Symmetry-protected Spinful Magnetic Weyl Nodal Loops and Multi-Weyl Nodes in $5d^n$ Cubic Double Perovskites $(n=1,2)$

Abstract

Using both an effective three-band model and {\it ab initio} calculations, we have investigated various topological features in the cubic ferromagnetic $5d^{1,2}$ systems showing large spin-orbit coupling (SOC): Ba${}_2$NaOsO${}_6$, Sr${}_2$SrOsO${}_6$, and Ba${}_2$$B$ReO${}_6$ ($B$= Mg, Zn). In the presence of time-reversal symmetry ($\mathcal{T}$), spinless Dirac nodal loops linked to each other at the $W$ points appear in the mirror planes. Remarkably, breaking $\mathcal{T}$ leads to spinful magnetic Weyl nodal loops (MWNLs) that are robust even at large SOC and correlation strength $U$ variation due to the combination of mirror symmetry and broken $\mathcal{T}$. Additionally, there are two types of magnetic Weyl points with chiral charges $|\chi |=1,2$ along the $C_{4v}$ symmetry line, and another type-II MWNL encircling the zone center, that are dependent on $U$. Furthermore, the ferromagnetic Ba${}_2$ZnReO${}_6$ is an ideal half semimetal with MWNLs and magnetic Weyl nodes at the Fermi level without the interference of topologically trivial bulk states. These systems give rise to a remarkably large anomalous Hall conductivity ${\sigma }_{xy}$ of up to 1160 ($\Omega$cm)${}^{-1}$. Our findings may apply widely for $t_{2g}$ systems with cubic (or slightly distorted) fcc-like structures.

10 pages with 9 embedded figures (mirror corrections)

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• Large anomalous Hall effect induced by gapped nodal lines in GdZn and GdCd
• Unique surface-state connection between Weyl and nodal ring fermions in ferromagnetic material Cs2MoCl6