Anisotropic exchange and non-collinear antiferromagnets on a noncentrosymmetric fcc structure as in the half-Heuslers

Abstract

The face-centered cubic (fcc) antiferromagnet is a typical example of a geometrically frustrated system in three dimensions: the classical nearest-neighbor fcc Heisenberg model exhibits a ground state manifold with large accidental degeneracy. Here, we study the most general nearest-and nextnearest-neighbor exchange model allowed by the space-group symmetry of the noncentrosymmetric half-Heusler compounds, which includes a variety of anisotropic coupling terms. We show that, while the so-called Kitaev and symmetric off-diagonal (Γ) interactions do not fully lift the accidental ground state degeneracy of the isotropic J1-J2 model, Dzyaloshinskii-Moriya interactions which are allowed in the half-Heuslers unambiguously select a noncollinear ground state. We then discuss the role of other effects in the ground state selection, such as quantum fluctuations and the coupling to a magnetic field, and show that these effects can stabilize noncoplanar (triple-q) orders. These results suggest that some half-Heusler antiferromagnets might host rare noncollinear/noncoplanar orders, which may in turn affect the transport properties of these semimetals.