  A joint theoretical approach, combining macroscopic symmetry analysis with
microscopic methods (density functional theory and model cluster Hamiltonian),
is employed to shed light on magnetoelectricity in Ba2CoGe2O7. We show that the
recently reported experimental trend of polarization guided by magnetic field
can be predicted on the basis of phenomenological Landau theory. From the
microscopic side, Ba2CoGe2O7 emerges as a prototype of a class of
magnetoelectrics, where the cross coupling between magnetic and dipolar degrees
of freedom needs, as main ingredients, the on-site spin-orbit coupling and the
spin-dependent O p - Co d hybridization, along with structural constraints
related to the noncentrosymmetric structural symmetry and the peculiar
configuration of CoO4 tetrahedrons.
