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 hetero-binuclear 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. Besides, 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 inter-orbital $4f$ repulsion, U$_{ff}$ and crystal field parameter, $\Delta_f$ 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$_{ff}$, $\Delta_f$, spin-orbit interaction strength $\lambda$ 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$_{ff}$ and $\Delta_f$. In case of half-filling (Gd(III)) we find a reentrant low-spin state as U$_{ff}$ is increased, for small values of $\Delta_f$, which explains the recently reported apparent anomalous anti-ferromagnetic behaviour of Gd(III)-radical complexes. By varying U$_{ff}$ 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 L-S or j-j coupling scheme and we find that spin-orbit coupling does not significantly alter the basic picture.