The polariton spectrum in a centrosymmetric TbMnO3 is considered at low temperatures in a commensurate antiferromagnetic state after the spin-flop transition in a magnetic field. It is shown that a linear dependence of the electric polarizationP on a magnetic fieldH, observed in this state, is caused by ordering spins of the terbium ions. The magnetoelectric energy PGH (G is the antiferromagnetic vector of terbium) induces in a centrosymmetric TbMnO3 without a linear magnetoelectric effect the non-reciprocal spectrum of TM and TE polaritons. In antiferromagnetic 180° terbium domains, the speed of electromagnetic waves turns out to be different, and directions of the electric field precession and the polarization plane rotation have opposite signs. The order of these effects were found to be 10−3.
12.E. A. Turov, A. V. Kolchanov, V. V. Men'shenin, I. F. Mirsaev, and V. V. Nikolaev, Simmetria i fizicheskie svoistva antiferromagnetikov (The symmetry and physical properties of antiferromagnets) (Fizmatlit, Moscow, 2001).
13.R. Kajimoto, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, Phys. Rev. B70, 012401 (2004).