Spin-orbit coupling in the double exchange model 1. Antisymmetric double exchange in a valence-delocalized [Fe2.5+Fe2.5+] cluster

The model of antisymmetric double exchange interaction is developed for a valence-delocalized [Fe2.5+Fe2.5+] cluster, in which strong Anderson-Hasegawa double exchange (DE) interaction HDE=Tˆabt0 forms isotropic delocalized ground DE state with maximal spin Sgr = (9/2)deloc. Antisymmetric DE interaction originates from the combined effect of the spin-orbit coupling at the Fe(II) center and electron transfer between the excited states of the Fe(II) ion and ground state of the Fe(III) ion. The effective Hamiltonian of the antisymmetric DE coupling H1=i{K→ab[(S→a-S→b)Tˆab+Tˆab(S→b-S→a)]} includes the isotropic DE operator Tˆab and the spin operators (S→i-S→j) in the scalar product with the antisymmetric vector constant K→ab(K→ab=-K→ba). The antisymmetric double exchange interaction H1 (spin-transfer coupling) acts between the cluster states of different localizations. The parameter of the antisymmetric double exchange KX = (Kab)X = −10BΔg⊥ϑ(1 + tξ/tu) of the valence-delocalized [Fe2.5+Fe2.5+] cluster is proportional to the DE parameter B (B = tu/5), anisotropy of the g-factor Δg⊥ of the Fe2+ ion and the angle ϑ of the deformation, tu (=t0) and tξ is the electron transfer parameter in the ground and excited states, respectively, KY = 0, KZ = 0. The antisymmetric DE interaction is strong (|KX| ⩽ 100 cm−1) in the valence-delocalized [Fe2.5+Fe2.5+] cluster with strong Anderson-Hasegawa double exchange (Bexp = 1350 cm−1). The antisymmetric double exchange interaction mixes the Anderson-Hasegawa double exchange states 1) Φ-0(S,M) with Φ+0(S,M′=M±1) having the same total spin S and different parity and 2) Φ±0(S,M) with Φ±0(S±1,M′=M±1) of the same parity having different S (S′ = S ± 1). This mixture contributes to the magnetic anisotropy of the system.