Ferri-chiral compounds with potentially switchable Dresselhaus spin splitting

Spin splitting of energy bands can be induced by relativistic spin-orbit interactions in materials without inversion symmetry. Whereas polar space-group symmetries permit Rashba (R-1) spin splitting with helical spin textures in momentum space, which could be reversed upon switching a ferroelectric polarization via applied electric fields, the ordinary Dresselhaus effect (D-1(A)) is active in materials exhibiting nonpolar noncentrosymmetric crystal classes with atoms occupying exclusively nonpolar lattice sites. Consequently, the spin-momentum locking induced by D-1(A) is not electric field switchable. Here we find a type of ferri-chiral materials with an alternative type of Dresselhaus symmetry, referred to as D-1(B), exhibiting crystal class constraints similar to D-1(A) (all dipoles add up to zero), but unlike D-1(A), at least one polar site is occupied. The spin splitting is associated with the crystalline chirality, which in principle could be reversed upon a change in chirality. Focusing on alkali metal chalcogenides, we identify NaCu5S3 in the nonenantiomorphic ferri-chiral structure, which exhibits CuS3 chiral units differing in the magnitude of their Cu displacements. We then synthesize NaCu5S3 (space group P6(3)22) and confirm its ferri-chiral structure with powder x-ray diffraction. Our electronic structure calculations demonstrate it exhibits D-1(B) spin splitting as well as a ferri-chiral phase transition, revealing spin splitting interdependent on chirality. Our electronic structure calculations show that a few percent biaxial tensile strain can reduce (or nearly quench) the switching barrier separating the monodomain ferri-chiral P6(3)22 states. We compute the circular dichroism absorption spectrum of the two ferri-chiral orientations and discuss what type of external stimuli might switch the chirality so as to reverse the (nonhelical) Dresselhaus D-1(B) spin texture. Our study suggests the design of ferri-chiral crystals as potential spintronic and optoelectronic materials.