Field-induced metal-insulator transition, Chern insulators, and topological semimetals in a clean magnetic semiconductor GdGaI

TL;DR

This paper investigates how magnetic order in GdGaI induces various topological phases, including Chern insulators and semimetals, and how external magnetic fields can tune these phases and metal-insulator transitions.

Contribution

It introduces an effective theory linking magnetic order to topological electronic phases in GdGaI, revealing tunable Chern insulators and semimetals driven by magnetic and external field manipulations.

Findings

Identifies trivial and nontrivial Chern insulator phases with Chern numbers 0 and ±4.

Shows the phase boundary involves double-Weyl semimetals explaining the Chern number jump.

Demonstrates magnetic field tuning induces insulator-metal transitions and stabilizes additional topological phases.

Abstract

Non-coplanar magnetic order in low-carrier-density semiconductors provides a platform on which spin-charge coupling can reshape the electronic structure and induce nontrivial topological phases. Motivated by the recent discovery of the four-sublattice triple-$q$ order in the magnetic semiconductor GdGaI, we study an effective theory that couples a Ga $4p$ hole pocket at the $\Gamma$ point to three Gd $5d$ electron pockets at the $M$ points through four exchange channels. For the antiferromagnetic umbrella state with zero net magnetization, the model hosts trivial ($C = 0$) and $C = \pm 4$ Chern insulator phases separated by metallic regions; by deriving an analytical low-energy theory at the $\Gamma$ point, we show that the topological phase boundary is described by two degenerate double-Weyl semimetals, naturally explaining the $\Delta C = 4$ jump in the Chern number. In addition, a nodal-line-like state pinned near the Fermi level emerges in the absence of the $p$-$d$ exchange coupling, which separates the $C=\pm4$ phases for $\theta=\arccos(1/3)$ into two. Tuning the canting angle by an external magnetic field drives an insulator-to-metal transition out of the Chern insulator phase while leaving the trivial insulator largely intact, and stabilizes an additional $C = \pm 2$ Chern insulator phase when the uniform-magnetization exchange couplings become appreciable. These results identify GdGaI and its sister compounds as highly tunable platforms for realizing topological phases and field-induced metal-insulator transitions in clean magnetic semiconductors.