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

TL;DR

This paper presents an exactly solvable model for dimer single molecule magnets with local spin anisotropy, analyzing their magnetization and specific heat, and providing insights into experimental observations and future research directions.

Contribution

The paper introduces a comprehensive exactly solvable model incorporating local and global anisotropic interactions in dimer magnets, with explicit solutions for various spins and analytic formulas for weak anisotropy.

Findings

Magnetization exhibits universal steps at non-universal level-crossing fields.

Specific heat shows zeroes and peaks at these crossing fields as temperature approaches zero.

Analytic formulas accurately describe low-temperature, high-field behavior for weak anisotropy.

Abstract

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.