The lanthaball molecules {Pr13}, {Nd13}, and {Ce13} - a family of classical Heisenberg systems?

The lanthaball molecules {Pr13}, {Nd13}, and {Ce13} are recently synthesized spherical polycarbonatolanthanoid clusters that show in- teresting magnetic properties. Within each molecule 12 rare-earth ions are located on the vertices of a slightly distorted icosahedron and one spin is placed in the center of the icosahedron. Recent measurements are indicative of intra-molecular antiferromagnetic coupling. However, because of the unquenched orbital momenta of the rare-earth ions one has to take into account spin-orbit-coupling effects which make an ex- act quantum mechanical treatment of such systems very difficult or even impossible. Here, we report on a classical approach based on a Heisenberg model where the total angular momenta of the rare-earth ions interact via a multiple exchange interaction scenario. We show that our calculations are in good agreement with our experimental data for all three molecules. Furthermore, we discuss extensions of our approach to include spin-orbit-coupling effects