Probability and spin densities of rare earth tri-positive ions

Abstract

Probability and spin densities for rare-earth tri-positive ions in their ground states are calculated using irreducible tensor operators and Racah double tensors, which enable an expansion of the densities in (vector) spherical harmonics. Graphical representation of such densities reveal characteristic features lost in schematic shapes predicted by considering only the sign of the electrostatic quadruple moments. As a rule, due to the spin–orbit coupling, the spin density is not collinear. The only exceptions are found in the fully aligned ( M=± J) states of the heavy rare earths, where J= L+ S and S( r)∥ z. The implications of spin-density patterns for the nature of anisotropic exchange interactions are discussed.