Lanthanide contraction and magnetism in the heavy rare earth elements

Abstract

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.

Theory of electronic transport in random alloys with short-range order: Korringa-Kohn-Rostoker nonlocal coherent potential approximation

“…In particular, in combination with density functional theory [2][3][4][5] ͑DFT͒ and the Korringa-Kohn-Rostoker method of band theory, [6][7][8] it provides a fully first-principles description of such systems. A long history of successful applications [9][10][11][12][13][14] attests to the utility and accuracy to which the method is capable.…”

Verification of Anderson Superexchange in MnO via Magnetic Pair Distribution Function Analysis andab initioTheory

“…To pursue this further, we turned to the disordered local moment DLM-DFT of finite-temperature magnetism [16] in which strong electronic correlations evident in transition metal oxides [17] and lanthanide compounds [26,27], for example, are treated with the self-interaction correction [15]. When applied to MnO, the theory accounts for the magnitude of the insulating gap and its persistence into the paramagnetic phase, the magnetic ordering temperature and the onset of the type-II AF state.…”

Deviations from Matthiessen's rule and resistivity saturation effects in Gd and Fe from first principles

“…2 in Ref. 46, which was obtained using the self-interaction-corrected LSDA. Although the Fermi surface features appearing in these plots are immediately identifiable with each other, there are notable differences in their shapes.…”