The different shapes of spin textures as a journey through Brillouin zone chiral and polar symmetries

Abstract

Crystallographic space group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin Zone (BZ) from one k-point to another for a fixed CPGS, it is expected that the wavevector point group symmetry (WPGS) can change, and consequently a qualitative change in the texture of the spin polarization (the expectation value of spin operator ${\vec{S}}^{n{k}_0}$ in Bloch state $u(n,k)$ and the wavevector $k_0$). However, the nature of the spin texture (ST) change is generally unsuspected. In this work, we determine a full classification of the linear-in-$k$ spin texture patterns based on the polarity and chirality reflected in the WPGS at $k_0$. The spin-polarization vector ${\vec{S}}^{n{k}_0}$ controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wavevector $k$ in non-polar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry of the crystal. For example, it is usually established that spin-momentum locking effect requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple ST near band edges at different $k$-valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different ST near band edges.

arXiv comment28 pages and 9 figures

References in corpus (25)

• Topological Insulators
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Type-II Weyl Semimetals
• New Perspectives for Rashba Spin-Orbit Coupling
• Topological Materials: Weyl Semimetals
• Topological quantum chemistry
• AFLOW: An automatic framework for high-throughput materials discovery
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• The (High Quality) Topological Materials In The World
• Topological classification of crystalline insulators through band structure combinatorics
• Giant momentum-dependent spin splitting in centrosymmetric low Z antiferromagnets
• Hidden spin polarization in inversion-symmetric bulk crystals
• Origin of giant bulk Rashba splitting: Application to BiTeI
• Ferroelectricity and Rashba effect in GeTe
• Ferroelectric Rashba Semiconductors as a novel class of multifunctional materials
• Higher-order contributions to the Rashba-Bychkov effect with application to Bi/Ag(111) surface alloy
• Radial spin texture in elemental tellurium with chiral crystal structure
• Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure
• Operando imaging of all-electric spin texture manipulation in ferroelectric and multiferroic Rashba semiconductors
• The Rashba Scale: Emergence of Band Anti-Crossing as a Design Principle for Materials with Large Rashba coefficient
• Zeeman-type spin splitting in non-magnetic three-dimensional compounds: Materials prediction and electrical control
• Spin-polarization control driven by a Rashba-type effect breaking the mirror symmetry in two-dimensional dual topological insulators
• Band splitting with vanishing spin polarizations in noncentrosymmetric crystals
• Digging up bulk band dispersion buried under a passivation layer
• First-principles theory of giant Rashba-like spin-splitting in bulk ferroelectrics

Cited by in corpus (34)

• Observation of Spin Splitting in Room-Temperature Metallic Antiferromagnet CrSb
• Long-range current-induced spin accumulation in chiral crystals
• Parallel spin-momentum locking in a chiral topological semimetal
• Analogs of Rashba-Edelstein effect from density functional theory
• Rashba and Dresselhaus effects in 2D Pb-I-based perovskites
• Antiferromagnetism, spin splitting, and spin-orbit interaction in MnTe
• Collinear Rashba-Edelstein effect in non-magnetic chiral materials
• Unconventional spin textures emerging from a universal symmetry theory of spin-momentum locking
• Unconventional Spintronics from Chiral Perovskites
• Ferroelectric control of charge-to-spin conversion in WTe${}_2$
• Diversity of Radial Spin Textures in Chiral Materials
• High throughput inverse design and Bayesian optimization of functionalities: spin splitting in two-dimensional compounds
• Robust Zeeman-type band splitting in sliding ferroelectrics
• Spin-momentum locking from topological quantum chemistry: applications to multifold fermions
• Full-zone Persistent Spin Textures with Giant Spin Splitting in Two-dimensional Group IV-V Compounds
• Projected spin texture as a bulk indicator of fragile topology
• Anomalous-Hall Neel textures in altermagnetic materials
• Unconventional Josephson supercurrent diode effect induced by chiral spin-orbit coupling
• Universal symmetry-protected persistent spin textures in nonmagnetic solids
• Moiré Collapse and Luttinger Liquids In Twisted Anisotropic Homobilayers
• Persistent spin textures, altermagnetism and charge-to-spin conversion in metallic chiral crystals TM${}_3$X${}_6$
• Understanding spin textures in PT-broken systems through universal symmetry-constrained rules
• Spin-deformation coupling in two-dimensional polar materials
• Surface ferromagnetism in a chiral topological semimetal CoSi
• Persistent Spin Textures in Nonpolar Chiral Systems
• Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials
• Matter with apparent and hidden spin physics
• Investigating Quantum Spin-Textures Using Universal MJ Hamiltonians
• Multiple types of spin textures and robust valley physics in MP${}_2$X${}_6$
• Orbital Hybridization Induces Giant Cubic Rashba Effect at Cu/WO${}_3$ Interface
• Physical Pictures for Quasisymmetry in Crystals
• High-Throughput Discovery of Two-Dimensional Materials Exhibiting Strong Rashba-Edelstein effect
• Radial Rashba spin-orbit fields in commensurate twisted transition-metal dichalcogenide bilayers
• Investigation of the intrinsic hidden spin texture and spin-state segregation in centrosymmetric monolayer dichalcogenide: effectiveness of the electric-field approach