Precise measurement of angles between two magnetic moments and their configurational stability in single-molecule magnets

A key parameter for the low-temperature magnetic coupling of in dinuclear lanthanide single-molecule magnets (SMMs) is barrier $U_{FA}$ resulting from exchange and dipole interactions between two $4f$ moments. Here we extend pseudospin model previously used to describe ground state endofullerenes account variations orientation single-ion anisotropy axes apply it SMMs Dy$_2$ScN@C$_{80}$ Dy$_2$TiC@C$_{80}$. While x-ray circular dichroism (XMCD) indicates same $J_z=15/2$ Dy groundstate both molecules, Dy-Dy strength stability magnetization distinct. We demonstrate that magnitude angle moments are determined directly precise temperature-dependent data an accuracy better than $1^{\circ}$. The experimentally found angles excellent agreement with calculated quantisation ions. Theory a larger deviation bond central ion This may explain lower magnetisation Dy$_2$TiC@C$_{80}$, although exhibits $\sim 49\%$ stronger Dy$_2$ScN@C$_{80}$.