Hund's coupling ($H_H=-J_H{\mathbf{S}}_1\cdot {\mathbf{S}}_2,J_H>0$)

An effective local exchange coupling can favor parallel electron spins in different orbitals on the same atom. The displayed sign convention represents that preference. It underlies the high-spin tendency in Hund's rules and the alignment of itinerant and core spins used in double exchange. The coupling is an effective description of intra-atomic Coulomb and exchange energies, rather than a separate classical magnetic force.