Numerical Analysis of the EPR Spectrum of a Ni$_{4}$ Single-Molecule Magnet through Direct Diagonalization of the Four-Spin Hamiltonian

EPR studies have established the Giant Spin (GS) Hamiltonian parameters, $D$, $B_{4}^{0}$ and $B_{4}^{4}$, for members of the [Ni(hmp)(ROH)X]$_{4}$ (R = Me, Et, etc., and X = Cl and Br) family of single-molecule magnets.$^{1}$ Four $S$ = 1 Ni$^{II}$ ions, aligned on corners of a cubic core, couple ferromagnetically creating a spin $S$~=~4 ground state. Experiments on an isostructural Ni/Zn alloy established single-ion $d_{i}$ and $e_{i}$ parameters, as well as the orientations of the local magnetic axes.$^{1}$ A numerical model utilizing matrix diagonalization has simulated EPR spectra for the coupled $S$~=~1 Ni$^{II}$ ions using parameters from the Ni/Zn studies. Fourth order anisotropy parameters in the giant spin model arise from the isotropic Heisenberg coupling, \textit{JS}$_{1}$.$S_{2}$, and quadratic single-ion anisotropy in the four-spin Hamiltonian. Heisenberg coupling causes higher energy states to influence the $S$ = 4 ground state addressed in the GS model. Matching the lowest nine energies of the four-spin model to those of the GS model allows direct spectroscopic determination of $J$. $^{1}$E.-C. Yang et al., Inorg. Chem. \textbf{44}, 3827-3836 (2005).