Symmetry-protected spinful magnetic Weyl nodal loops and multi-Weyl nodes in 5dn cubic double perovskites (n=1,2)

Using both an effective three-band model and ab initio calculations, we have investigated various topological features in the cubic ferromagnetic $5{d}^1,2$ systems showing large spin-orbit coupling (SOC): ${\mathrm{Ba}}₂{\mathrm{NaOsO}}₆, {\mathrm{Sr}}₂{\mathrm{SrOsO}}₆$, and ${\mathrm{Ba}}₂B{\mathrm{ReO}}₆$ ($B$=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 $|\ensuremath{\chi}|=1,2$ along the ${C}_4v$ symmetry line, and another type-II MWNL encircling the zone center, that are dependent on $U$. Furthermore, the ferromagnetic ${\mathrm{Ba}}₂{\mathrm{ZnReO}}₆$ 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 ${\ensuremath{\sigma}}_xy$ of up to 1160 (${\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$. Our findings may apply widely for ${t}_2g$ systems with cubic (or slightly distorted) fcc-like structures.