Exchange interaction in binuclear complexes with rare-earth and copper ions: A many-body model study

Abstract

We have used a many-body model Hamiltonian to study the nature of the magnetic ground state of heterobinuclear complexes involving rare-earth and copper ions. We have taken into account all diagonal repulsions involving the rare-earth $4f$ and $5d$ orbitals and the copper $3d$ orbital. In addition, we have included direct exchange interaction, crystal field splitting of the rare-earth atomic levels and spin-orbit interaction in the $4f$ orbitals. We have identified the interorbital $4f$ repulsion ${U}_{\mathrm{ff}}$ and crystal field parameter ${\ensuremath{\Delta}}_{f}$ as the key parameters involved in controlling the type of exchange interaction between the rare earth $4f$ and copper $3d$ spins. We have explored the nature of the ground state in the parameter space of ${U}_{\mathrm{ff}},$ ${\ensuremath{\Delta}}_{f},$ spin-orbit interaction strength $\ensuremath{\lambda},$ and the $4f$ filling ${n}_{f}.$ We find that these systems show low-spin or high-spin ground state depending on the filling of the $4f$ levels of the rare-earth ion and ground state spin is critically dependent on ${U}_{\mathrm{ff}}$ and ${\ensuremath{\Delta}}_{f}.$ In case of half filling [Gd(III)] we find a reentrant low-spin state as ${U}_{\mathrm{ff}}$ is increased, for small values of ${\ensuremath{\Delta}}_{f},$ which explains the recently reported apparent anomalous antiferromagnetic behavior of Gd(III)-radical complexes. By varying ${U}_{\mathrm{ff}}$ we also observe a switch over in the ground state spin for other fillings. We have introduced a spin-orbit coupling scheme which goes beyond the $L\ensuremath{-}S$ or $j\ensuremath{-}j$ coupling scheme and we find that spin-orbit coupling does not significantly alter the basic picture.