Electronic structure and magnetism ofMn12O12clusters

To address the ferrimagnetic state of the ${\mathrm{Mn}}_{12}$ acetate matrix $\left[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}{(\mathrm{C}\mathrm{H}}_3{\mathrm{C}\mathrm{O}\mathrm{O})}_{16}{(\mathrm{H}}_2{\mathrm{O})}_4\right]$ we have performed all-electron gradient-corrected density-functional calculations on $(\mathrm{MnO}{)}_n$ with $n=1,$ 2, 4, and 12. In contrast to bulk MnO which is antiferromagnetic, the small $(\mathrm{MnO}{)}_n$ ($n=1,$ 2, and 4) clusters are ferromagnetic with Mn moments of $5.0{\mu }_B$ but the ground state of ${\mathrm{Mn}}_{12}{\mathrm{O}}_{12}$ is ferrimagnetic with a total magnetic moment of $20.0{\mu }_B$ as observed experimentally. The inner Mn sites in ${\mathrm{Mn}}_{12}{\mathrm{O}}_{12}$ are found to have localized moments of $4.1{\mu }_B$ which are antiferromagnetically coupled to two types of outer Mn with moments of $4.2{\mu }_B.$ The cluster is shown to be marked by ionic as well as covalent bonds between Mn $d$ and O $p$ electrons and a strong intracluster magnetic coupling.