  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-1A) is ac-tive only in materials exhibiting nonpolar noncentrosymmetric
crystal classes with atoms occupy-ing exclusively non-polar lattice sites.
Consequently, the spin-momentum locking induced by D-1A is not electric
field-switchable. An alternative type of Dresselhaus symmetry, referred to as
D-1B, exhibits crystal class constraints similar to D-1A (all dipoles add up to
zero), but unlike D-1A, at least one polar site is occupied. We find that this
behavior exists in a class of ferri-chiral crys-tals, which in principle could
be reversed upon a change in chirality. Focusing on alkali metal chalcogenides,
we identify NaCu5S3 in the nonentiamorphic ferri-chiral structure, which
exhibits CuS3 chiral units differing in the magnitude of their Cu
displacements. We then synthesize NaCu5S3 (space group P6322) and confirm its
ferri-chiral structure with power x-ray diffraction. Our electronic structure
calculations demonstrate it exhibits D-1B spin splitting as well as a
ferri-chiral phase transition, revealing spin splitting interdependent on
chirality. Our electronic struc-ture calculations show that a few percent
biaxial tensile strain can reduce (or nearly quench) the switching barrier
separating the monodomain ferri-chiral P6322 states. We discuss what type of
external stimuli might switch the chirality so as to reverse the (non-helical)
Dresselhaus D-1B spin texture, offering an alternative to the traditional
reversal of the (helical) Rashba spin texture.
