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 nonzero, 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 $d_{\mathrm{xy}}$ states. The current pattern around the impurity in this state is evaluated.

• Received 6 May 1999

DOI:https://doi.org/10.1103/PhysRevB.60.9744