Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations
Résumé
The radio-frequency dielectric response of the lead-free BaðZr 0.5 Ti 0.5 ÞO 3 relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio–based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors. Relaxors with a perovskite structure form an important family of functional materials that exhibit intriguing dielectric properties [1,2]: the real part of the frequency-dependent dielectric permittivity has a maximum with temperature, at T max , while the system remains macro-scopically paraelectric down to the lowest temperature, and T max depends on the frequency of the applied electric field, a phenomenon called dielectric relaxation. Different suggestions have been proposed to explain these macroscopic properties, such as nonlocal (electric or elastic) random fields (RFs) (electric or elastic fields on site i depending on the chemical disorder surrounding i) [3], and the possible existence and interplay of polar nanoregions (PNRs), i.e., polar instabilities that correlate the elementary dipoles on a few lattice constants. The location and properties of these PNRs would be dependent on the local chemical disorder that relaxors can exhibit on one of their sublattices [4]. The dynamics of the electric dipoles of such structures is believed to be associated with characteristic times much larger than typical atomic times, and being temperature dependent (as a result of thermal activation). These large time scales are responsible for the frequency dependence of the dielectric permittivity in the radio-frequency domain (from kHz up to several tens of MHz). Recently, microscopic description of relaxors, based on model Hamiltonians derived from first principles coupled to Monte Carlo (MC) or molecular dynamics (MD) simulations , have provided precious information about the effect of RFs on relaxor properties and the nature of these PNRs [5–12]. In heterovalent relaxors such as PbMg 1=3 Nb 2=3 O 3 (PMN) [13–16], the PNRs are suggested to arise from complex phenomena including strong nonlocal electric RFs [17,18]. In contrast, in homovalent relaxors such as BaðZr; TiÞO 3 (BZT), Ref. [9] numerically found that PNRs appear in regions where the chemical species driving the polar instability (Ti) is more abundant; i.e., it is the local RFs arising from the difference in polarizability between Ti and Zr ions that induce relaxor behavior, while nonlocal electric and elastic RFs have a rather negligible effect. Note that local RFs can lead to very long relaxation times in disordered magnets [19], which may also be the case for relaxors [15]. In order to gain a deeper understanding of relaxor ferroelectrics, it is highly desired to have numerical schemes that are able to simulate the most striking characteristics of relaxors, i.e., the radio-frequency dielec-tric relaxation. However, to the best of our knowledge, such schemes do not exist. One reason behind this paucity is that MD simulations are limited to a few nanoseconds, and thus cannot give access to the time scales required to mimic the radio-frequency dielectric response of relaxors. However, the kinetic Monte Carlo (KMC) method, which we recently applied to simulate the radio-frequency dielectric response of Li-doped KTaO 3 (KLT) [20], is able to reproduce such time scales. Nevertheless, in KLT, the elementary processes driving the dielectric response involve few degrees of freedom (hoppings of individual Li impurities), with rather temperature-independent energy barriers [20], two assumptions clearly not obeyed in relaxor ferroelectrics; this is evidenced, e.g., by the fact that PNRs do not exist above the Burns temperature and that the processes responsible for the dielectric response involve the collective motion of several microscopic degrees of freedom, since a PNR should extend over several unit cells.
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