Local spin anisotropy effects upon the magnetization and specific heat of dimer single molecule magnets

We present an exactly solvable model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general quadratic global and local (single-ion) anisotropic spin interactions, and with the magnetic induction ${\bf B}$. For antiferromagnetic couplings and $s_1>1/2$, the low temperature $T$ magnetization ${\bm M}({\bm B})$ exhibits $2s_1$ steps of universal height and midpoint slope, the $s$th step of which occurs at the non-universal level-crossing magnetic induction $B_{s,s_1}^{\rm lc}(\theta,\phi)$, where $\theta,\phi$ define the direction of ${\bm B}$. The specific heat $C_V$ exhibits zeroes as $T\to0$ at these $B_{s,s_1}^{\rm lc}(\theta,\phi)$ values, which are equally surrounded by universal peak pairs as $T\to0$. The non-universal $B_{s,s_1}^{\rm lc}(\theta,\phi)$ values lead to a rich variety of magnetization plateau behavior, the structure and anisotropy of which depend upon the various global and local anisotropic spin interaction energies. We solve the model exactly for $s_1=1/2$, 1, and 5/2, and present ${\bm M}({\bm B})$ and $C_V({\bm B})$ curves at low $T$ for these cases. For weakly anisotropic dimers, rather simple analytic formulas for ${\bm M}({\bm B})$ and $C_V({\bm B})$ at arbitrary $s_1$ accurately fit the exact solutions at sufficiently low $T$ or large $B$. An expression for $B_{s,s_1}^{\rm lc}(\theta,\phi)$ accurate to second order in the four independent anisotropy energies is derived. Our results are discussed with regard to existing experiments on $s_1=5/2$ Fe$_2$ dimers, suggesting further experiments on single crystals of these and some $s_1=9/2$ Mn$_4$]$_2$ dimers are warranted.