Anomalous penetration of a magnetic field into ferromagnetic superconductors

An anomalous behavior of the magnetic induction $B$ is theoretically predicted near the surface of a semi-infinite crystal of a ferromagnetic superconductor. By taking account of the persistent current and the rare-earth magnetic moments, we solve Maxwell's equation under the condition that an external magnetic field $H_0$ is applied parallel to the surface. At high temperatures $T,B$ decays monotonically, and the penetration depth decreases with decreasing $T$. When $T$ becomes comparable to the exchange interaction energy, $B$ begins to effect an oscillatory damping. By decreasing $T$ further, we find that the oscillation amplitude of $B$ becomes anomalously large, and $\frac{B}{H_0}$ near the surface diverges at a critical temperature, below which a spontaneous magnetization bound near the surface appears. The origin of the spontaneous surface magnetization is discussed on the basis of an effective exchange interaction, for which the original ferromagnetic exchange interaction is screened by the persistent current, but the screening effect is imperfect near the surface.