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