Long-range current-induced spin accumulation in chiral crystals

The study addresses how chirality and spin–orbit coupling in non-centrosymmetric crystals give rise to current-induced spin accumulation (CISP) that is collinear with charge current, i.e., a collinear Rashba–Edelstein effect (REE). While chirality-induced spin selectivity (CISS) has been widely reported in molecules and recently in solids, a reliable quantitative description of current-induced spin accumulation in bulk chiral materials has been lacking. The authors develop a first-principles-based computational framework to quantify CISP in periodic systems and apply it to two prototypical chiral materials with strong SOC, elemental tellurium (Te) and the disilicide TaSi2. They aim to connect crystal symmetry–enforced radial (Weyl-type) spin textures to the magnitude, anisotropy, and chirality dependence of charge-to-spin conversion, and to elucidate the intrinsic protection of spin transport due to a quasi-persistent spin helix emerging from the Weyl SOC.

The work builds on prior observations of chirality-induced spin selectivity (CISS) in molecules and solids, and on reports of chirality-dependent charge-to-spin conversion in materials with strong SOC. Traditionally, CISP has been studied in Rashba-type systems (2DEGs, interfaces, surfaces), with less attention to other SOC types (Dresselhaus, Weyl). Symmetry analyses and model studies have been used to attribute chirality-dependent responses to the collinear REE, but a quantitative, first-principles description remained missing. Recent experiments in Te and chiral disilicides (NbSi2, TaSi2) observed current-induced bulk magnetization and long-range spin transport; theoretical works have mapped gyrotropic responses in Te, identified Weyl-node-induced radial spin textures in chiral crystals, and established symmetry constraints on linear response tensors and unconventional spin Hall effects. This paper integrates these insights with an ab initio computational pipeline to compute spin accumulation beyond Rashba-only models.

• Spin accumulation formalism: Using semi-classical Boltzmann transport, the non-equilibrium spin density δs is obtained from the shift of the spin-polarized Fermi surface under an applied electric field. The spin accumulation tensor χ is defined as the ratio of spin-weighted to charge-weighted relaxation contributions (constant relaxation time approximation), enabling δs = χ j for current density j along arbitrary directions. The induced magnetization per unit cell is computed as m = − g μB V δs / h.
• Electronic-structure to tight-binding workflow: Self-consistent DFT calculations produce Bloch wavefunctions which are projected onto pseudoatomic orbitals to build accurate PAO tight-binding Hamiltonians with PAOFLOW. These are interpolated on ultra-dense k meshes to evaluate band velocities (from Hamiltonian gradients) and spin expectation values for all eigenstates, entering the χ tensor evaluation across energies and temperatures via the derivative of the Fermi–Dirac distribution.
• DFT details: QUANTUM ESPRESSO with fully relativistic pslibrary pseudopotentials, plane-wave cutoff 80 Ry, PBE GGA exchange–correlation. For Te: hexagonal 3-atom unit cell fully relaxed; ACBNO DFT+U (U=3.81 eV) applied, optimized lattice constants a=b=4.51 Å, c=5.86 Å; k grid 22×22×16. For TaSi2: hexagonal 9-atom cell, experimental lattice parameters a=b=4.78 Å, c=6.57 Å; internal coordinates relaxed; k grid 16×16×12. Gaussian smearing 0.001 Ry; SOC included self-consistently in all runs.
• PAOFLOW transport setup: Interpolated k meshes Te 140×140×110 and TaSi2 80×80×60 (up to 140×140×100 for convergence). Group velocities computed as (1/ħ) ∂H/∂k; spin expectation values ⟨ψ(k)|S|ψ(k)⟩. Zero-temperature δ(Ek−E) approximated by a Gaussian; for T>0 the exact Fermi–Dirac derivative used. Temperature effects on band structures themselves were not included.
• Symmetry and model analysis: Group-theoretical identification of allowed spin textures at high-symmetry points (D3h space-group context) using Bilbao server. Mapping to a linear-in-k Weyl SOC Hamiltonian HSO = αx kx σx + αy ky σy + αz kz σz added to free-electron dispersion, used to demonstrate an SU(2)-symmetry-related (quasi-)persistent spin helix protecting spin transport when αz ≫ αx, αy, consistent with DFT spin textures in Te and TaSi2.

• Te (trigonal, chiral SG 152/154): DFT reveals radial, nearly k-parallel (hedgehog) spin textures centered at H/H′ with a dominant Sz component enforced by screw symmetry, indicative of Weyl-type SOC and quasi-persistent character. Fermi surface comprises small hole pockets near H/H′ due to intrinsic p-type doping.
• Collinear REE response in Te: For j = 100 A cm−2, δsz (current along z) is the largest component; δsx and δsy (currents along x and y) are present but an order of magnitude smaller. The energy dependence of δsz reflects the top valence band structure, peaking near the local minimum at H (−8 meV below EF) and decreasing toward the next valence band of opposite polarization; doping to reach −130 meV would require unrealistically high hole densities (~2.3×10^19 cm−3 vs typical 10^14–10^17 cm−3). δsz reduces by about a factor of two from 0 K to 300 K, while δsx, δsy show weak temperature/doping dependence. The induced magnetization per unit cell is predicted to be ~10^9 μB/u.c. (at 0 K, magnitude depending on EF), matching model expectations but about an order of magnitude lower than estimates from NMR-derived experimental values (~10^10 μB). The sign of the induced magnetization reverses between enantiomers, consistent with chirality-dependent charge-to-spin conversion.
• TaSi2 (Weyl semimetal, SG 180/181): Complex multi-sheet Fermi surface with predominantly radial spin textures near high-symmetry points (e.g., K) and a persistent Sz component; symmetry analysis indicates most high-symmetry k-points can host Weyl-type radial textures (D3 or D6 little groups), with M (D2) allowing Weyl/Dresselhaus mixing. For j = 100 A cm−2, δs at EF is nearly two orders of magnitude smaller than in lightly doped Te (~10^11 vs ~10^13 cm−3); δsx is about one order smaller. The reduced magnitude is attributed to simultaneous crossing of oppositely polarized bands at EF. δs increases above EF due to an isolated strongly spin-polarized pocket at +20 meV. Unconventional SHE is symmetry-forbidden in SG 180, so it does not contribute to collinear spin transport.
• Spin-transport protection: The linear Weyl SOC with αz ≫ αx, αy yields an SU(2)-like symmetry and a (quasi-)persistent spin helix along the screw axis, protecting bulk spin accumulation from dephasing and enabling long spin lifetimes and macroscopic spin diffusion. Weak in-plane SOC breaks exact SU(2) but still permits sizable spin relaxation lengths, aligning with recent micrometer-scale spin transport observations in chiral crystals.
• Quantitative highlights: j = 100 A cm−2; Te δs magnitude near EF ~10^13 cm−3; TaSi2 δs near EF ~10^11 cm−3; room-temperature reduction of δsz in Te by ~2×; unrealistic doping threshold to reach −130 meV (~2.3×10^19 cm−3) contrasted with typical 10^14–10^17 cm−3.

The work quantitatively links chiral crystal symmetries and Weyl-type spin–orbit fields to collinear REE in bulk materials, addressing the lack of first-principles predictions for current-induced spin accumulation. In Te, the radial spin texture with dominant alignment along the screw axis enables spin accumulation parallel to current in all principal directions, with chirality controlling the sign. The computed energy and temperature dependences track the detailed valence-band structure and agree with experimental trends in Te nanowires, supporting a CISP origin of chirality-dependent CSC. In TaSi2, smaller δs values are rationalized by multi-band compensation at EF, while symmetry excludes unconventional SHE contributions to collinear transport, pointing again to CISP as the driver of observed chirality-dependent signals. The model analysis shows that Weyl SOC in chiral crystals induces a (quasi-)persistent spin helix, intrinsically protecting spin accumulation against scattering and enabling long-range transport, a crucial distinction from conventional REE where spins rapidly dephase. These insights clarify mechanisms behind macroscopic spin transport in chiral solids and inform materials/device design for efficient charge-to-spin conversion.

The authors introduce an ab initio DFT+PAOFLOW framework to compute current-induced spin accumulation in periodic crystals with arbitrary SOC and apply it to chiral Te and TaSi2. They demonstrate that radial (Weyl-type) spin textures in chiral crystals yield a collinear REE with chirality-dependent sign and, importantly, that a Weyl SOC–induced (quasi-)persistent spin helix intrinsically protects spin transport over long distances. Quantitative results for Te reproduce experimental trends and predict magnetization magnitudes within an order of experimental estimates; TaSi2 exhibits smaller δs at EF due to multi-band compensation but retains the symmetry-enabled transport protection. The approach enables predictive screening of chiral materials for spintronics. Future work could include explicit temperature-dependent band structures and scattering mechanisms, beyond constant relaxation time, and quantitative comparison to spin transport device measurements across broader chiral material families.

• Constant relaxation time approximation used in evaluating χ may oversimplify scattering; explicit momentum- and band-dependent τk and disorder effects are not included.
• Temperature dependence of electronic structures (band renormalization, phonon effects) was not considered; only the Fermi–Dirac derivative accounts for T.
• Predicted magnetization in Te is an order of magnitude lower than NMR-derived experimental estimates; underlying causes (e.g., τ, sample quality, dimensionality) remain to be clarified.
• The reduction of δsz at room temperature by about a factor of two lacks a full explanation and requires further systematic studies.
• For TaSi2, comparisons with experiments are qualitative due to limited quantitative transport data and complexities of multi-band compensation.
• The SU(2)-like protection is demonstrated within a linear Weyl SOC model; real materials have additional anisotropies and higher-order terms that may reduce ideal spin lifetimes.