The Role of Crystal Symmetry in the Magnetic Instabilities of $β$-YbAlB$_4$ and $α$-YbAlB$_4$

Details The Role of Crystal Symmetry in the Magnetic Instabilities of $β$-YbAlB$_4$ and $α$-YbAlB$_4$ The Role of Crystal Symmetry in the Magnetic Instabilities of $β$-YbAlB$_4$ and $α$-YbAlB$_4$

2010-12-06

arxiv.org/abs/1012.1249v1

Phys. Rev. B 82, 235101 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

9 pages, 9 figures, 2 tables

Scientific paper

10.1103/PhysRevB.82.235101

Density functional theory methods are applied to investigate the properties of the new superconductor $\beta$-YbAlB$_4$ and its polymorph $\alpha$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $\beta$-YbAlB$_4$ and $\alpha$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $\beta$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $\beta$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.

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