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Understanding the valency of rare earths from first-principles theory

机译：从第一性原理了解稀土的化合价

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The rare-earth metals have high magnetic moments and a diverse range of magnetic structures. Their magnetic properties are determined by the occupancy of the strongly localized 4f electronic shells, while the outer s-d electrons determine the bonding and other electronic properties. Most of the rare-earth atoms are divalent, but generally become trivalent in the metallic state. In some materials, the energy difference between these valence states is small and, by changing some external parameter (such as pressure), a transition from one to the other occurs. But the mechanism underlying this transition and the reason for the differing valence states are not well understood. Here we report first-principles electronic-structure calculations that enable us to determine both the valency and the lattice size as a function of atomic number, and hence understand the valence transitions. We find that there are two types of f electrons: localized core-like f electrons that determine the valency, and delocalized band-like f electrons that are formed through hybridization with the s-d bands and which participate in bonding. The latter are found only in the trivalent systems; if their number exceeds a certain threshold, it becomes energetically favourable for these electrons to localize, causing a transition to a divalent ground state.
机译：稀土金属具有高磁矩和各种各样的磁结构。它们的磁性能由强定位的4f电子壳的占有率决定，而外部s-d电子则决定键合和其他电子性质。大多数稀土原子是二价的，但通常在金属状态下变为三价。在某些材料中，这些化合价态之间的能量差很小，并且通过更改某些外部参数（例如压力），会发生从一个到另一个的过渡。但是，这种转变的机理和价态不同的原因尚不十分清楚。在这里，我们报告第一性原理电子结构计算，这些计算使我们能够确定化合价和晶格尺寸作为原子序数的函数，从而了解化合价跃迁。我们发现有两种类型的f电子：决定价态的局域核状f电子和通过与s-d谱带杂交形成并参与键合的局域性带状f电子。后者仅在三价系统中发现。如果它们的数量超过某个阈值，则这些电子在能量上有利于局部化，从而导致转变为二价基态。

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