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Register a new userEffective-Hamiltonian modeling of external pressures in ferroelectric perovskites
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The phase-transition sequence of a ferroelectric perovskite such as BaTiO_3 can be simulated by computing the statistical mechanics of a first-principles derived effective Hamiltonian [Zhong, Vanderbilt and Rabe, Phys. Rev. Lett. 73, 1861 (1994)]. Within this method, the effect of an external pressure (in general, of any external field) can be studied by considering the appropriate enthalpy instead of the effective Hamiltonian itself. The legitimacy of this approach relies on two critical assumptions that, to the best of our knowledge, have not been adequately discussed in the literature to date: (i) that the zero-pressure relevant degrees of freedom are still the only relevant degrees of freedom at finite pressures, and (ii) that the truncation of the Taylor expansion of the energy considered in the effective Hamiltonian remains a good approximation at finite pressures. Here we address these issues in detail and present illustrative first-principles results for BaTiO_3. We also discuss how to construct effective Hamiltonians in cases in which these assumptions do not hold.
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THz-range dielectric spectroscopy and first-principle-based effective-Hamiltonian molecular dynamics simulations were employed to elucidate the dielectric response in the paraelectric phase of (Ba,Sr)TiO3 solid solutions. Analysis of the resulting dielectric spectra suggests the existence of a crossover between two different regimes: a higher-temperature regime governed by the soft mode only versus a lower-temperature regime exhibiting a coupled soft mode/central mode dynamics. Interestingly, a single phenomenological coupling model can be used to adjust the THz dielectric response in the entire range of the paraelectric phase (i.e., even at high temperature). We conclude that the central peak is associated with thermally activated processes, and that it cannot be discerned anymore in the dielectric spectra when the rate of these thermally activated processes exceeds certain characteristic frequency of the system.
Ewald summation is an important technique used to deal with long-range Coulomb interaction. While it is widely used in simulations of molecules and solid state materials, many important results are dispersed in literature and their implementations are often buried deep in large software packages. Since reliable and systematic calculation of Coulomb interaction is critical for the investigation of perovskites, here we start from the fundamentals of Ewald summation and derive clear expressions for long-range charge-charge, dipole-dipole, and charge-dipole interactions, which can be readily used for numerical computations. We also provide the interaction matrix for efficient Monte Carlo simulations involving charges and dipoles, implementing them in a Python software package. A new type of interaction matrix, which accounts for the electrostatic energy change when ions are displaced, is also derived and implemented. These results are the foundations for the investigation of ferroelectric perovskites.
In published papers, the Gibbs free energy of ferroelectric materials has usually been quantified by the retention of 6th or 8th order polarization terms. In this paper, a newly analytical model of Gibbs free energy, thereout, a new model of polarization-electric field hysteresis loops in ferroelectric materials has been derived mathematically. As a model validation, four patterns of polarization-electric field hysteresis loops of ferroelectric materials have been depicted by using the model. The calculated results indicated that the self-similar model can characterize the various patterns of hysteresis loops in ferroelectric materials through adjusting the external excitation or the synthetically parameter (e.g., electric, temperature, and stress, etc.) employed in the model.
In order to understand the physical hysteresis loops clearly, we constructed a novel model, which is combined with the electric field, the temperature, and the stress as one synthetically parameter. This model revealed the shape of hysteresis loop was determined by few variables in ferroelectric materials: the saturation of polarization, the coercive field, the electric susceptibility and the equivalent field. Comparison with experimental results revealed the model can retrace polarization versus electric field and temperature. As a applications of this model, the calculate formula of energy storage efficiency, the electrocaloric effect, and the P(E,T) function have also been included in this article.
Recent experimental and theoretical work has shown that the double perovskite NaLaMnWO$_6$ exhibits antiferromagnetic ordering owing to the Mn $d$ states, and computational studies further predict it to exhibit a spontaneous electric polarization due to an improper mechanism for ferroelectricity [King textit{et al., Phys. Rev. B}, 2009, textbf{79}, 224428; Fukushima textit{et al., Phys. Chem. Chem. Phys.}, 2011, textbf{13}, 12186], which make it a candidate multiferroic material. Using first-principles density functional calculations, we investigate nine isostructural and isovalent $AA^{prime}$MnWO$_6$ double perovskites ($A$=Na, K, and Rb; $A^{prime}$=La, Nd, and Y) with the aim of articulating crystal-chemistry guidelines describing how to enhance the magnitude of the electric polarization through chemical substitution of the $A$-site while retaining long-range magnetic order. We find that the electric polarization can be enhanced by up to 150% in compounds which maximize the difference in the ionic size of the $A$ and $A^{prime}$ cations. By examining the tolerance factors, bond valences, and structural distortions (described by symmetry-adapted modes) of the nine compounds, we identify the atomic scale features that are strongly correlated with the ionic and electronic contributions to the electric polarization. We also find that each compound exhibits a purely electronic remnant polarization, even in the absence of a displacive polar mode. The analysis and design strategies presented here can be further extended to additional members of this family ($B$=Fe, Co, etc.), and the improper ferroelectric nature of the mechanism allows for the decoupling of magnetic and ferroelectric properties and the targeted design of novel multiferroics.
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