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 ${\mathrm{Dy}}_2\mathrm{ScN}$@${\mathrm{C}}_{80}$.

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精确测量两个磁矩之间的角度及其在单分子磁体中的配置稳定性

双核镧系元素单分子磁体（SMM）低温磁耦合的一个关键参数是势垒 ${你}_{F\mathrm{一种}}$ 由于两者之间的交换和偶极相互作用 $4F$时刻。在这里，我们扩展了先前用于描述双核内富勒烯基态的赝自旋模型，以解释单离子各向异性轴方向的变化，并将其应用于两个 SMM${\mathrm{染料}}_2\mathrm{神经网络}$@${\mathrm{C}}_{80}$ 和 ${\mathrm{染料}}_2\mathrm{碳化硅}$@${\mathrm{C}}_{80}$. 而 X 射线磁圆二色性 (XMCD) 表明相同$J_z=15/2$两种分子中的Dy基态，Dy-Dy耦合强度和磁化稳定性都不同。我们证明了障碍的大小${你}_{F\mathrm{一种}}$ 以及两者之间的角度 $4F$ 磁矩直接从精确的温度相关磁化数据中确定，精度优于 $1^{\circ }$. 实验发现的夹角$4F$矩与计算的两个 Dy 离子的量化轴之间的角度非常一致。理论表明 Dy 磁矩的方向从 Dy 键轴到中心离子的更大偏差${\mathrm{染料}}_2\mathrm{碳化硅}$@${\mathrm{C}}_{80}$. 这可能解释了磁化强度较低的原因${\mathrm{染料}}_2\mathrm{碳化硅}$@${\mathrm{C}}_{80}$，虽然它表现出 $～49\%$ 更强的交换耦合 ${\mathrm{染料}}_2\mathrm{神经网络}$@${\mathrm{C}}_{80}$.