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 ${ \bf B}$. We solve the model exactly for $s_1=1/2, 1, 5/2$, and for antiferromagnetic Heisenberg couplings ($J<0$), present ${ \bf M}({ \bf B})$ curves at low $T$ for these cases. Low-$T$ $C_V({ \bf B})$ curves for $s_1=1/2$ and electron paramagnetic susceptibility $\chi({ \bf B},\omega)$ for $s_1=1$ are also provided. For weak anisotropy interactions, we employ a perturbative treatment, and show that the Hartree and extended Hartree approximations lead to reliable analytic results at low $T$ and large $B$ for these quantities and for the inelastic neutron scattering cross-section $S({ \bf B}, { \bf q},\omega)$. Our results are discussed with regard to existing ${ \bf M}({ \bf B})$ experiments on $s_1=5/2$ Fe$_2$ dimer single molecule magnets, and suggest that one of them contains a substantial amount of single-ion anisotropy, without any sizeable global spin anisotropy. We urge further experiments of the above types on single crystals of Fe$_2$ and on some $s_=9/2$ [Mn$_4$]$_2$ dimers, in order to elucidate the precise values of the various microscopic interactions.
Categories: cond-mat.mes-hall cond-mat.stat-mech
