Magnetization-induced local electric dipoles and multiferroic properties of Ba2CoGe2 O7

Ba2CoGe2O7, crystallizing in the noncentrosymmetric but nonpolar P4¯21m structure, belongs to a special class of multiferroic materials, whose properties are featured by the presence of rotoinversion symmetry. Unlike inversion, the rotoinversion symmetry can be easily destroyed by magnetization. Moreover, due to the specific structural pattern, in which magnetic Co2+ ions are separated by nonmagnetic GeO4 tetrahedra, the magnetic structure of Ba2CoGe2O7 is relatively soft. Altogether, this leads to a rich variety of multiferroic properties, where the magnetic structure of Ba2CoGe2O7 can be easily deformed by the magnetic field, inducing the net electric polarization in the direction depending on the magnetic symmetry of the system, which itself depends on the direction of the magnetic field. In this paper, we show that all these properties can be successfully explained on the basis of a realistic low-energy model, derived from first-principles electronic structure calculations for the magnetically active Co 3d bands, and the Berry-phase theory of electronic polarization. Particularly, we argue that the magnetization-induced electric polarization in Ba2CoGe2O7 is essentially local and can be expressed via the expectation values (p)=Tr[p] of some dipole matrices p and the site-diagonal density matrices D of the magnetic Co atoms. Thus, the basic aspects of multiferroic properties of Ba2CoGe2O7 can be understood already in the atomic limit, where both magnetic anisotropy and magnetoelectric coupling are specified by D. Then, the observable polarization is the macroscopic average over the microscopic electric dipoles (p). We discuss the behavior of interatomic magnetic interactions, the main contributions to the magnetocrystalline anisotropy, and the spin canting in the xy plane, as well as the similarities and differences between the proposed picture and the phenomenological model of spin-dependent p-d hybridization. © 2015 American Physical Society