Antisymmetric double exchange in mixed-valence dimeric clusters

Abstract

Abstract The model of an antisymmetric double exchange (AS DE) interaction is developed for the mixed-valence (MV) d n –d n +1 clusters of orbitally nondegenerate transition metal ions. The spin–orbit coupling effect is considered for the MV dimers, in which strong isotropic Anderson–Hasegawa (AH) double exchange and Heisenberg exchange interactions ( t – J model) between ions form isotropic states E ± 0 ( S ). The spin–orbit coupling effect in the AH double exchange (the Moriya spin-flop hopping) is described by the effective Hamiltonian of the AS double exchange interaction H ASDE =2 i K ab T ⌢ ab ( S b − S a ) , where K ab =− K ba is a real antisymmetric vector constant, T ⌢ ab is the isotropic transfer operator. Analytical expressions for the matrix elements of the AS DE interaction were obtained in the spin representation for all d n –d n +1 clusters. The AS DE interaction (vector transfer) results in the dependence of the double exchange matrix elements on the projection M of the total spin S . The AS double exchange mixes the AH double exchange states E + 0 ( S ) and E − 0 ( S ) with the same S of the different parity and also the AH states with different S of the same parity. AS DE forms the effective spin S ′ . The AS DE mixing of the AH levels results in the AS DE contributions to the zero-field splittings, which depend on S and parity. In the d 1 –d 2 (d 9 –d 8 ) cluster in the t – J model with an initial ZFS ( H ZFS 0 = D S 0 [ S z 2 − S ( S +1)/3]), the AS DE contributions δ K ± (3/2) to ZFS parameters Δ ZFS ± (3/2)=2 D S ± (3/2)=2[ D S 0 + δ K ± (3/2)] are different for the AH high-spin states E + (3/2) and E − (3/2): δ K ± (3/2)=4[ K z 2 −( K x 2 + K y 2 )/2] J /3 t ( t ±6 J ). The AS DE contributions δ K ± (5/2) to the ZFS parameters D S ± (5/2)= D S 0 + δ K ± (5/2) are different for the E + (5/2) and E − (5/2) states of the d 2 –d 3 cluster: δ K ± (5/2)=2 K z 2 J / t ( t ±15 J ). In the MV clusters, the AS double exchange contribution to the cluster ZFS parameters are more essential than the pure Dzialoshinsky–Moriya AS exchange contribution. The microscopic origin of the AS DE parameters K ab and anisotropy was considered for the d 9 –d 8 (d 1 –d 2 ) and d 1 –d 0 , d 9 –d 10 clusters with the taking into account the detailed crystal field states of d-ions and the spin–orbit coupling admixture of the excited states. An antisymmetric double exchange leads to noncollinear orientation of spins in the MV pair and anisotropy of g -factors. An anisotropic double exchange contributes to zero-field splittings.