Charge-induced maximal spin states of a polynuclear transition-metal complex

We theoretically investigate the ground state spin of a polynuclear transition-metal complex as a function of the number of added electrons taking into account strong electron correlations. Our phenomenological model of the so-called [$2\times2$]-grid molecule incorporates the relevant electronic degrees of freedom on the four transition-metal centers (either Fe$^{2+}$ or Co$^{2+}$) and the four organic bridging ligands. Extra electrons preferably occupy redox orbitals on the ligands. Magnetic interactions between these ligands are mediated by transition-metal ions {\em and vice versa}. Using both perturbation theory and exact diagonalization we find that for certain charge states the maximally attainable total spin (either $S_{\mathsf{tot}}=3/2$ or $S_{\mathsf{tot}}=7/2$) may actually be achieved. Due to the Nagaoka mechanism, all unpaired electron spins couple to a total maximal spin, including unpaired electron spins on the metal-ions in the case of Co$^{2+}$. The parameters are chosen to be consistent with cyclovoltammetry experiments in which up to twelve redox states have been observed. The above effect may also be realized in other complexes with an appropriate connectivity between the redox sites. The maximal spin states of such a charge-switchable molecular magnet may be experimentally observed as spin-blockade effects on the electron tunneling in a three-terminal transport setup.