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

Abstract

One of the signatures of the face-centered cubic (fcc) antiferromagnet as a typical example of a geometrically frustrated system is the large ground state degeneracy of the classical nearest neighbor and next-nearest neighbor Heisenberg (isotropic) model on this lattice. In particular, collinear states are degenerate with non-collinear and non-coplanar ones: this degeneracy is accidental and is expected to be lifted by anisotropic exchange interactions. In this work, we derive the most general nearest and next-nearest neighbor exchange model allowed by the space-group symmetry of the noncentrosymmetric half-Heusler compounds, which includes three anisotropic terms: the so-called Kitaev, Gamma and Dzyaloshinskii-Moriya interactions -- most notably, the latter is allowed by the breaking of inversion symmetry in these materials and has not been previously been studied in the context of the fcc lattice. We compute the resulting phase diagram and show how the different terms lift the ground state degeneracy of the isotropic model, and lay emphasis on finding regimes where multi-q (non-collinear/non-coplanar) states are selected by anisotropy. We then discuss the role of quantum fluctuations and the coupling to a magnetic field in the ground state selection, and show that these effects can stabilize non-coplanar (triple-q) states. These results suggest that some half-Heusler antiferromagnets might host rare non-collinear/non-coplanar orders, which may in turn explain the unusual transport properties detected in these semimetals.

20 pages, 10 figures, 4 tables

References in corpus (14)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Topological $R$PdBi half-Heusler semimetals: a new family of non-centrosymmetric magnetic superconductors
• Half-Heusler topological insulators
• Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites
• Real space Berry curvature of itinerant electron systems with spin-orbit interaction
• Magnetotransport properties and giant anomalous Hall angle in half-Heusler compound TbPtBi
• Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions
• Monte Carlo study of first-order transition in Heisenberg fcc antiferromagnet
• Magnetism in S=1/2 Double-Perovskites with Strong Spin-Orbit Interactions
• Field-induced magnetic phase transitions and the resultant giant anomalous Hall effect in antiferromagnetic half-Heusler DyPtBi
• Frustrated antiferromagnets at high fields: the Bose-Einstein condensation in degenerate spectra
• Real-space perturbation theory for frustrated magnets: application to magnetization plateaus
• Quantum versus thermal fluctuations in the fcc antiferromagnet: alternative routes to order by disorder
• Magnon spectrum of the Weyl semimetal half-Heusler compound GdPtBi

Cited by in corpus (5)

• Anisotropic spin model and multiple-$Q$ states in cubic systems
• Unconventional Surface State Pairs in a High-Symmetry Lattice with Anti-ferromagnetic Band-folding
• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
• Pulling order back from the brink of disorder: Observation of a nodal line spin liquid and fluctuation stabilized order in K${}_2$IrCl${}_6$
• Analytic Formulas for the Anomalous Hall Effect in Itinerant Magnets