Symmetry Analysis with Spin Crystallographic Groups: Disentangling Spin-Orbit-Free Effects in Emergent Electromagnetism

Abstract

Recent studies identified spin-order-driven phenomena such as spin-charge interconversion without relying on the relativistic spin-orbit interaction. Those physical properties can be prominent in systems containing light magnetic atoms due to sizable exchange splitting and may pave the way for realizations of giant responses correlated with the spin degree of freedom. In this paper, we present a systematic symmetry analysis based on the spin crystallographic groups and identify physical property of a vast number of magnetic materials up to 1500 in total. Absence of spin-orbital entanglement leads to the spin crystallographic symmetry having richer property compared to the well-known magnetic space group symmetry. By decoupling the spin and orbital degrees of freedom, our analysis enables us to take a closer look into the relation between the dimensionality of spin structures and the resultant physical properties and to identify the spin and orbital contributions separately. In stark contrast to the established analysis with magnetic space groups, the spin crystallographic group manifests richer symmetry including spin translation symmetry and leads to nontrivial emergent responses. For representative examples, we discuss geometrical nature of the anomalous Hall effect and magnetoelectric effect, and classify the spin Hall effect arising from the spontaneous spin-charge coupling. Using the power of computational analysis, we apply our symmetry analysis to a wide range of magnets, encompassing complex magnets such as those with noncoplanar spin structures as well as collinear and coplanar magnets. We identify emergent multipoles relevant to physical responses and argue that our method provides a systematic tool for exploring sizable electromagnetic responses driven by spin ordering.Comment: 58 pages, 7 figures, 6 table