Antisymmetric double exchange and zero-field splittings in mixed-valence clusters

Abstract

The effect of an antisymmetric double exchange (AS DE) interaction in the mixed-valence (MV) dimeric dn−dn+1 and trimeric dn−dn−dn+1 clusters of orbitally non-degenerate ions is considered. In the dimeric clusters, strong isotropic Anderson–Hasegawa (AH) DE and Heisenberg exchange interactions (t–J model) form isotropic DE states E±0(S). In the MV dimers, the Moriya spin-flop hopping, which is determined by the spin-orbit coupling, is described by the effective Hamiltonian of an AS DE interaction HASDE=2iKabTab(Sb−Sa), where Kab=−Ka is a real AS vector coefficient, Tab is the isotropic transfer operator. The operator HASDE has a form of the spin-transfer interaction. Analytical expressions for the matrix elements of HASDE were obtained for dn−dn+1 clusters. The AS DE matrix elements depend on the projection M of S. AS DE mixes the AH DE states E+0(S) and E−0(S) with the same S of the different parity. The AS DE coupling and the Dzialoshinsky–Moriya (DM) AS exchange (HDM=Gab[Sa×Sb]) mix the AH states with different S of the same parity. AS DE forms the effective spin S′. In the d1−d2 and d9−d8 clusters, the AS DE contributions to the zero-field splitting (ZFS) parameters are different for the AH high-spin states E+(3/2) and E−(3/2). An AS DE leads to non-collinear orientation of spins in the MV pair and anisotropy of g-factors. An anisotropic DE contributes to ZFS. In the trimeric MV clusters, the isotropic DE forms the isotropic trigonal 2S+1Γ terms, Γ=A1, A2, E. The AS DE results in the new effect: the linear fine splittings Δ of the degenerate 2S+1E DE terms. The fine splittings Δ are proportional to the AS DE parameter KZ=(KZab+KZbc+KZca)/3 of the MV trimer. The vector of the AS DE interaction KZ is directed along the trigonal Z-axis of the MV trimer. The AS DE mixes the 2S+1A1 and 2S+1A2, 2S+1E and 2S+1E DE terms (ΔS=0, 1). In the trimeric MV clusters with high individual spins si, the AS DE and DM AS exchange mixing of the DE levels 2S+1Γ determines the contributions of the second order to the ZFS parameters DS, which are different for the Ai and E DE terms. For the [Cu(II)Cu2(I)] delocalized cluster, the AS DE ZFS Δ=2KZ√3of the ground 2E DE term determines strong anisotropy of the Zeeman splittings, anisotropy of g-factors (gZ≠0, gX,Y=0) and magnetic properties.