Strong Spin-orbit Coupling Research Articles

Room-Temperature Ferromagnetism with Strong Spin-Orbit Coupling Achieved in CaRuO3 Interfacial Phase via Magnetic Proximity Effect.

Recently, theoretical and experimental research predicted that ferromagnets with strong spin-orbit coupling (SOC) could serve as spin sources with dramatically enhanced spin-orbit torque (SOT) efficiency due to the combination of spin Hall effect and anomalous Hall effect (AHE), presenting potential advantages over conventional nonmagnetic heavy metals. However, materials with a strong SOC and room-temperature ferromagnetism are rare. Here, we report on a ferromagnetic (FM) interfacial phase with Curie temperature exceeding 300 K in the heavy transition-metal oxide CaRuO3, in proximity to La0.67Sr0.33MnO3. Electron energy loss and polarized neutron reflectometry spectra reveal the strong charge transfer from Ru to Mn at the interface, triggering antiferromagnetic exchange interactions between interfacial Ru/Mn ions and thus transferring magnetic order from La0.67Sr0.33MnO3 to CaRuO3. An obvious advantage of such interfacial phase is the enhanced anomalous Hall effect at temperatures from 150 to 300 K. Compared to the most promising room-temperature ferromagnetic oxide La0.67Sr0.33MnO3, the anomalous Hall conductivity σxyAHE (or anomalous Hall angle θH) of CaRuO3/La0.67Sr0.33MnO3 superlattices is increased by 30 (or 31) times at 150 K and 10 (or 3) times at 300 K. This work demonstrates a special approach for inducing ferromagnetism in heavy transition-metal oxides with strong SOC, offering promising prospects for all-oxide-based spintronic applications.

Embedding Plate‐Like Pyrochlore in Perovskite Phase to Enhance Energy Storage Performance of BNT‐Based Ceramic Capacitors

AbstractNext‐generation electrical and electronic systems rely on the development of efficient energy‐storage dielectric ceramic capacitors. However, achieving a synergistic enhancement in the polarization and in the breakdown field strength (Eb) presents a considerable challenge. Herein, a heterogeneous combination strategy involving embedding a high Eb plate‐like pyrochlore phase in a high‐polarization perovskite phase is proposed. The embedded plate‐like pyrochlore increases the breakdown field strength and promotes the dynamic polarization response. Meanwhile, the strong spin–orbit coupling effect of the 5d electrons is conducive to the maintenance of the high polarization value of the perovskite. Consequently, the prepared multilayer ceramic capacitor (MLCC) exhibits an ultrahigh Eb and a high polarization. More specifically, an energy storage density (Wrec) of 14.9 J cm−3 with an efficiency of up to 93.4% is achieved for the optimized pyrochlore/perovskite phase. Furthermore, the MLCCs also exhibits an Wrec of ≈ 7.7 J cm−3 ± 4.5% in the temperature range of −50–180 °C. Therefore, this heterogeneous combination strategy therefore provides a simple and effective method for improving the energy‐storage performances of dielectric ceramic capacitors.

Revisiting the global minimum of Au10 clusters.

This study employs high-level quantum chemical calculations to determine the global minimum structure of Au10 clusters definitively. Contrary to previous reports, coupled-cluster singles and doubles with perturbative triples [CCSD(T)] calculations with sizable quadruple-ζ basis sets incorporating the spin-orbit (SO) effect reveal that the planar 10.b structure is the true global minimum for Au10, not the three-dimensional 10.a structure. Two-component spin-orbit density functional theory calculations demonstrate that the SO effect is minimal for most Au10 isomers, except for the 10.f structure. A straightforward diagnostic tool is proposed for identifying Au cluster structures with strong spin-orbit coupling based on 6p orbital occupation. The calculated IR spectra based on Boltzmann averaging the six Au10 isomers show good agreement with recent experimental spectra although minor discrepancies are noted potentially due to interactions with Kr. The results suggest that the transition point to non-planar global minimum structures for Au clusters lies beyond Au10 but is nearby.

Observation of Highly Spin-Polarized Dangling Bond Surface States in Rare-Earth Pnictide Tellurides.

To generate and manipulate spin-polarized electronic states in solids are crucial for modern spintronics. The textbook routes employ quantum well states or Shockley/topological type surface states whose spin degeneracy is lifted by strong spin-orbit coupling and inversion symmetry breaking at the surface/interface. The resultant spin polarization is usually truncated because of the intertwining between multiple orbitals. Here a unique type of surface states is realized, namely, dangling bond surface states in a family of ternary rare-earth pnictide tellurides RePnTe (Re = La, Gd, Ce; Pn = Sb, Bi), with robust band structure and sizeable spin splitting. Spin and angle-resolved photoemission spectroscopy measurements reveal high spin polarization and distinct spin-momentum locking texture, which, according to the theoretical analysis, arise from local site asymmetry and surface-purified spin-orbital texture. The work extends the so-called "hidden spin polarization" from the bulk to the surface, presenting an intriguing spin-orbital-momentum-layer locking phenomenon, which may shed lights on potential spintronic applications.

Resonant spin dynamics of 2D electrons with strong Rashba and Zeeman couplings

Two-dimensional (2D) systems enable enhancing and diversifying the spin–orbit coupling of carriers, a key factor for better charge-spin conversion efficiencies in modern spintronic devices. Increasing 2D spin interactions also modifies dynamical spin-dependent properties of 2D materials, enabling to display resonant phenomena. In this work we focus on dynamical properties of the charge-spin conversion and analyze the resonant spin dynamics of 2D electrons upon strong spin–orbit coupling and Zeeman spin splittings, possibly exceeding the inverse relaxation times of electrons. We derive resonant frequencies and relaxation rates from the Bloch kinetic equations and examine how the trajectories of spin susceptibility poles change with variations in spin splittings and the relaxation time, paying special attention to the interplay between competing Rashba and Zeeman effect.

Fractional quantum Hall phases in high-mobility n-type molybdenum disulfide transistors

AbstractTransistors based on semiconducting transition metal dichalcogenides can, in theory, offer high carrier mobilities, strong spin–orbit coupling and inherently strong electronic interactions at the quantum ground states. This makes them well suited for use in nanoelectronics at low temperatures. However, creating robust ohmic contacts to transition metal dichalcogenide layers at cryogenic temperatures is difficult. As a result, it is not possible to reach the quantum limit at which the Fermi level is close to the band edge and thus probe electron correlations in the fractionally filled Landau-level regime. Here we show that ohmic contacts to n-type molybdenum disulfide can be created over a temperature range from millikelvins to 300 K using a window-contacted technique. We observe field-effect mobilities of over 100,000 cm2 V−1 s−1 and quantum mobilities of over 3,000 cm2 V−1 s−1 in the conduction band at low temperatures. We also report evidence for fractional quantum Hall states at filling fractions of 4/5 and 2/5 in the lowest Landau levels of bilayer molybdenum disulfide.

Magnetic Field-Induced Polar Order in Monolayer Molybdenum Disulfide Transistors.

In semiconducting monolayer transition metal dichalcogenides (ML-TMDs), broken inversion symmetry and strong spin-orbit coupling result in spin-valley lock-in effects so that the valley degeneracy may be lifted by external magnetic fields, potentially leading to real-space structural transformation. Here, magnetic field (B)-induced giant electric hysteretic responses to back-gate voltages are reported in ML-MoS2 field-effect transistors (FETs) on SiO2/Si at temperatures <20 K. The observed hysteresis increases with |B| up to 12 T and is tunable by varying the temperature. Raman spectroscopic and scanning tunneling microscopic studies reveal significant lattice expansion with increasing |B| at 4.2 K, and this lattice expansion becomes asymmetric in ML-MoS2 FETs on rigid SiO2/Si substrates, leading to out-of-plane mirror symmetry breaking and the emergence of a tunable out-of-plane ferroelectric-like polar order. This broken symmetry-induced polarization in ML-MoS2 shows typical ferroelectric butterfly hysteresis in piezo-response force microscopy, adding ML-MoS2 to the single-layer material family that exhibits out-of-plane polar order-induced ferroelectricity, which is promising for such technological applications as cryo-temperature ultracompact non-volatile memories, memtransistors, and ultrasensitive magnetic field sensors. Moreover, the polar effect induced by asymmetric lattice expansion may be further generalized to other ML-TMDs and achieved by nanoscale strain engineering of the substrate without magnetic fields.

Magnetic and magnetocaloric dynamics in [formula omitted] double perovskites: Impact of A and B site variations analyzed through Monte Carlo simulation and Ab initio calculations

We investigate the magnetic and magnetocaloric properties of the double perovskites Sr2FeOsO6,Sr2FeCoO6,Dy2FeOsO6 and Dy2FeCoO6 using a combination of Monte Carlo simulations and Density Functional Theory (DFT). The exchange couplings were calculated using DFT. Sr2FeOsO6 exhibits antiferromagnetic ordering with two transitions at 50 and 150 K, driven by strong antiferromagnetic exchange interactions between Fe³⁺ and Os⁵⁺ ions. In contrast, Sr2FeCoO6 shows ferrimagnetic behavior with a single transition around 75 K, attributed to ferromagnetic coupling between Co2⁺ and Fe³⁺ ions. For the rare-earth-containing compounds, Dy2FeOsO6 demonstrates complex magnetic ordering with transitions at approximately 20 K and 140 K, influenced by the strong spin-orbit coupling of Dy³⁺ ions. Similarly, Dy2FeCoO6 exhibits two transitions at around 60 K and 170 K, reflecting a mix of ferromagnetic and antiferromagnetic interactions involving Dy³⁺, Co2⁺, and Fe³⁺ ions. Sr2FeOsO6 shows a peak magnetic entropy change ΔSm of 0.22 J/kg.K under a 5 T field at 50 K, while Sr2FeCoO6 exhibits a broader peak at 75 K with ΔSm of 1.5 J/kg·K. Dy2FeOsO6 presents significant ΔSm peaks at 20 K and 140 K, reaching 1.9 J/kg·K under a 5 T field. Dy2FeCoO6 displays the highest ΔSm of 4.0 J/kg·K at 60 K.

Intercalation-Induced Monolayer Behavior in Bulk NbSe2.

Superconductivity at the 2D limit is significant for advancing fundamental physics, leading to extensive research on monolayer two-dimensional materials. In particular, monolayer transition metal dichalcogenides such as NbSe2 exhibit Ising superconductivity due to broken in-plane inversion symmetry and strong spin-orbit coupling, which has garnered significant attention. In this letter, we adopted an organic cation intercalation technique to modulate the interlayer interaction of NbSe2 by expanding the interlayer distance, thereby making intercalated NbSe2 behave similarly to monolayer NbSe2. The interlayer distances of NbSe2 intercalated with THA+, CTA+, and TDA+ cations are almost double or triple that of pristine NbSe2. The superconducting transition temperature (Tc) of THA-NbSe2 is comparable to that of pristine NbSe2, while the charge density wave (CDW) transition temperature is higher. The Tc of intercalated NbSe2 decreases with a reduced hole concentration, and the enhanced CDW is ascribed to the dimensional reduction. Notably, the in-plane upper critical field of intercalated NbSe2 significantly exceeds the Pauli paramagnetic limit, which is similar to the Ising superconductivity observed in monolayer NbSe2. Our work demonstrates that the organic cations intercalated two-dimensional materials exhibit behavior similar to their monolayer counterparts, providing a convenient platform for exploring and modulating physical phenomena at the two-dimensional limit.

Chiral Organometallic Complexes Derived from Helicenic N-Heterocyclic Carbenes (NHCs): Design, Structural Diversity, and Chiroptical and Photophysical Properties.

ConspectusRecently, helicene derivatives have emerged as an important class of molecules with potential applications spanning over asymmetric catalysis, biological activity, magnetism, spin filtering, solar cells, and polymer science. To harness their full potential, especially as emissive components in circularly polarized organic light-emitting diodes (CP-OLEDs), generating structural chemical diversity and understanding the resulting photophysical and chiroptical properties are crucial. In this Account, we shed light on chemical engineering combining helicene and N-heterocyclic carbene (NHC) chemistries to create transition-metal complexes with unique architectures and describe their photophysical and chiroptical attributes. The σ-donating and π-accepting capabilities of the helically chiral π-conjugated NHCs endow the complexes with remarkable structural and electronic features. These characteristics manifest in phenomena such as chirality induction, very long-lived phosphorescence, and strong chiroptical signatures (electronic circular dichroism and circularly polarized luminescence).We describe the different classes of ligands primarily developed in our group by classifying them according to their connection between the helicenic moiety and the imidazole precursor. This connection is essential in determining the degree of π-conjugation and characterizing the emissive state. We comprehensively discuss 6-coordinate, 4-coordinate, and 2-coordinate complexes, delving into their structural nuances and examining how the interplay between metals and auxiliary ligands shapes their photophysical properties, with interpretations enriched by DFT calculations. Helicenes are known to promote intersystem crossing thanks to strong spin-orbit coupling, while metals offer robust frameworks leading to a variety of molecular architectures with specific topologies together with distinct excited-state properties. The electronic configurations and energy levels of the ligand and metal orbitals thus significantly modulate the photophysical and chiroptical behaviors of these complexes. In-depth analysis of chiroptical properties, notably electronic circular dichroism and circularly polarized luminescence, emphasizes the influence of different stereogenic elements on the chiroptical responses across various energy ranges with appealing "match-mismatch" effects. Finally, we describe future prospects of helicene NHCs, particularly in the context of emerging research on cost-effective and abundant transition metals for materials science and for photocatalysis. Indeed, the inherent long-lived MLCT, excited-state delocalization, structural rigidity, and intrinsic chirality of these complexes present intriguing avenues for future investigations.

Bragg resonances in the yttrium iron garnet – platinum – yttrium iron garnet layered structure

We studied theoretically the interaction between the spin current in a conductor with a strong spin-orbit coupling (platinum, Pt) and the spin wave in yttrium iron garnet ferromagnetic layers (YIG) with periodic thickness modulation under conditions of Bragg resonances and interlayer coupling. It is shown that in the YIG/Pt/YIG sandwich structure the conditions for two Bragg resonances in the first Brillouin area in the spin wave spectrum are fulfilled. The spin current in Pt allows frequency tuning of the resonances and control the depth of the spin wave band gap corresponding to the resonance conditions.

Manipulating Charge-to-Spin conversion via insertion layer control at the interface of topological insulator and ferromagnet

Strong spin–orbit coupling and highly spin-polarized surface states in topological insulators (TIs) are key parameters that explain their extremely high charge-to-spin conversion (CSC) efficiency at interfaces with ferromagnetic materials (FMs). This study focused on the influence of the insertion layer on the proximity effect occurring in a Co4Fe4B2/Bi2Se3 interface. Various insertion layers, including Au, MgO, and Se, were introduced to modulate the proximity effect from TI to FM and vice versa. X-ray photoelectron spectroscopy and transmission electron microscopy revealed that the Se insertion layer effectively suppresses the formation of an additional Bi layer, reducing intermixing against Co4Fe4B2. Electrical transport properties such as RXX and RXY under a vertical magnetic field show that the Se-inserted structure features the lowest anomalous Hall angle and exhibits a pristine topological surface state, indicating its potential for improving CSC efficiency. The Se-inserted structure exhibits the highest spin Hall angle among various heterostructures, according to results obtained from spin-torque ferromagnetic resonance. These findings highlight the importance of selecting an insertion layer and controlling the interface to optimize the spin-transport properties of TI-based spintronic devices and provide insights into the design of future spin devices.

Indirect-To-Direct Bandgap Crossover and Room-Temperature Valley Polarization of Multilayer MoS2 Achieved by Electrochemical Intercalation.

Monolayer (1L) group VI transition metal dichalcogenides (TMDs) exhibit broken inversion symmetry and strong spin-orbit coupling, offering promising applications in optoelectronics and valleytronics. Despite their direct bandgap, high absorption coefficient, and spin-valley locking in K or K' valleys, the ultra-short valley lifetime limits their room-temperature applications. In contrast, multilayer TMDs, with more absorptive layers, sacrifice the direct bandgap and valley polarization upon gaining inversion symmetry from the bilayer structure. It is demonstrated that multilayer molybdenum disulfide (MoS2) can maintain 1) a structure with broken inversion symmetry and strong spin-orbit coupling, 2) a direct bandgap with high photoluminescence (PL) intensity, and 3) stable valley polarization up to room temperature. Through the intercalation of organic 1-ethyl-3-methylimidazolium (EMIM+) ions, multilayer MoS2 not only exhibits layer decoupling but also benefits from an electron doping effect. This results in a hundredfold increase in PL intensity and stable valley polarization, achieving 55% and 16% degrees of valley polarization at 3 K and room temperature, respectively. The persistent valley polarization at room temperature, due to interlayer decoupling and trion dominance facilitated by a gate-free method, opens up potential applications in valley-selective optoelectronics and valley transistors.

Dynamic Jahn-Teller effect in the strong spin-orbit coupling regime

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions. Here we demonstrate that a highly-symmetrical 5d1 double perovskite Ba2MgReO6, comprising a 3D array of isolated ReO6 octahedra, represents a rare example of a dynamic Jahn-Teller system in the strong spin-orbit coupling regime. Thermodynamic and resonant inelastic x-ray scattering experiments, supported by quantum chemistry calculations, undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, resolving a long-standing puzzle in this family of compounds. The dynamic state of ReO6 octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

Origins of Electromagnetic Radiation from Spintronic Terahertz Emitters: A Time-Dependent Density Functional Theory plus Jefimenko Equations Approach.

Microscopic origins of charge currents and electromagnetic (EM) radiation generated by them in spintronic THz emitters-such as, femtosecond laser pulse-driven single magnetic layer or its heterostructures with a nonmagnetic layer hosting strong spin-orbit coupling (SOC)-remain poorly understood despite nearly three decades since the discovery of ultrafast demagnetization. We introduce a first-principles method to compute these quantities, where the dynamics of charge and current densities is obtained from real-time time-dependent density functional theory, which are then fed into the Jefimenko equations for properly retarded electric and magnetic field solutions of the Maxwell equations. By Fourier transforming different time-dependent terms in the Jefimenko equations, we unravel that in the 0.1-30THz range the electric field of far-field EM radiation by the Ni layer, chosen as an example, is dominated by charge current pumped by demagnetization, while often invoked magnetic dipole radiation from the time-dependent magnetization of a single magnetic layer is a negligible effect. Such an effect of charge current pumping by a time-dependent quantum system, whose magnetization is shrinking while its vector does not rotate, does not require any spin-to-charge conversion via SOC effects. In the Ni/Pt bilayer, EM radiation remains dominated by the charge current within the Ni layer, whose magnitude is larger than in the case of a single Ni layer due to faster demagnetization, while often invoked spin-to-charge conversion within the Pt layer provides an additional but smaller contribution. By using the Poynting vector and its flux, we also quantify the efficiency of conversion of light into emitted EM radiation, and its angular distribution.

Carrier-density-determined Magnetoresistance in Semimetal SrIrO3

Abstract SrIrO3, a Dirac material with a strong spin-orbit coupling (SOC), is a platform for studying topological properties in strongly correlated systems, where its band structure can be modulated by multiple factors, such as crystal symmetry, elements doping, oxygen vacancies, magnetic field, and temperature. Here, we discover that the engineered carrier density plays a critical role on the magnetoelectric transport properties of the topological semimetal SrIrO3. The decrease of carrier density subdues the weak localization (WL) and the associated negative magnetoresistance, while enhancing the SOC-induced weak anti-localization (WAL). Notably, the sample with the lowest carrier density exhibited high-field positive magnetoresistance, suggesting the presence of a Dirac cone. In addition, the anisotropic magnetoresistance (AMR) indicates the anisotropy of the electronic structure near the Fermi level. The engineering of carrier density provides a general strategy to control the Fermi surface and electronic structure in topological materials.

Synthesis, Crystal and Electronic Structures, and Magnetic and Electrical Transport Properties of Bismuthides NdZn0.6Bi2 and (La0.5RE0.5)Zn0.6Bi2 (RE = Pr or Nd).

Bismuth is a good constituent element for many quantum materials due to its large atomic number, 6s26p3 orbitals, and strong spin-orbital coupling. In this work, three new bismuthides, NdZn0.6Bi2, (La0.5Pr0.5)Zn0.6Bi2, and (La0.5Nd0.5)Zn0.6Bi2, were grown by a metal flux method, and their crystal structures were accurately determined by single-crystal X-ray diffraction. These new bismuthides belong to the RE-T-Pn2 (RE = La-Lu, T = Mn, Fe, Co, Ni, or Zn, and Pn = P, As, Sb, or Bi) family, are isostructural, and crystallize in the HfCuSi2 structure type. The bismuth elements have two possible oxidation states, Bi3- and Bi-, which were studied by X-ray photoelectron spectroscopy (XPS). Two binding energy peaks of 155.91 and 161.23 eV were observed for Bi atoms within NdZn0.6Bi2, and similar binding energy peaks were detected in NdBi and LiBi. XPS also confirmed the trivalent nature of Nd, which was further verified by magnetic measurements. Additionally, magnetic measurements revealed that NdZn0.6Bi2 exhibits an antiferromagnetic transition around 3 K, while the mixed-cation compounds do not show any magnetic transition down to 2 K. Electronic transport measurements reveal weak magnetoresistance in all three compounds, with a maximum value of ∼25% at 2 K and 9 T for (La0.5Nd0.5)Zn0.6Bi2.

Progress in Superconductor-Semiconductor Topological Josephson Junctions

Majorana bound states (MBSs) are quasiparticles that are their own antiparticles. They are predicted to emerge as zero-energy modes localized at the boundary of a topological superconductor. No intrinsic topological superconductor is known to date. However, by interfacing conventional superconductors and semiconductors with strong spin-orbit coupling, it is possible to create a system hosting topological states. Hence, epitaxial superconductors and semiconductors have emerged as an attractive material system with atomically sharp interfaces and broad flexibility in device fabrications incorporating Josephson junctions. We discuss the basics of topological superconductivity and provide insight into how to go beyond current state-of-the-art experiments. We argue that the ultimate success in realizing MBS physics requires the observation of non-Abelian braiding and fusion experiments. Published by the American Physical Society 2024

A singlet-triplet hole-spin qubit in MOS silicon

Holes in silicon quantum dots are promising for spin qubit applications due to the strong intrinsic spin-orbit coupling. The spin-orbit coupling produces complex hole-spin dynamics, providing opportunities to further optimise spin qubits. Here, we demonstrate a singlet-triplet qubit using hole states in a planar metal-oxide-semiconductor double quantum dot. We demonstrate rapid qubit control with singlet-triplet oscillations up to 400 MHz. The qubit exhibits promising coherence, with a maximum dephasing time of 600 ns, which is enhanced to 1.3 μs using refocusing techniques. We investigate the magnetic field anisotropy of the eigenstates, and determine a magnetic field orientation to improve the qubit initialisation fidelity. These results present a step forward for spin qubit technology, by implementing a high quality singlet-triplet hole-spin qubit in planar architecture suitable for scaling up to 2D arrays of coupled qubits.

Spin Space Groups: Full Classification and Applications

In this work, we exhaust all the spin space symmetries, which fully characterize collinear, noncollinear, and commensurate spiral as well as incommensurate spiral magnetism, etc., and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs)—joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the energy scale of interest), but we also show that specific SSGs could remain valid even in the presence of strong SOC. In recent years, SSGs have played increasingly pivotal roles in various fields such as altermagnetism, topological electronic states, and topological magnon, etc. However, due to its complexity, a complete SSG classification has not been completed up to now. By representing the SSGs as O(N) representations, we—for the first time—obtain the complete classifications of 1421, 9542, and 56 512 distinct SSGs for collinear (N=1), coplanar (N=2), and noncoplanar (N=3) magnetism, respectively. SSG not only fully characterizes the symmetry of spin degrees of freedom, but also gives rise to exotic electronic states, which, in general, form projective representations of magnetic space groups (MSGs). Surprisingly, electronic bands in SSGs exhibit features never seen in MSGs, such as (i) nonsymmorphic SSG Brillouin zone, where SSG operations behave as a glide or screw when acting on momentum, (ii) effective π flux, where translation operators anticommute with each other and yield duplicate bands, (iii) higher-dimensional representations unexplained by MSGs, and (iv) unconventional spin texture on a Fermi surface, which is completely determined by SSGs, independent of Hamiltonian details. To apply our theory, we identify the SSG for each of the 1595 published magnetic structures in the MAGNDATA database on the Bilbao Crystallographic Server. Material examples exhibiting the novel features (i)–(iv) are discussed with emphasis. We also investigate new types of SSG-protected topological electronic states that are unprecedented in MSGs. In particular, we propose a 3D Z2 topological insulator state with a fourfold degenerate Dirac point on the surface and a new scenario of anomalous Z2 helical states that appear on magnetic domain walls. Published by the American Physical Society 2024