Spin-orbit coupling in the double exchange model 2. Comparison of the antisymmetric double exchange with the Dzialoshinsky-Moriya antisymmetric exchange, spin canting and ZFS

摘要

The Dzialoshinsky-Moriya (D-M) antisymmetric exchange interaction is considered and compared with antisymmetric (AS) double exchange in the mixed-valence [Fe(II)Fe(III)] clusters. It is shown that the antisymmetric double exchange interaction (H-lX = iK(X)[((S) over cap (aX)-(S) over cap (bX))(T) over cap (ab) + (T) over cap (ab)((S) over capb(X)-(S) over cap (aX))]) is stronger than the D-M exchange interaction (H-DM(X) = G(X)[(S) over right arrow (a) x (S) over right arrow (b)](X)) in the valence-delocalized [Fe2.5+ Fe2.5+] cluster with strong double exchange, K-X/G(X) = -5B/2J, K-X G(X). The mixing of the ground valence-delocalized state Phi(0)(-) (S 9/2, M) with the first excited Phi(0)(-) (7/2, M') state (S' = S-1) of the same parity depends on both the AS double exchange and D-M exchange. In the valence-delocalized cluster, the admixture of the excited double exchange states to the ground valence-delocalized state Phi(0)(-) (S = 9/2) by the AS double exchange and D-M exchange results in non-zero expectation values of the local spins < S-aY > = -< S-bY > in Y-direction, that leads to the canting of the spins in the plane (YZ) perpendicular to the direction of the vectors K-X of the antisymmetric double exchange and G(X) of the D-M exchange. In the valence-delocalized S-gr = (9/2)(deloc) state, the deviations of spins from the parallel alignment, anisotropy of hyperfine (internal) fields on the Fe nuclei, anisotropy of the hyperfine constants depend on the parameters K-X, G(X), B and J. The spin canting induced by the AS double exchange and D-M exchange in the valence-delocalized [Fe2.5+FC2.5+] cluster (Sr = (9/2)(deloc)) is larger than the spin canting induced by the D-M exchange in the ferromagnetic localized [Fe(II)-Fe(III)](loc) cluster (S-gr = (9/2)(loc)). The mixing of the double exchange levels results in the antisymmetric double exchange and D-M exchange contributions to the ZFS parameters of the ground valence-delocalized state S-gr = (9/2)(deloc). (c) 2006 Elsevier B.V. All rights reserved.