Zero- and finite-temperature mean field study of magnetic field induced electric polarization in Ba2CoGe2O7: Effect of the antiferroelectric coupling

Abstract

We investigate the spin induced polarization in the multiferroic compound Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ using variational and finite-temperature mean field approaches, with the aim to reproduce the peculiar behavior of the induced polarization in a magnetic field observed experimentally in Murakawa et al. [Phys. Rev. Lett. 105, 137202 (2010)]. The compound is usually described by a spin-3/2 Heisenberg model extended with easy-plane anisotropy and Dzyaloshinskii-Moriya (DM) interaction. By applying a magnetic field parallel to the $[110]$ axis, three phases can be distinguished in this model: (i) At high magnetic field, we find a partially magnetized phase with spins parallel to the fields and uniform polarization. (ii) Below a critical field, the ground state is a twofold-degenerate canted antiferromagnet, where the degeneracy can be lifted by a finite DM interaction. (iii) At zero field, a U$(1)$ symmetry-breaking phase takes place, exhibiting a Goldstone mode. We find that extending the Hamiltonian with an antiferroelectric term results in the appearance of a canted ferrimagnetic phase for $h\ensuremath{\lesssim}1$ T. This phase is characterized by a finite staggered polarization, as well as by a magnetization closing a finite angle with the applied field leading to torque anomalies.