RESPONSE OF A D(X(2)-Y(2)) SUPERCONDUCTOR TO A ZEEMAN MAGNETIC-FIELD

We study the response of a two-dimensional d(x2-y2) superconductor to a magnetic field that couples only to the spins of the electrons. In c ontrast to the s-wave case, the d(x2-y2) state is modified even at sma ll magnetic fields, with the gap nodes widening into normal, spin pola rized, pockets. We discuss the promising prospects for observing this in the cuprate superconductors in fields parallel to the Cu-O planes. We also discuss the phase diagram, inclusive of a finite momentum pair ing state with a linkage between the momentum of the pairs and the nod es of the relative wave function.