Symmetry requirements for current-induced spin magnetization specific to chiral crystals: Multipole analysis and the hidden spin glide symmetry

Current-induced spin magnetization (CISM) specific to chiral crystals is microscopically analyzed using multipole theory to identify the necessary hopping and spin-orbit couplings (SOCs). Tight-binding models capturing the essence of chiral crystals are introduced to investigate the multipole degrees of freedom possessed by the Hamiltonian. The results reveal that chiral SOC has a multipole degree of freedom specific to chiral crystals. Subsequently, the CISM is evaluated numerically and analytically. The results show that in addition to the chiral SOC, hopping along the $z$-axis, which is irrelevant from a multipole perspective, is crucial for CISM. This hopping is required to break the combined symmetry of wavevector translation and spin flipping, which we refer to as spin glide symmetry. This confirms that hopping irrelevant to chirality can play a crucial role in physical properties arising from chirality without contradicting the framework of multipole theory.