Persistent spin textures, altermagnetism and charge-to-spin conversion in metallic chiral crystals TM$_{3}$X$_{6}$

TL;DR

This paper investigates PST and altermagnetism in the chiral metallic TM$_3$X$_6$ family, focusing on NiTa$_3$S$_6$ and NiNb$_3$S$_6$. Using first-principles DFT calculations (VASP/PAOFLOW) and Kubo linear response, the authors map PST across large Fermi surfaces in the nonmagnetic phase and quantify charge-to-spin conversion via Rashba-Edelstein and spin Hall effects, including both $ ext{T}$-even and $ ext{T}$-odd contributions. They further analyze how antiferromagnetic ordering leads to altermagnetism, with spin textures and spin-transport tensors highly sensitive to the Néel vector orientation, sometimes suppressing REE but inducing additional symmetry-allowed components. Overall, TM$_3$X$_6$ emerge as a tunable platform for efficient charge-to-spin conversion and robust spin transport, leveraging crystallographic chirality, PST, and altermagnetism to enable directionally controlled spin phenomena.

Abstract

Chiral crystals, due to the lack of inversion and mirror symmetries, exhibit unique spin responses to external fields, enabling physical effects rarely observed in high-symmetry systems. Here, we show that materials from the chiral dichalcogenide family TM$_3$X$_6$ (T = 3d, M = 4d/5d, X = S) exhibit persistent spin texture (PST) - unidirectional spin polarization of states across large regions of the reciprocal space - in their nonmagnetic metallic phase. Using the example of NiTa$_{3}$S$_{6}$ and NiNb$_{3}$S$_{6}$, we show that PSTs cover the full Fermi surface, a rare and desirable feature that enables efficient charge-to-spin conversion and suggests long spin lifetimes and coherent spin transport above magnetic ordering temperatures. At low temperatures, the materials that order antiferromagnetically become chiral altermagnets, where spin textures originating from spin-orbit coupling and altermagnetism combine in a way that sensitively depends on the orientation of the Neel vector. Using symmetry analysis and first-principles calculations, we classify magnetic ground states across the family, identify cases with weak ferromagnetism, and track the evolution of spin textures and charge-to-spin conversion across magnetic phases and different Neel vector orientations, revealing spin transport signatures that allow one to distinguish Neel vector directions. These findings establish TM$_3$X$_6$ as a tunable platform for efficient charge-to-spin conversion and spin transport, combining structural chirality, persistent spin textures, and altermagnetism.

Figures (4)

• Figure 1: Geometry and nonrelativistic electronic properties of altermagnetic NiTa$_3$S$_6$. (a) Crystal structure. (b) Magnetization density isosurface ($M_s= \pm$0.02 $\mu_B$/cell) calculated around the Ni sites. (c) Band structure along the $H_1-\Gamma-H_2$ line. (d) Spin-polarized Fermi surface ($E=E_F$); only the outermost pair of Fermi sheets is shown. The red and blue colors correspond to spin-up and spin-down states, respectively.
• Figure 2: Relativistic electronic structure of NiTa$_3$S$_6$. (a) Band structure calculated for the nonmagnetic phase (left-hand panel), and the representative Fermi sheets (right-hand panels). The narrow cylindrical sheet corresponds to the innermost band, while the larger sheet below originates from one of the outermost bands. Note that the inequivalent high-symmetry points $H^{+}$ and $H^{-}$ are different from those in the nonrelativistic magnetic phase shown in Fig. 1. (b) Same as (a) but calculated for the altermagnetic phase with the Néel vector along the [001] direction. The color of the bands represents the $S_z$ projection of spin texture; $S_x$ and $S_y$ are negligible and they are not shown. Note that the inequivalent high-symmetry points are different from those in Fig. 1. The full set of Fermi surfaces for both phases is provided in the Supplementary Information.
• Figure 3: Collinear Rashba-Edelstein effect in NiTa$_3$S$_6$. $\mathcal{T}$-even REE response tensor $\chi$ vs chemical potential calculated for nonmagnetic phase (dashed lines), and altermagnetic phase with the Néel vector along the z-direction (solid lines). In both cases, we used the parameter $\Gamma$ = 0.03 eV determined from the comparison of measured and calculated charge conductivity (see Sec. S3 in the Supplementary Information.)
• Figure 4: Relativistic calculations of the spin Hall effect in NiTa$_3$S$_6$. (a) All $\mathcal{T}$-even spin Hall conductivity tensor components calculated for nonmagnetic (dashed lines) and altermagnetic phase with Néel vector along the z-direction (solid lines). (b) $\mathcal{T}$-odd spin Hall conductivity $\sigma^{x}_{xx}$ calculated for altermagnetic phase, assuming different values of $\Gamma$ = 10, 20, 30 and 40 meV. As shown in Table I, only one independent $\mathcal{T}$-odd component is present.