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

Abstract

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 1 X = i K X [ ( S ^ aX - S ^ bX ) T ^ ab + T ^ ab ( S ^ bX - S ^ aX ) ] ) is stronger than the D–M exchange interaction ( H DM X = G X [ S → a × S → b ] X ) in the valence-delocalized [Fe 2.5+ Fe 2.5+] cluster with strong double exchange, K X / G X = −5 B/2 J, K X ≫ G X . 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 〈 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 [Fe 2.5+Fe 2.5+] cluster ( S gr = (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.