Sr₂ Ru O₄ : Broken Time-Reversal Symmetry in the Superconducting state

Using a phenomenological two-fluid model we derive the Kerr rotation of the polarization direction of reflected light from the surface of a superconductor in a state breaking time-reversal symmetry. We argue that this effect found recently in the superconducting state of $Sr_2RuO_4$ by Xia et al (Phys.Rev.Lett. {\bf 97}, 167002 (2006)) originates from the spontaneous magnetization in this superconductor. The temperature and the frequency dependencies of the effect are established. It is shown that the effect is determined by one of two mechanisms depending on the frequency of light that is larger or smaller than the plasma frequency. The mechanism originating from the gradient of chemical potential created by the electric field of light penetrating into the skin layer and important at frequencies larger than the plasma frequency was missed in the preliminary version of this paper (V.P.Mineev, arXiv:cond-mat/0703624v2).