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 4 f repulsion, U f f and crystal field parameter, ∆ f as the key parameters involved in controlling the type of exchange interaction between the rare earth 4 f and copper 3d spins. We have explored the nature of the ground state in the parameter space of U f f , ∆ f , spin-orbit interaction strength λ and the 4 f filling n f . We find that these systems show low-spin or high-spin ground state depending on the filling of the 4 f levels of the rare-earth ion and ground state spin is critically dependent on U f f and ∆ f . In case of half-filling (Gd(III)) we find a reentrant low-spin state as U f f is increased, for small values of ∆ f , which explains the recently reported apparent anomalous antiferromagnetic behaviour of Gd(III)-radical complexes. By varying U f f we also observe a switch over in the ground state spin for other fillings . We have introduced a spinorbit 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.