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

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 Uff and crystal field parameter Δf 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 Uff, Δf, spin-orbit interaction strength λ, and the $4f$ filling nf. 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 Uff and Δf. In case of half filling [Gd(III)] we find a reentrant low-spin state as Uff is increased, for small values of Δf, which explains the recently reported apparent anomalous antiferromagnetic behavior of Gd(III)-radical complexes. By varying Uff 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-S or j-j coupling scheme and we find that spin-orbit coupling does not significantly alter the basic picture.