Spin-polarized sextuple excitations in ferromagnetic materials

Abstract

The most fundamental symmetry in condensed matter physics is the crystallographic symmetry, such that solids could exhibit unconventional excitations beyond Dirac and Weyl fermions. Among the unconventional fermions, the sextuple excitation has been predicted in many nonmagnetic materials. However, the study of magnetic sextuple excitations has fallen behind because of the complicated magnetic structures of materials. Here we perform a systematic search for ferromagnetic (FM) sextuple points (SPs) in the absence of spin-orbit coupling. Based on 230 space groups (SGs), we find there are 5 SGs that could host SPs at high-symmetry points. Regarding the stability of the sextuple excitation, we reveal that the minimum little point group at where the SP locates is ${\mathrm{T}}_{d}$. To support this result, we construct the effective model based on the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ method, from which the linear dispersion can be read off. Via first-principles calculations, we also identify 67 FM material candidates, which realize the SPs with completely/incompletely spin polarized. To support our theory, we pick one of the FM materials, ${\mathrm{Rb}}_{4}{\mathrm{O}}_{6}$, as an example in which there is a fully spin-polarized SP. Finally, our work paves the way to study the spin-polarized SPs and provides a platform to realize the spintronic associated with sextuple excitations.