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We investigate the spin-induced polarization in the multiferroic compoundBa2CuGe2O7 using variarional and finite temperature mean field approaches. Thecompound is described by a spin-3/2 Heisenberg model extended with easy planeanisotropy and Dzyaloshinskii-Moriya (DM) interaction. Applying magnetic fieldparallel to the [110] axis, three phases can be distinguished: (i) At highmagnetic field we find a partially magnetized phase with spins parallel to thefields and uniform polarization; (ii) Below a critical field the ground stateis a twofold degenerate canted antiferromagnet, where the degeneracy can belifted by a finite DM interaction; (iii) At zero field a U(1) symmetry breakingphase takes place, exhibiting a Goldstone-mode. To reproduce the magnetizationand polarization measurements reported in Murakawa et al. [Phys. Rev. Lett.105, 137202 (2010)], we introduce an additional term in the Hamiltonian thatcouples the polarizations on neighboring tetrahedra. This results in theappearance of a canted ferrimagnetic phase for h < 1 T, characterized by afinite staggered polarization, as well as by a finite magnetization along the[-1,1,0] axis that leads to torque anomalies.

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