Antisite disorder and Berry curvature driven anomalous Hall effect in the spin gapless semiconducting Mn$_2$CoAl Heusler compound

Spin gapless semiconductors exhibit a finite band gap for one spin channel and a closed gap for another spin channel, and they have emerged as a new state of magnetic materials with a great potential for spintronic applications. The first experimental evidence for spin gapless semiconducting behavior was observed in an inverse Heusler compound Mn$_2$CoAl. Here, we report a detailed investigation of the crystal structure and anomalous Hall effect in Mn$_2$CoAl using experimental and theoretical studies. The analysis of the high-resolution synchrotron x-ray diffraction data shows antisite disorder between Mn and Al atoms within the inverse Heusler structure. The temperature-dependent resistivity shows semiconducting behavior and follows Mooij's criteria for disordered metal. The scaling behavior of the anomalous Hall resistivity suggests that the anomalous Hall effect in Mn$_2$CoAl is primarily governed by an intrinsic mechanism due to the Berry curvature in momentum space. The experimental intrinsic anomalous Hall conductivity (AHC) is found to be ∼35 S/cm, which is considerably larger than the theoretically predicted value for ordered Mn$_2$CoAl. Our first-principles calculations conclude that the antisite disorder between Mn and Al atoms enhances the Berry curvature and hence the value of intrinsic AHC, which is in very good agreement with the experiment