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 $1^{\circ }$. 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 $\sim 49\%$ stronger exchange coupling than in ${\mathrm{Dy}}_2\mathrm{ScN}$@${\mathrm{C}}_{80}$.

• Received 21 May 2021
• Revised 4 November 2021
• Accepted 8 November 2021
• Corrected 5 December 2022

DOI:https://doi.org/10.1103/PhysRevB.104.224401

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Published by the American Physical Society