Automated Generation of Commensurate Magnetic Structures based on Spin Space Groups and Graph Theory

Abstract

Magnetic structures with symmetry constraints are candidates for energetically favorable configurations. Enumerating these structures is essential for identifying experimental observations and provides unbiased, linearly stable, and optimally sampled reference configurations for energy fitting when extracting spin interactions. We present SpinGraph, an automated workflow generating symmetry-distinct magnetic configurations. SpinGraph is not only compatible with the more general spin space groups, but also allows precise control of the prescribed single- or multi-Q states superposition. For finite groups, we enumerate compatible subgroups directly. For spin space groups with a continuous or special spin-only part, the finite component is enumerated first and then combined with the compatible exact spin-only constraints. These actions are translated into graph constraints in real or Fourier space. The symmetry of every generated structure is re-evaluated after construction. Finally, we integrate SpinGraph with the magnetic analysis code AMATIS to perform a thorough calculation for the spin interactions of the insulating monolayer CrI3. SpinGraph complements the last part of AMATIS and realizes the fully automated workflow for the spin Hamiltonian construction, which is essential for studying phase transitions, spin textures, magnons, and spin dynamics.