation of the order parameter behaviour near ferroelectric phase transition point is suggested. The short range and dipole interactions between particles are taken into account. The logarithmic corrections and effective critical exponents are calculated and discussed.

Ferroelectricity observed in thin film $\mathrm{HfO_2}$, either doped with Si, Al, etc. or in the $\mathrm{Hf_{0.5}Zr_{0.5}O_2}$ form, has gained great technical significance. However, the soft mode theory faces a difficulty in explaining the origin of such ferroelectricity. In this work, we propose that the 7 cation coordination number of $\mathrm{HfO_2/ZrO_2}$ lies at the heart of this ferroelectricity, which stems from the proper ionic radii of Hf/Zr compared with O. Among...

Heat bath Monte Carlo simulations have been used to study a 12-state discretized Heisenberg model with a new type of random field on simple cubic lattices of size $128 \times 128 \times 128$. The 12 states correspond to the [110] directions of a cube. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $h_R$ to two of the 12 spin states, chosen randomly and independently at each site. We re...