Magnetic structure of orthorhombic Dirac nodal line metal GdAlGe

Belonging to the rare-earth (R) RAlX (X=Si or Ge) family of materials, GdAlX is unique in that the increase in chemical pressure from substituting Ge for Si causes a structural phase transition from tetragonal (GdAlSi) to orthorhombic (GdAlGe). While there exists DFT analyses of the magnetism in GdAlGe based on the GdAlSi structure, yielding the A-type antiferromagnet, the analysis has yet to be done on the orthorhombic structure. In this pursuit, we performed DFT calculations to obtain the exchange-coupling constants for GdAlGe based on the Heisenberg model to create a simple physical picture of magnetism for this orthorhombic structure. Among the resulting exchange coupling constants J_i, where i denotes the ith nearest-neighboring Gd-Gd pairs, J₂, J₄, and J₆ are dominant and result in distorted triangular lattice layers formed by J₂ and J₄ in the bc plane—in contrast to the crystallographic layers in the ab plane—with inter-layer coupling J₆ along the a axis. Minimizing the exchange energy in reciprocal space results in a spiral phase with the wave vector Q=(0.94π,0,0), different from Q=(0,0,2π) for the A-type antiferromagnet. Our results call for experimental verification by resonant elastic x-ray scattering (REXS).