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

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 (H1X=iKX[(S^aX-S^bX)T^ab+T^ab(S^bX-S^aX)]) is stronger than the D-M exchange interaction (HDMX=GX[S→a×S→b]X) in the valence-delocalized [Fe2.5+ Fe2.5+] cluster with strong double exchange, KX/GX = −5B/2J, KX ≫ GX. The mixing of the ground valence-delocalized state Φ-0(S=9/2,M) with the first excited Φ-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 Φ-0(S=9/2) by the AS double exchange and D-M exchange results in non-zero expectation values of the local spins 〈saY〉 = −〈sbY〉 in Y-direction, that leads to the canting of the spins in the plane (YZ) perpendicular to the direction of the vectors KX of the antisymmetric double exchange and GX of the D-M exchange. In the valence-delocalized Sgr = (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 KX, GX, B and J. The spin canting induced by the AS double exchange and D-M exchange in the valence-delocalized [Fe2.5+Fe2.5+] cluster (Sgr = (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 (Sgr = (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 Sgr = (9/2)deloc.