Studies of Mn$_{12}$-Ph Single Molecule Magnets by LT-STM and Modeling of Magnetic Stability Under Perturbation*

We study Mn$_{12}$O$_{12}$(C$_6$H$_5$COO)$_{16}$(H$_2$O)$_4$ (Mn$_{12}$-Ph) single-molecule magnets on a Cu(111) surface using low temperature scanning tunneling microscopy, LT-STM. We report the observation of Mn$_{12}$-Ph in isolation and in thin films, deposited through vacuum spray deposition onto clean Cu(111). The local tunneling current observed within the molecular structure shows a strong bias voltage dependency, which is distinct from that of the Cu surface. Furthermore, we identify an internal inhomogeneity in the bias behavior within a single molecule. To further understand the stability of the magnetic properties of the molecules while on the surface, we develop a theoretical model to study the stability of the net magnetic moment under deformation of the spin-spin interaction graph. We develop a spin Hamiltonian-type model to predict magnetic moments that are intrinsically robust under random shape deformations to the spin-graph structure. This spin moment is shown to be a weak topological invariant for molecules with sufficiently many spin centers, approximately 20 to 50.