The Role of Crystal Symmetry in the Magnetic Instabilities of $\beta$-YbAlB$_4$ and $\alpha$-YbAlB$_4$

TL;DR

This study uses density functional theory to explore how crystal symmetry influences magnetic instabilities and superconductivity in $eta$-YbAlB$_4$ and $ ext{α}$-YbAlB$_4$, highlighting the role of boron coordination and structural angles.

Contribution

It reveals the impact of crystal symmetry and boron coordination on the electronic structure and Kondo scale in YbAlB$_4$ polymorphs, advancing understanding of their magnetic and superconducting properties.

Findings

Strong hybridization of 4f electrons with conduction electrons in both polymorphs.

The Kondo scale varies with the angle between B neighbors and Yb ion.

Structural differences influence electronic properties and superconductivity.

Abstract

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.