Long-range current-induced spin accumulation in chiral crystals

Chirality, a geometric property lacking inversion, mirror, and roto-inversion symmetries, governs various natural phenomena. Chiral materials exhibit intriguing effects, differing between enantiomers. Chirality-induced spin selectivity (CISS) generates a collinear spin current from a charge current, a phenomenon recently observed in solid-state materials with strong spin-orbit coupling (SOC). This chirality-dependent charge-to-spin conversion (CSC) has been attributed to the collinear REE. However, a reliable quantitative description of current-induced spin accumulation in chiral materials was lacking. This paper develops a computational approach using DFT and tight-binding Hamiltonians generated by the PAOFLOW code to calculate current-induced spin accumulation in periodic systems. The calculations are performed on tellurium (Te) and tantalum disilicide (TaSi2), comparing results with experimental data. The authors analyze the spin-orbit field's landscape and symmetry to explain spin transport properties in chiral crystals, demonstrating that Weyl-type SOC can generate a quasi-persistent spin helix that prevents spin randomization and leads to a long spin lifetime. This contrasts with conventional REE, where spin decoherence is a significant factor. The long spin lifetime in chiral materials due to this protection has significant implications for designing spintronics devices.

The introduction thoroughly reviews existing literature on chirality, CISS, and the REE in chiral materials. It highlights the lack of a reliable quantitative method for calculating current-induced spin accumulation and the intriguing observation of chirality-dependent charge-to-spin conversion in various materials, including tellurium and tantalum disilicide. The authors cite relevant studies exploring similar phenomena in various materials, highlighting the significance of their work in providing a comprehensive theoretical framework for understanding and predicting these effects.

The researchers employed a computational approach based on density functional theory (DFT) and tight-binding Hamiltonians generated using the PAOFLOW code. The spin accumulation, or current-induced spin polarization (CISP), is a non-equilibrium magnetization induced by an electric current flowing through a non-magnetic material with strong SOC. The approach calculates spin accumulation for arbitrary SOC, starting with the equilibrium electron distribution described by the Fermi distribution function. The non-equilibrium distribution due to charge current generates a net spin polarization, which can be calculated using semi-classical Boltzmann transport theory. This involves calculating the spin accumulation tensor χ, which is the ratio of spin polarization and charge current density. The induced spin accumulation per unit volume is calculated using the formula δs = χj, where j is the charge current. The induced magnetization per unit cell is then calculated. Accurate ab initio tight-binding (TB) Hamiltonians, constructed from self-consistent quantum-mechanical wavefunctions projected onto atomic orbitals, are used to evaluate the quantities required to compute the tensor χ. Calculations are performed for tellurium (Te) and tantalum disilicide (TaSi2), two chiral materials with strong SOC, and the results are compared with experimental data. The electronic structure of each material is analyzed to understand the spin texture and its influence on spin transport. The calculations consider temperature effects and compare results with values from nuclear magnetic resonance measurements.

The study calculated current-induced spin accumulation in Te and TaSi2. In Te, the spin texture is radial around the H and H' points, enforced by threefold screw and twofold rotational symmetries. The spin accumulation is largely parallel to the screw axis (kz), with smaller perpendicular components. The spin accumulation shows a strong dependence on chemical potential and temperature. The calculated magnetization agrees well with a previous model but is an order of magnitude lower than experimental estimates. The REE yields opposite magnetization signs for different enantiomers, confirming the chirality-dependent charge-to-spin conversion. In TaSi2, the spin texture is radial, with a persistent Sz component due to the elongated band shapes. Spin accumulation is considerably lower than in Te, possibly due to multiple bands with opposite polarization crossing the Fermi level. The analysis of spin textures, using a general Weyl Hamiltonian, demonstrates that chiral materials host a quasi-persistent spin helix in real space. This helix, a consequence of crystal symmetry, protects spins against scattering and ensures a large spin relaxation length, facilitating detection of bulk spin accumulation. This differs from conventional REE, where bulk spin accumulation randomizes easily. The generation of spin accumulation with a long spin lifetime is significant for spintronics applications.

The findings address the research question by quantitatively calculating the collinear REE in chiral crystals and explaining its long-range nature. The results show good agreement with recent experiments for Te, confirming that spin accumulation is responsible for the observed chirality-dependent charge-to-spin conversion. The demonstration of a quasi-persistent spin helix in chiral materials explains the observed long-range spin transport, unlike conventional REE where spin decoherence is prominent. This understanding of long-range spin transport, especially the effect of the quasi-persistent spin helix, is crucial for developing spintronics devices. The difference in spin accumulation between Te and TaSi2 is discussed, emphasizing the role of multiple bands in TaSi2. The method used, implemented in PAOFLOW, enables further calculations of spin transport in various materials. The authors note that while the experimental data for TaSi2 is not quantitative, their findings are consistent with the observed chirality-dependent spin transport.

The study successfully calculated the collinear REE for Te and TaSi2 using a DFT-based approach, validating the role of spin accumulation in chirality-dependent charge-to-spin conversion. The demonstration of a quasi-persistent spin helix protecting spins against scattering is a crucial finding, explaining long-range spin transport in chiral materials. This work significantly impacts spintronics device design, and the presented method allows for further exploration of spin transport in various materials. Future work could focus on investigating other chiral materials and exploring the influence of material defects and external fields on spin transport.

The calculated magnetization in Te is an order of magnitude lower than the experimental estimate. This discrepancy requires further investigation. The temperature dependence of spin accumulation in Te also needs further study. While the approach provides a quantitative method, direct comparison with experimental data for TaSi2 is limited by the qualitative nature of the existing experimental results.