Metaferroics: Quantum Electric Dipoles Under Strong Magnetic and Electric Fields

We present properties of a Hamiltonian that has been developed to serve as a model for a multiferroic with quantum spins and a quantum electric dipole, under the influence of high fields. The Hamiltonian describes both the electric and magnetic degrees of freedom and is similar to the s = 1 model used by Shivaram et al (Phys. Rev. B89, 241107 (2014)) to study metamagnetism in heavy fermions. The two fields interact via a bilinear intereaction. We show the results for the temperature dependence of the linear as well as nonlinear susceptibilities. The linear susceptibility scales inversely with the energy gap between the s = 0 and s = +1, -1 levels. As in the single field case, the nonlinear third order susceptibility is negative at high temperatures. It has a positive peak at a lower temperature. In contrast, the fifth order susceptibility is positive at high temperatures and has a negative peak at lower temperatures. The cross response (dM/dE = dp/dB) is negative, at high temperatures it scales as T^-2 and has a peak at a critical temperature. There are a variety of profiles M(B, E, T), depending on the parameters, including some where the meta response consists of more than one step.