SYMMETRY, SPIN-ORBIT INTERACTIONS, AND SPIN ANISOTROPIES

The origins of anisotropy in the effective spin Hamiltonian, describin g the ground manifold of Hubbard models with spin-orbit interactions, are critically discussed. For tetragonal symmetry, we shaw exactly tha t spin anisotropy can arise only if one includes both spin-orbit and C oulomb exchange interactions. For lower symmetries, additional anisotr opies arise from terms which were hitherto neglected. Our analytic res ults are supported by numerical solutions for single bond clusters. Th ese results can explain the easy plane anisotropy in the antiferromagn etic cuprates.