Influence of anisotropic magnetoelectric interaction on the spontaneous magnetocapacitance in TbMnO3

The spontaneous magnetocapacitance (i.e., the temperature dependence of dielectric constant in the absence of a magnetic field) of the orthorhombic ferroelectromagnet TbMnO3 in the incommensurable antiferromagnetic states is phenomenologically and numerically analyzed. It is shown that both the inhomogeneous magnetoelectric (ME) energy of the third order, which creates the electric polarization, and the ME anisotropy of the fourth order must be considered to get qualitative agreement with the experiment. The inhomogeneous ME energy induces the peak on the εzz(T) which satisfies the Curie law, and a small peak on the εxx(T) at the vicinity of the temperature of the ferroelectric (FE) ordering. The anisotropic ME energy of the fourth order is responsible for the appearance and character of the breaks on the εzz and εxx temperature dependences at the Néel temperature, namely, a decrease in εzz and an increase in εxx in the event of antiferromagnetic ordering. It is shown that the competition of the anisotropic ME energies of the fourth and third orders leads to the minimum on εzz(T) near the FE-transition temperature. The numerical calculation of spontaneous magnetocapacitance with the use of experimental data was performed. The signs and the orders of the constants of anisotropic ME-interactions in TbMnO3 were determined.