Rare Earth-Iron Exchange Interaction and Crystal Field-Like Terms in Garnets

Abstract

For ions with unquenched orbital angular momentum, the simple Heisenberg-Dirac form of exchange interaction between total spins ${\vec S_1}$ and ${\vec S_2},H = - 2J{\vec S_1} \cdot {\vec S_2}$ is no longer justified. Different orbitals lead generally to different exchange effects and this should be reflected in the form of the exchange Hamiltonian. The orbital operators are therefore to be introduced as discussed for the case of the direct exchange by Levy¹.