Co-existence of Topological Non-trivial and Spin Gapless Semiconducting Behavior in MnPO$_4$: A Composite Quantum Compound

Composite quantum compounds (CQC) are a classic example of quantum materials, which host more than one apparently distinct quantum phenomenon in physics. Magnetism, topological superconductivity, Rashba physics, etc. are a few such quantum phenomenon, which are ubiquitously observed in several functional materials and can coexist in CQCs. In this paper, we use ab initio calculations to predict the coexistence of two incompatible phenomena, namely topologically nontrivial Weyl semimetal and spin-gapless semiconducting (SGS) behavior, in a single crystalline system. SGS belongs to a special class of spintronics material, which exhibits a unique band structure involving a semiconducting state for one spin channel and a gapless state for the other. We report such a SGS behavior in conjunction with the topologically nontrivial multi-Weyl fermions in ${\mathrm{MnPO}}_{4}$. Interestingly, these Weyl nodes are located very close to the Fermi level with the minimal trivial band density. A drumhead-like surface state originating from a nodal loop around $Y$ point in the Brillouin zone is observed. A large value of the simulated anomalous Hall conductivity (1265 ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}{\mathrm{cm}}^{\ensuremath{-}1}$) indirectly reflects the topological nontrivial behavior of this compound. Such co-existent quantum phenomena are not common in condensed matter systems and hence it opens up a fertile ground to explore and achieve newer functional materials.