Simulating the radiofrequency dielectric response of relaxor ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo

The radiofrequency dielectric response of the lead-free Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from Real-Space Renormalization Group theories, allows depicting the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this {\it ab-initio}-based approach, and used as input data of Kinetic Monte Carlo simulations. The resulting numerical scheme allows to simulate the dielectric response for external field frequencies ranging from the kHz up to a few tens of MHz for the first time, and to, e.g., demonstrate that local (electric or elastic) random fields lead to the dielectric relaxation in the radiofrequency range that has been observed in relaxors.