A first-principles-based approach is developed to simulate dynamical properties, including complex permittivity and permeability in the GHz-THz range, of multiferroics at finite temperatures. It includes both structural degrees of freedom and magnetic moments as dynamic variables in Newtonian and Landau-Lifshitz-Gilbert (LLG) equations within molecular dynamics, respectively, with the couplings between these variables being incorporated. The use of a damping coefficient and of the fluctuation field in the LLG equations is required to obtain equilibrated magnetic properties at any temperature. No electromagnon is found in the spin-canted structure of BiFeO3. On the other hand, two magnons with very different frequencies are predicted via the use of this method. The smallest-in-frequency magnon corresponds to oscillations of the weak ferromagnetic vector in the basal plane being perpendicular to the polarization while the second magnon corresponds to magnetic dipoles going in and out of this basal plane. The large value of the frequency of this second magnon is caused by static couplings between magnetic dipoles with electric dipoles and oxygen octahedra tiltings.

The dynamic properties of elastic domain walls in BaTiO 3 were investigated using resonance ultrasonic spectroscopy (RUS). The sequence of phase transitions is characterized by minima in the temperature dependence of RUS resonance frequencies and changes in Q factors (resonance damping). Damping is related to the friction of mobile twin boundaries (90• ferroelectric walls) and distorted polar nanoregions (PNRs) in the cubic phase. Damping is largest in the tetragonal phase of ceramic materials but very low in single crystals. Damping is also small in the low-temperature phases of the ceramic sample and slightly increases with decreasing temperature in the single crystal. The phase angle between the real and imaginary part of the dynamic response function changes drastically in the cubic and tetragonal phases and remains constant in the orthorhombic phase. Other phases show a moderate dependence of the phase angle on temperature showing systematic changes of twin microstructures. Mobile twin boundaries (or sections of twin boundaries such as kinks inside twin walls) contribute strongly to the energy dissipation of the forced oscillation while the reduction in effective modulus due to relaxing twin domains is weak. Single crystals and ceramics show strong precursor softening in the cubic phase related to polar nanoregions (PNRs). The effective modulus decreases when the transition point of the cubic-tetragonal transformation is approached from above. The precursor softening follows temperature dependence very similar to recent results from Brillouin scattering. Between the Burns temperature (≈586 K) and T c at 405 K, we found a good fit of the squared RUS frequency [∼ (C 11 − C 12 )] to a Vogel-Fulcher process with an activation energy of ∼0.2 eV. Finally, some first-principles-based effective Hamiltonian computations were carried out in BaTiO 3 single domains to explain some of these observations in terms of the dynamics of the soft mode and central mode.

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THz-range dielectric spectroscopy and first-principle-based effective-Hamiltonian molecular dynamics simulations were used to elucidate the dielectric response in the paraelectric phase of (Ba, Sr)TiO 3 solid solutions. Our analysis suggests a crossover between two regimes: a highertemperature regime governed by the soft mode only versus a lower-temperature regime exhibiting a coupled soft mode/central mode dynamics. Interestingly, a single model can be used to adjust the THz dielectric response in the entire range of the paraelectric phase. The central peak cannot be discerned anymore in the dielectric spectra when the rate of underlying thermally activated processes exceeds certain characteristic frequency of the system.It is well known that the static permittivity of ferroelectric materials is related to frequencies of all polar phonon modes through the Lyddane-Sachs-Teller formula. [1] Near the phase transition, however, an additional low-frequency mode has to be often taken into account-the so-called central mode (CM). [2][3][4][5] A generic reason for this additional Debye-type excitation seems to be large-amplitude fluctuations between quasi-stable off-center ionic positions. Existence of such intrinsic CM could be very clearly demonstrated, e.g., below the cubic-tetragonal phase transition T C of BaTiO 3 . [6] Similar CM is also known to exist in the paraelectric phase. Phenomenological theories of the paraelectric CM have been developed by several authors. [2][3][4][5]7] All these approaches led to a coupled relaxator-oscillator dielectric response. However, an important question has been left open so far: whether the CM persists up to the highest temperatures, or rather it progressively disappears, or whether it disappears at some well-defined temperature T CM (>T C ).Unfortunately, it is much more difficult to obtain a clear-cut experimental evidence for the dielectric CM in the cubic perovskite phase. [2,4,8,9] The characteristic frequencies of the soft phonon-oscillator and CM in KNbO 3 and BaTiO 3 are so broad and close together that they can hardly be disentangled. Here, we describe a combined experimental and theoretical study of the technologically relevant mixed Ba x Sr (1-x) TiO 3 system (BST). Established characteristic temperature trends in the model parameters of the relaxator-oscillator dielectric response allow one to understand the existence of the temperature T CM , at which the CM in the dielectric spectra is appearing or disappearing.Basic dielectric properties of BST solid solutions were discussed, e.g., in Refs. 10 and 11 and works cited therein. Present experiments were carried out with a set of high-density BST ceramics with Ba:Sr ratio ranging from x = 0 to x = 1, prepared by methods described elsewhere (see Refs. 12 and 13). Low-frequency permittivity obtained from standard dielectric measurements (10 kHz) in the paraelectric phase was fitted to a Curie-Weiss law:As expected, [2,10] Curie constants were of the order of 10 5 K for all concentrations, while the extrapolation temper...

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The low-frequency (< 80cm −1 ) optical modes appearing in the dielectric spectra at low temperature are determined across the morphotropic phase boundary of disordered Pb(Zr,Ti)O3 solid solutions from the use of first-principles-based molecular dynamics simulations. In particular, the number of these modes, their resonant frequencies and dielectric spectral weights are obtained for any Ti composition ranging between 45% and 56% -which, according to the simulations, allows the existence of three different equilibrium phases all exhibiting both long-range-ordered ferroelectric motions and oxygen octahedral tiltings, that are of rhombohedral R3c, monoclinic Cc and tetragonal I4cm space groups. In particular, a compositional-induced anticrossing occurring within the bridging Cc state is revealed, and the difference in frequency between A ′ and A ′′ modes in the Cc state is linked to a quantity introduced here and termed the monoclinic depth. Moreover, the coupling between ferroelectric degrees of freedom and oxygen octahedral tiltings is found to play a crucial role on the characteristics of the low-frequency optical modes in the R3c, Cc and I4cm phases. Analytical models are further developed to reproduce and better understand such characteristics.

Ferroelectric and multiferroic materials form an important class of functional materials. Over the last twenty years, first-principles-based effective Hamiltonian approaches have been successfully developed to simulate these materials. In recent years, effective Hamiltonian approaches were further combined with molecular dynamics methods to investigate terahertz dynamical properties of various perovskites. With this combination, a variety of ferroelectric and multiferroic materials, including BaTiO3, Ba(Sr,Ti)O3, Pb(Zr,Ti)O3, BiFeO3, and SrTiO3 bulks and films have been simulated, which led to the understanding of complex phenomena and discovery of novel effects. In this review, we first provide technical details about effective Hamiltonians and molecular dynamics simulation. Then, we present applications of the combination of these two techniques to different perovskites. Finally, we also briefly discuss possible future directions of this approach.

The second harmonic (SH) generation from the highly epitaxial Al-doped ZnO film on sapphire was measured, using the femtosecond Ti:Sapphire laser at the near-resonant SH wavelength, in reflection geometry to avoid the sapphire's contribution in the conventional Maker fringes technique. By investigating SH intensities as a function of the azimuthal angle along the film's normal, we found that the sapphire substrate had a negligible contribution to the reflective SH signal and the film had a pure and well-aligned c-domain. We also developed a new method to calculate the component's ratios of the nonlinear susceptibility tensor by analyzing the polarization diagrams of SH intensities under the incidence with two different angles. The ratios indicate that Kleinman's symmetry is broken due to the absorption at SH wavelength and the dominant component of the nonlinear susceptibility tensor is d(33). Calibration using the Z-cut quartz shows a possible overestimate of the nonlinear response by Maker fringes technique.