Numerical Simulations of the Magnetodielectric response in Ising Pyrochlores
In this paper, we examine the magnetoelectric response of Ising pyrochlores, focusing on both the ordered antiferromagnetic state and the frustrated ferromagnetic case known as "spin-ice". We employ a model which accounts for magnetoelastic effects by considering the interplay between oxygen distortions and superexchange magnetic interactions within pyrochlores. This, together with numerical simulations, provides a tool to make quantitative comparisons with experiments. Our main target is then to see how to extract relevant information from this simple model, and to explore its limitations. We obtain a direct estimation of quantities such as the electric dipole moment, the central oxygen displacement and the effective magnetoelastic energy for the canonical spin-ice material \DTO. We also inquire about the possibility of using the electric dipole carried by magnetic monopoles to obtain a direct measure of their density. In each studied scenario the correlations between monopoles, induced by their number or by the magnetic background,renders these findings less straightforward than initially anticipated. Furthermore, the coupling between electrical and magnetic degrees of freedom provides additional tools to investigate magnetic order in these systems. As an example of this we discuss the phase diagram of the antiferromagnetic pyrochlore under applied magnetic field along the [111] direction. We find an instance where the phase stability at nonzero temperatures is not dictated by the energy associated with different ground states but (akin to the phenomenon of order-by-disorder) is instead determined by their accessibility to thermal fluctuations.