Isotropic and Antisymmetric Double-Exchange, Zero-Field, Zeeman, and Hyperfine Splittings in Trinuclear Valence-Delocalized [Cu37+] Clusters

Abstract

Valence delocalization in the [Cu3(7+)] trimer is considered in the model of the double-exchange coupling, in which full delocalization corresponds to the migration of the single d(x2-y2) hole and relatively strong isotropic double-exchange coupling. Strong double exchange results in the pairing of the individual spins in the delocalized trimer even at room temperature. The model explains the delocalized singlet 1A1 ground state in the planar Cu3(mu3-O) core by strong double exchange with positive double-exchange parameter t(0), whereas the delocalized triplet ground state of the [Cu3(7+)] trimer, which was observed in the Cu3(mu3-S)2 cluster, may be explained by the double exchange with relatively weak positive t(0): 0 < t(0) < 2J (degenerate 3E ground state) or negative t(0) (triplet 3A2 ground state). An analysis of the splitting of the delocalized degenerate 3E term requires inclusion of the antisymmetric double-exchange interaction, which takes into account the spin-orbit coupling in the double-exchange model. The cluster parameter KZ of the antisymmetric double-exchange coupling is proportional to t(0) and anisotropy of the g factor Deltag(parallel)[Cu(II)], KZ << t(0). Antisymmetric double exchange is relatively large in the [Cu3(7+)] cluster with the d(x2-y2) magnetic orbitals lying in the Cu3 plane [Cu3(mu3-O) core], whereas for the d(x2-y2) magnetic orbitals lying in the plane perpendicular to Cu3, antisymmetric double-exchange coupling is weak [Cu3(mu3-S)2 cluster]. The antisymmetric double-exchange coupling results in the linear zero-field splitting DeltaK = 2[equation: see text]KZ (approximately t(0)) of the delocalized degenerate 3E term that leads to strong anisotropy of the Zeeman splittings in the external magnetic field and a complex electron paramagnetic resonance (EPR) spectrum. The delocalized model of hyperfine interaction explains the hyperfine structure [10 hyperfine lines with the relative intensities 1:3:6:10:12:12:10:6:3:1 and the interval a/3] of the EPR transitions in the triplet states that was observed in the EPR spectra of the Cu3(mu3-S)2 cluster.