We predict a magnetic Weyl semimetal in the inverse Heusler ${\mathrm{Ti}}_2\mathrm{MnAl}$, a compensated ferrimagnet with a vanishing net magnetic moment and a Curie temperature of over 650 K. Despite the vanishing net magnetic moment, we calculate a large intrinsic anomalous Hall effect (AHE) of about 300 S/cm. It derives from the Berry curvature distribution of the Weyl points, which are only 14 meV away from the Fermi level and isolated from trivial bands. Different from antiferromagnets ${\mathrm{Mn}}_{3}X$ ($X=\mathrm{Ge}$, Sn, Ga, Ir, Rh, and Pt), where the AHE originates from the noncollinear magnetic structure, the AHE in ${\mathrm{Ti}}_2\mathrm{MnAl}$ stems directly from the Weyl points and is topologically protected. The large anomalous Hall conductivity (AHC) together with a low charge carrier concentration should give rise to a large anomalous Hall angle. In contrast to the Co-based  ferromagnetic Heusler compounds, the Weyl nodes in ${\mathrm{Ti}}_2\mathrm{MnAl}$ do not derive from nodal lines due to the lack of mirror symmetries in the inverse Heusler structure. Since the magnetic structure breaks spin-rotation symmetry, the Weyl nodes are stable without SOC. Moreover, because of the large separation between Weyl points of opposite topological charge, the Fermi arcs extent up to $75\%$ of the reciprocal lattice vectors in length. This makes ${\mathrm{Ti}}_2\mathrm{MnAl}$ an excellent candidate for the comprehensive study of magnetic Weyl semimetals. It is the first example of a material with Weyl points, large anomalous Hall effect, and angle despite a vanishing net magnetic moment.

• Received 24 October 2017
• Revised 11 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.060406