The Linear and Non-linear Magnetic Response of a Tri-Uranium Single Molecule Magnet

We report here low temperature magnetization isotherms for the single molecule magnet, $(U{O}_2-L{)}_3$. By analyzing the low temperature magnetization in terms of $M=X_1\ast B+X_3\ast B^3$ we extract the linear susceptibility $X_1$ and the leading order nonlinear susceptibility $X_3$. We find that $X_1$ exhibits a peak at a temperature of $T_1=10.4K$ with $Ch{i}_3$ also exhibiting a peak but at a reduced temperature $T3=5K$. At the lowest temperatures the isotherms exhibit a critical field $B_c=11.5T$ marked by a clear point of inflection. A minimal Hamiltonian employing S=1 (pseudo) spins with only a single energy scale (successfully used to model the behavior of bulk f-electron metamagnets) is shown to provide a good description of the observed linear scaling between $T_1,T_3$ and $B_c$. We further show that a Heisenberg Hamiltonian previously employed by Carretta et al. (2013 J. Phys.Cond. Matt. 25 486001) to model this single molecule magnet gives formulas for the angle averaged susceptibilities (in the Ising limit) very similar to those of the minimal model.