Magnetic Impurities in d-wave Superconductors

We solve the problem of a magnetic impurity in a $d_{x^2-y^2}$-wave superconductor by a variational method. A moment is found to exist in the superconducting state only if the Kondo-temperature in the normal state is larger than the maximum in the superconducting gap-function. If a moment exists in the superconducting state, and provided spin-orbit coupling is non-zero, it induces a time-reversal breaking superconducting state locally around the inpurity which is a linear combination of the $d_{x^2-y^2}$ and $d_{xy}$ states. The current pattern around the impurity in this state are evaluated.