Magnetic properties of anisotropic superconductors

We calculate the frequency- and wave-vector-dependent particle-hole spin susceptibilities χ(q,ω) of anisotropic superconductors, such as heavy-fermion and, possibly, high-$T_c$ systems. This information is used to analyze the outcome of proposed neutron scattering experiments on these systems. It is found that the dependence of the cross sections on q can give detailed information about the anisotropic modification of the excitation spectrum. In addition, the polarization dependence of the cross section reflects directly the vector structure of the gap function, so that ultimately complete identification of a superconducting phase is possible. We discuss the implications of our results for the question of the relative thermodynamic stability of the various phases in the presence of external magnetic fields. A table of static susceptibilities for some possible phases of a cubic system with spin-orbit coupling is given. The large energy scales in high-$T_c$ systems make them ideal for these experiments.