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

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.

9 pages, 9 figures, 2 tables

References in corpus (4)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Modelling the Localized to Itinerant Electronic Transition in the Heavy Fermion System CeIrIn5
• Layered Kondo lattice model for quantum critical beta-YbAlB4

Cited by in corpus (4)

• Anisotropic heavy Fermi-liquid formation in the valence fluctuating $\alpha$-YbAlB${}_4$
• Theory of the Electron Spin Resonance in the Heavy Fermion Metal β-YbAlB4
• High temperature antiferromagnetism in Yb based heavy fermion systems proximate to a Kondo insulator
• Intact Quasiparticles at an Unconventional Quantum Critical Point