Spin Anisotropy Effects in Dimer Single Molecule Magnets

We present a model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general set of four quadratic anisotropic spin interactions with respective strengths $J$ and $\{J_j\}$, and with the magnetic induction ${\bf B}$. For antiferromagnetic Heisenberg couplings ($J<0$) and weak anisotropy interactions ($|J_j/J|\ll 1$), the low temperature $T$ magnetization ${\boldmath M}({\boldmath B})$ exhibits $2s_1$ steps, the height and midpoint slope of the $s$th step differing from their isotropic limits by corrections of ${\cal O}(J_j/J)^2$, but the position occurring at the energy level-crossing magnetic induction $B_ {s,s_1}^{\rm lc}(\theta,\phi)$, where $\theta,\phi$ define the direction of ${\boldmath B}$. We solve the model exactly for $s_1=1/2$, 1, and 5/2. For weakly anisotropic dimers, the Hartree approximation yields analytic formulas for ${\boldmath M}({\boldmath B})$ and $C_V({\boldmath B})$ at arbitrary $s_1$ that accurately fit the exact solutions at sufficiently low $T$ or large $B$. Low-$T$ formulas for the inelastic neutron scattering $S({\boldmath q},\omega)$ and the EPR $\chi(\omega)$ in an extended Hartree approximation are given. 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.