We present the first experimental determination of the intra-atomic exchange energy between the inner $4f$ and the outer $6s5d$ shells in rare-earth elements. Inelastic electron tunneling spectroscopy on individual rare-earth atoms adsorbed on metal-supported graphene reveals an element-dependent excitation, with energy between 30 and 170 meV, linearly increasing with the spin angular momentum of the $4f$ shell. This observation is possible owing to the strong spin polarization of the outer shells, characteristic of rare-earth adatoms on graphene. This polarization gives rise to a giant magnetoresistance of up to 75% observed for Dy on $\mathrm{graphene}/\mathrm{Ir}(111)$ single-atom magnets. Density functional theory calculations of the $6s5d$ shell spin polarizations and of their intra-atomic exchange constants with the $4f$ shell yield exchange energies in agreement with the experimental values. These results prove that the description of the spin dynamics in RE considering only the $4f-5d$ interaction is oversimplified. A more realistic treatment requires us to consider a multishell intra-atomic exchange in which both $6s$ and $5d$ shells are taken into account, with the $4f-6s$ contribution possibly prevailing over the $4f-5d$ one. Our findings are important for the general understanding of magnetism in rare earths, whether they are in bulk compounds or as surface adsorbed atoms and clusters. The results presented here also push for a revision of the description of the spin dynamics in rare-earth-based systems.

中文翻译：

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测量稀土原子中的原子内交换能

我们提出了内部之间原子间交换能量的第一个实验确定 $4F$ 和外 $6s5d$稀土元素中的贝壳。对吸附在金属负载的石墨烯上的各个稀土原子的非弹性电子隧穿光谱学揭示了一种与元素有关的激发，其能量在30到170 meV之间，随分子的自旋角动量线性增加。$4F$贝壳。由于外壳的强自旋极化，这是可能的观察结果，这是石墨烯上稀土原子的特征。这种极化产生了高达75％的Dy上观察到的巨磁电阻$\mathrm{石墨烯}/铱（111）$单原子磁体。密度泛函理论的计算$6s5d$ 壳自旋极化及其与原子之间的原子内交换常数 $4F$壳的交换能量与实验值一致。这些结果证明，在RE中自旋动力学的描述仅考虑了$4F-5d$交互过于简单。更现实的治疗要求我们考虑多壳原子内交换，$6s$ 和 $5d$ 考虑到了炮弹 $4F-6s$ 贡献可能超过 $4F-5d$一。我们的发现对于一般了解稀土中的磁性非常重要，无论它们是散装化合物还是表面吸附的原子和团簇。此处提供的结果还推动修订基于稀土的系统中自旋动力学的描述。