Extended Berry Curvature Tail in Ferromagnetic Weyl Semimetals NiMnSb and PtMnSb

Heusler compounds belong to a large family of materials and exhibit numerous physical phenomena with promising applications, particularly ferromagnetic Weyl semimetals for their use in spintronics and memory devices. Here, anomalous Hall transport is reported in the room-temperature ferromagnets NiMnSb (half-metal with a Curie temperature (TC) of 660 K) and PtMnSb (pseudo half-metal with a TC of 560 K). They exhibit 4 mu B/f.u. magnetic moments and non-trivial topological states. Moreover, NiMnSb and PtMnSb are the first half-Heusler ferromagnets to be reported as Weyl semimetals, and they exhibit anomalous Hall conductivity (AHC) due to the extended tail of the Berry curvature in these systems. The experimentally measured AHC values at 2 K are 1.8 x 102 Omega-1 cm-1 for NiMnSb and 2.2 x 103 Omega-1 cm-1 for PtMnSb. The comparatively large value between them can be explained in terms of the spin-orbit coupling strength. The combined approach of using ab initio calculations and a simple model shows that the Weyl nodes located far from the Fermi energy act as the driving mechanism for the intrinsic AHC. This contribution of topological features at higher energies can be generalized. Anomalous Hall conductivity (AHC) is strongly influenced by topological property type and its proximity to the Fermi energy (EF). It is generally assumed that the topology near to the EF has a greater impact on the AHC than the topology further away from the EF. However, the new discovery, as reported in the manuscript, demonstrates that the AHC is determined solely by Berry curvature (BC), even when it is located far away from the EF (right panel). This effect is named as extended Berry curvature tail effect, where the source of BC, i.e., Weyl node does not necessarily have to be close to EF. The effect can spread beyond EF as long as the topological band is clean (left panel: orange and gree bands)and there is no interference from other trivial bands. image