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We have used a many-body model Hamiltonian to study the nature of themagnetic ground state of hetero-binuclear complexes involving rare-earth andcopper ions. We have taken into account all diagonal repulsions involving therare-earth 4f and 5d orbitals and the copper 3d orbital. Besides, we haveincluded direct exchange interaction, crystal field splitting of the rare-earthatomic levels and spin-orbit interaction in the 4f orbitals. We have identifiedthe inter-orbital $4f$ repulsion, U$_{ff}$ and crystal field parameter,$\Delta_f$ as the key parameters involved in controlling the type of exchangeinteraction between the rare earth $4f$ and copper 3d spins. We have exploredthe 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 findthat these systems show low-spin or high-spin ground state depending on thefilling of the $4f$ levels of the rare-earth ion and ground state spin iscritically 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, forsmall values of $\Delta_f$, which explains the recently reported apparentanomalous anti-ferromagnetic behaviour of Gd(III)-radical complexes. By varyingU$_{ff}$ we also observe a switch over in the ground state spin for otherfillings . We have introduced a spin-orbit coupling scheme which goes beyondL-S or j-j coupling scheme and we find that spin-orbit coupling does notsignificantly alter the basic picture.Comment: 22 pages, 11 ps figure

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