Hughes I D, Däne M, Ernst A, Hergert W, Lüders M, Poulter J, Staunton J B, Svane A, Szotek Z, Temmerman W M
Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK.
Nature. 2007 Apr 5;446(7136):650-3. doi: 10.1038/nature05668.
The heavy rare earth elements crystallize into hexagonally close packed (h.c.p.) structures and share a common outer electronic configuration, differing only in the number of 4f electrons they have. These chemically inert 4f electrons set up localized magnetic moments, which are coupled via an indirect exchange interaction involving the conduction electrons. This leads to the formation of a wide variety of magnetic structures, the periodicities of which are often incommensurate with the underlying crystal lattice. Such incommensurate ordering is associated with a 'webbed' topology of the momentum space surface separating the occupied and unoccupied electron states (the Fermi surface). The shape of this surface-and hence the magnetic structure-for the heavy rare earth elements is known to depend on the ratio of the interplanar spacing c and the interatomic, intraplanar spacing a of the h.c.p. lattice. A theoretical understanding of this problem is, however, far from complete. Here, using gadolinium as a prototype for all the heavy rare earth elements, we generate a unified magnetic phase diagram, which unequivocally links the magnetic structures of the heavy rare earths to their lattice parameters. In addition to verifying the importance of the c/a ratio, we find that the atomic unit cell volume plays a separate, distinct role in determining the magnetic properties: we show that the trend from ferromagnetism to incommensurate ordering as atomic number increases is connected to the concomitant decrease in unit cell volume. This volume decrease occurs because of the so-called lanthanide contraction, where the addition of electrons to the poorly shielding 4f orbitals leads to an increase in effective nuclear charge and, correspondingly, a decrease in ionic radii.
重稀土元素结晶为六方密堆积（h.c.p.）结构，并具有共同的外层电子构型，仅在其4f电子数量上有所不同。这些化学惰性的4f电子形成局域磁矩，通过涉及传导电子的间接交换相互作用耦合。这导致形成各种各样的磁结构，其周期性通常与底层晶格不匹配。这种不匹配的有序性与分隔占据和未占据电子态（费米面）的动量空间表面的“网状”拓扑结构相关。已知重稀土元素的该表面形状以及因此的磁结构取决于h.c.p.晶格的面间距c与原子间、面内间距a的比值。然而，对这个问题的理论理解还远未完成。在这里，我们以钆作为所有重稀土元素的原型，生成了一个统一的磁相图，明确地将重稀土元素的磁结构与其晶格参数联系起来。除了验证c/a比值的重要性外，我们发现原子晶胞体积在确定磁性质方面起着单独且独特的作用：我们表明随着原子序数增加，从铁磁性到不匹配有序性的趋势与晶胞体积的相应减小有关。这种体积减小是由于所谓的镧系收缩，即在屏蔽性差的4f轨道中添加电子会导致有效核电荷增加，相应地离子半径减小。
