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 wave-vector 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.