The symmetry and magnetoelectric effects in garnet crystals and films
  The magnetoelectricity of garnets is considered by means of a symmetry and quantum mechanical combined analysis. It is shown, that the magnetoelectric effect is not realized in most garnets although the necessary condition of the crystal magnetic structure antisymmetry in them is held at low temperatures. Nevertheless, the effect can be observed in some garnets as well as other odd effects, namely, piezomagnetic effect, magnetic field evoked piezoelectric one, etc. It is also discovered that magnetic fields can induce specific antiferroelectric structures in garnet crystals and produce electric polarization in epitaxial films. The polarization can also be caused in a bulk crystal by an inhomogeneous magnetic field. 
A.I. Popov, D.I. Plokhov, and A.K. Zvezdin
cond-mat.mes-hall