Spin anisotropy effects in dimer single molecule magnets

TL;DR

This paper models spin anisotropy effects in dimer single molecule magnets, providing exact solutions for specific spins, analyzing magnetic properties, and comparing results with experiments to infer microscopic interactions.

Contribution

It offers an exact solution for the spin interactions in dimer magnets with various spins and analyzes anisotropy effects, extending understanding of magnetic behavior in these systems.

Findings

Exact solutions for $s_1=1/2, 1, 5/2$ dimers with antiferromagnetic coupling.

Low-temperature magnetic and thermodynamic properties derived.

Evidence suggesting substantial single-ion anisotropy in Fe$_2$ dimers.

Abstract

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.