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Zero and finite temperature mean field study of magnetic field induced electric polarization in Ba2CoGe2O7

We investigate the spin-induced polarization in the multiferroic compound Ba2CuGe2O7 using variarional and finite temperature mean field approaches. The compound is described by a spin-3/2 Heisenberg model extended with easy plane anisotropy and Dzyaloshinskii-Moriya (DM) interaction. Applying magnetic field parallel to the [110] axis, three phases can be distinguished: (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. To reproduce the magnetization and polarization measurements reported in Murakawa et al. [Phys. Rev. Lett. 105, 137202 (2010)], we introduce an additional term in the Hamiltonian that couples the polarizations on neighboring tetrahedra. This results in the appearance of a canted ferrimagnetic phase for h < 1 T, characterized by a finite staggered polarization, as well as by a finite magnetization along the [-1,1,0] axis that leads to torque anomalies.