Spin Splitting Research Articles

Nanophotonic resonator assisted photonic spin Hall enhancement for sensing application

This manuscript presents a dielectric resonator structure with altered dispersion characteristics to enhance the photonic spin Hall effect (PSHE). The structural parameters are optimized to enhance the PSHE at 632.8 nm operating wavelength. The thickness-dependent angular dispersion analysis is carried out to optimize the structure and obtain the exceptional points. The PSHE-induced spin splitting shows a high sensitivity to the optical thickness of the defect layer. This gives a maximum PSHE-based transverse displacement (PSHE-TD) of around 56.66 times the operating wavelength at an incidence angle of 61.68°. Moreover, the structure’s capability as a PSHE-based refractive index sensor is also evaluated. The analytical results demonstrate an average sensitivity of around 33,720 μm/RIU. The structure exhibits around five times higher PSHE-TD and approximately 150% improvement in sensitivity than the recently reported values in lossy mode resonance structures. Due to the purely dielectric material-assisted PhC resonator configurations and significantly higher PSHE-TD, the development of low-cost PSHE-based devices for commercial applications is envisaged.

Inverse Altermagnetic Spin Splitting Effect‐Induced Terahertz Emission in RuO2

AbstractThe relativistic inverse spin Hall effect (ISHE) plays a pivotal role in terahertz (THz) emission in magnet/heavy metal bilayers. Here, THz emission from RuO2/Py bilayers is reported due to not only the relativistic ISHE but also the nonrelativistic inverse altermagnetic spin splitting effect (IASSE) in RuO2. For the (100)‐oriented RuO2/Py bilayers, the THz emission is greatly enhanced owing to IASSE once the polarization direction of the spin current (from the Py layer induced by pump laser) is parallel to the Néel vector of RuO2, producing the anisotropic THz emission with twofold symmetry. In contrast, the RuO2(110)/Py bilayer only exhibits isotropic THz emission because of the absence of IASSE‐induced spin‐charge conversion in the (110)‐oriented RuO2 films. Apart from the fundamental significance of exploring the IASSE‐induced spin‐to‐charge conversion, the finding also enriches the physical mechanism and modulation method of THz emission in spintronic systems.

Modulation of edge defects on dual-spin filtering in zigzag β-SiC7 nanoribbons.

The unique edge states of the zigzag β-SiC7 nanoribbons aroused our attention, and therefore, based on first-principles calculations, we investigated their spin-dependent electronic transport properties by constructing controllable defects to modulate these special edge states. Interestingly, by introducing rectangular edge defects in the SiSi and SiC edge-terminated systems, not only the spin-unpolarized is successfully converted to completely spin-polarized, but also the direction of polarization can be switched, thus enabling a dual spin filter. The analyses further reveal that the two transmission channels with opposite spins are spatially separated and that the transmission eigenstates are highly concentrated at the relative edges. The specific edge defect introduced only suppresses the transmission channel at the same edge but reserves the transmission channel at the other edge. In addition, for the CSi and CC edge-terminated systems, an additional spin-down band exists due to spin splitting in the spin-up band at EF, so that besides the original spatially separated two spin-opposite channels, an extra spin channel is distributed at the upper edge, resulting in unidirectional fully spin-polarized transport. The peculiar spatially separated edge states and excellent spin filtering properties could open up further possibilities for β-SiC7-based electronic devices in spintronics applications.

Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet RuO_{2}.

The relativistic spin Hall effect and inverse spin Hall effect enable the efficient generation and detection of spin current. Recently, a nonrelativistic altermagnetic spin splitting effect (ASSE) has been theoretically and experimentally reported to generate time-reversal-odd spin current with controllable spin polarization in antiferromagnet RuO_{2}. The inverse effect, electrical detection of spin current via ASSE, still remains elusive. Here we show the spin-to-charge conversion stemming from ASSE in RuO_{2} by the spin Seebeck effect measurements. Unconventionally, the spin Seebeck voltage can be detected even when the injected spin current is polarized along the directions of either the voltage channel or the thermal gradient, indicating the successful conversion of x- and z-spin polarizations into the charge current. The crystal axes-dependent conversion efficiency further demonstrates that the nontrivial spin-to-charge conversion in RuO_{2} is ascribed to ASSE, which is distinct from the magnetic or antiferromagnetic inverse spin Hall effects. Our finding not only advances the emerging research landscape of altermagnetism, but also provides a promising pathway for the spin detection.

Anisotropy in colossal piezoelectricity, giant Rashba effect and ultrahigh carrier mobility in Janus structures of quintuple Bi2X3 (X = S, Se) monolayers

Due to the asymmetric structures, two-dimensional Janus materials have gained significant attention in research for their intriguing piezoelectric and spintronic properties. In the present work, quintuple Bi2X3 (X = S, Se) monolayers (MLs) have been modified to create stable Janus Bi2X2Y (X ≠ Y = S, Se) MLs that display piezoelectricity in both the planes along with Rashba effect. The out-of-plane piezoelectric constant (d 33) is 41.18 (−173.14) pm V−1, while the in-plane piezoelectric constant (d 22) is 5.23 (6.21) pm V−1 for Janus Bi2S2Se (Bi2Se2S) ML. Including spin–orbit coupling in the Janus MLs results in anisotropic giant Rashba spin splitting (RSS) at the Γ point in the valence band, with RSS proportional to d 33. The Rashba constant along the Γ–K path, , is 3.30 (2.27) eV Å, whereas along Γ–M, is 3.58 (3.60) eV Å for Janus Bi2S2Se (Bi2Se2S) ML. The MLs exhibit ultrahigh electron mobility (∼5442 cm2V−1s−1) and have electron to hole mobility ratio of more than 2 due to their tiny electron-effective masses. The flexibility of the MLs allows for a signification alteration in its properties, like band gap, piezoelectric coefficient, and Rashba constant, via mechanical (biaxial) strain. For the MLs, band gap and d 33 value are enhanced with compressive strain. The d33 value of Janus Bi2Se2S reaches 4886.51 pm V−1 under compressive strain. The coexistence of anisotropic colossal out-of-plane piezoelectricity, giant RSS, and ultrahigh carrier mobilities in Janus Bi2S2Se and Bi2Se2S MLs showcase their tremendous prospects in nanoelectronic, piezotronics, and spintronics devices.

Enhancing the Rashba spin splitting at X/Au/Si(111) surface by induced intrinsic spin-polarization

Adsorbed/modified surface is usually treated as a prototype to study Rashba spin splitting. Using first-principles calculations and analyses, we first explain the Rashba spin splitting of monovalent alkali metal adsorbed on Au/Si(111) surface as realized in experiment. We clearly identify that Na adatom donates one electron to pristine Au/Si(111) surface, leading to the Fermi level shift upward to the parabolic range of Au d and Si p hybridized states and thus leading to large Rashba spin splitting in Na/Au/Si(111) system. However, for the larger intra-atomic spin-orbit coupling Cs adsorbate, it not only plays the identical role to Na adatom, but induces intrinsic spin-polarization surprisingly, which further enhances the Rashba spin splitting on the Cs/Au/Si(111) surface up to ∼200 meV. Our proposed mechanism that intrinsic spin-polarization significantly enhancing the Rashba spin splitting is generally applicable and can be extended readily to alkali-earth metal as epitaxial layer grown on Au/Si(111) surface.

High magnetic field superconductivity in a two-band superconductor

We present a mechanism allowing for superconductivity at high magnetic fields, beyond the Pauli-Chandrasekhar-Clogston limit. We consider spin splitting induced by an in-plane external magnetic field in a superconductor with two relevant bands close to the Fermi level. The magnetic field therefore controls which bands are available for Cooper pair formation. The presence of interband superconducting pairing, i.e., Cooper pairs formed by electrons with different band indices, produces high-field reentrant superconducting domains, whose critical magnetic field violates the Pauli-Chandrasekhar-Clogston limit. We analyze how the interband superconducting domains are influenced by the band parameters, and show that, for a certain range of parameters, the system presents two separate superconducting regions, for low and high magnetic field.

Valley and spin splittings in a valley layer locked monolayer via atomic adsorption

To date, a number of valley materials have been discovered with spin-valley or valley-layer couplings. It is highly desirable to realize the interplay of more electronic degrees of freedom in a valley material. Based on the first-principles calculations, we demonstrate the valley and spin degeneracy liftings in the band structure of a TiSiCO monolayer, with the help of the selective expression of the layer pseudospin via atomic adsorption. The introduction of the transition-metal adatoms provides an effective electric field and magnetic proximity effect, giving rise to considerable valley and spin splittings. The larger valley splitting and the largest spin splitting for the band-edge states have magnitudes of up to 190 meV and 148 meV, respectively. The valley and spin splittings can be further tuned by applying an external electric field. According to the modified band structure, various interlayer excitons with different combinations of spins and electric dipoles are selectively created under the optical field of appropriate frequencies. The tunable spin and valley splittings in atom-adsorbed TiSiCO monolayer offer opportunities for exploring the interactions between spin, valley, and layer pseudospins and designing advanced optoelectronic devices.

Thickness-dependent in-plane shift of photonic spin Hall effect in an anisotropic medium.

As the in-plane spin splitting (IPSS) has a broad application for the precision measurement and sensing, it is extremely important to explore its enhancement mechanism via the photonic spin Hall effect (PSHE). However, for a multilayer structure, the thickness in most of previous works is generally set as a fixed value, lacking the deeply exploration of the influence of thickness on the IPSS. By contrast, here we demonstrate the comprehensive understanding of thickness-dependent IPSS in a three layered anisotropic structure. As thickness increases, near the Brewster angle, the enhanced in-plane shift exhibits a thickness-dependently periodical modulation, besides with much wider incident angle than that in an isotropic medium. While near the critical angle, it becomes thickness-dependently periodical or linear modulation under different dielectric tensors of the anisotropic medium, no longer keeps almost constant in an isotropic medium. In addition, as exploring the asymmetric in-plane shift with arbitrary linear polarization incidence, the anisotropic medium could bring more obvious and wider range of thickness-dependently periodical asymmetric splitting. Our results deepen the understanding of enhanced IPSS, which is expected to promise a pathway in an anisotropic medium for the spin control and integrated device based on PSHE.

Controllable and enormous spin splitting in antiferromagnetic MnPSe3 through interfacial coupling with Janus MoSSe

The manipulation of spin and valley degree of freedom in two-dimensional materials is desirable for emerging applications in next-generation electronics. Here, we report a regulation of the spin splitting in monolayer antiferromagnetic MnPSe3 through stacking van der Waals (vdW) heterostructures with transition-metal dichalcogenides (TMDs). Different TMDs including Janus MoSSe, MoSe2, and MoS2 are engaged and the spin and valley dependences on stacking configurations, interfacial atoms, and interlayer spacings are comprehensively investigated based on first-principles calculations. The results show that spin degeneracy of MnPSe3 can be lifted through the interfacial interaction in the vdW heterostructures. Compared with the MnPSe3 interfacing with traditional TMDs (MoSe2 and MoS2), those with Janus TMDs (MoSSe or MoSeS) have larger spin splitting. A maximal spin splitting of 50.8 meV at valence band maximum is achieved in MoSSe/MnPSe3 heterostructure, and such splitting is further enhanced to 243.0 meV when the interlayer spacing is reduced to 2.9 Å. It is found that the different hybridizations between the d-orbitals of the two inequivalent Mn atoms in MnPSe3 and the above TMDs lead to the occurrence of net magnetic moments, and thus induce spin splitting. This work paves a novel way to modify the spin-valley properties of two-dimensional semiconductors.

Spin-orbit-coupling-induced band splitting in two-dimensional hybrid organic-inorganic perovskites: Importance of organic cations

We investigate how the spin-orbit-coupling-induced lifting of the spin degeneracy depends indirectly on constituting organic motifs in two-dimensional hybrid organic-inorganic perovskites. We examine experimentally synthesized structures using first-principles electronic structure theory. In particular, the effect of the organic spacer cation packing and of the methyl ammonium orientation within the inorganic layer are elucidated. Both the organic spacer packing and subtle changes in methyl ammonium orientations can cause enough distortions of lead iodide octahedral cages to induce the spin splitting. Interestingly, the momentum-independent persistent spin texture splitting rather than the traditional Rashba/Dresselhaus splitting is observed for a structure in which organic spacer molecules are modified with fluorine substitution. Our calculation on these experimentally reported structures highlights the important role of the organic constituents in these hybrid organic inorganic perovskites for the spin splitting.

Prediction of wide-gap topological insulating phase in metastable BiTeI

BiTeI crystals possess many unique pressure-induced electronic properties; however, high-pressure conditions limit their practical applications to some extent. We conducted crystal structure prediction from 3000 structures to determine several structures with high thermodynamic stability. By studying the topological invariants, we found one strong topological insulator with inversion symmetry and one weak topological insulator. Spin splitting was found in two structures, and their spin texture was analyzed by effective SOC Hamiltonian and symmetry. Our study showed that some structures are not only topologically nontrivial but can also simultaneously possess Rashba-type spin splitting with a band gap of up to 860 meV.

Three-dimensional Rashba spin splitting dominated by out-of-plane spin polarization

Three-dimensional Rashba spin splitting dominated by out-of-plane spin polarization

Surface electronic structure of Re(0001): A spin-resolved photoemission study

The surface electronic structure of Re(0001) has been investigated in a combined experimental and theoretical study. Spin- and angle-resolved photoemission was employed to unravel the spin-dependent $E({\mathbf{k}}_{\ensuremath{\parallel}})$ dispersion of electronic states along the $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{M}}$ and $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{K}}$ directions. The results are compared with band-structure calculations based on density-functional theory. Additional calculations include transitions into final states by taking into account the corresponding matrix elements. Recently, Shockley- and Tamm-type surface states close to ${E}_{\mathrm{F}}$ were identified, which were found to be mixed by spin-orbit coupling. Here, we determined the Rashba parameter ${\ensuremath{\alpha}}_{\mathrm{R}}$ of the surface state around $\overline{\mathrm{\ensuremath{\Gamma}}}$ to 0.32 and $0.34\phantom{\rule{4pt}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\stackrel{\ifmmode \mathring{}\else \r{}\fi{}}{\mathrm{A}}$ along $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{M}}$ and $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{K}}$, respectively. Furthermore, we extend our analysis to a wider $E({\mathbf{k}}_{\ensuremath{\parallel}})$ range revealing a multitude of electronic states along both high-symmetry directions. In particular, Rashba-type spin splittings are observed around the high-symmetry $\overline{\mathrm{\ensuremath{\Gamma}}}$ and $\overline{\mathrm{M}}$ points. At variance with theoretical predictions for a perfect hcp(0001) surface, we do not find any out-of-plane spin polarization. This is caused by monatomic steps of a real Re(0001) surface with alternating terminations, leading on average to an effective sixfold surface symmetry and vanishing net out-of-plane spin polarization.

Electric-Field Control of Spin Polarization above Room Temperature in Single-Layer A-Type Antiferromagnetic Semiconductor

Two-dimensional (2D) antiferromagnets have drawn great interest for absence of stray fields in antiferromagnetic (AFM) spintronics. However, it remains challenging to manipulate their spin polarization above room temperature for practical applications. Herein, a general strategy is reported to realize the control of spin polarization above room temperature in 2D A-type AFM semiconductors by external electric field based on first-principles calculations, exemplified by transition metal monohalide MnCl and carbide MXenes Cr2CX2 (X = F, Cl, OH). It shows that 100% spin polarization can be induced around Fermi level with spin splitting gap related to the spatial distribution of spin density in real space. Meanwhile, the Neél temperature of 2D MnCl and Cr2CF2 remains above room temperature under external electric field up to 0.6 V/Å. This study exhibits the potential for application of 2D AFM semiconductors in electric-field-controlled spintronics.

Critical behavior and exchange splitting in the two-dimensional antiferromagnet Mn on Re(0001)

We investigated the temperature-dependent electronic structure of the antiferromagnetic fcc-monolayer Mn on Re(0001) using vacuum-ultraviolet momentum microscopy. At $T=25$ K the collinear, row-wise antiferromagnetic phase of the Mn monolayer results in a spin splitting of states. Density-functional theory, being in good agreement with the experimental results, reveals the spin and orbital projection of the observed electronic bands. The exchange split bands shift in opposite directions with increasing temperature, decreasing the exchange splitting of a pair of itinerant bands from $280\ifmmode\pm\else\textpm\fi{}10$ meV at 25 K down to $185\ifmmode\pm\else\textpm\fi{}10$ meV at the N\'eel temperature ${T}_{\text{N}}=75\ifmmode\pm\else\textpm\fi{}5$ K. The exchange splitting remains constant for $T>{T}_{\text{N}}$. The persisting exchange splitting is attributed to a remaining short-range, fluctuating antiferromagnetic order far above ${T}_{\text{N}}$.

A type-II MnPSe3/GeC heterostructure with tunable spin and valley splitting

The ternary chalcogenide MnPSe3 monolayer recently gets a lot of attention because of its two nonequivalent energy valleys. The existence of spin–orbit coupling (SOC) effect can cause the valley splitting of around 24 meV. However, the spin degeneracy is still kept in MnPSe3 monolayer owing to the antiferromagnetic coupling between Mn2+ ions. The interlayer coupling effect in the van der Waals (vdW) heterostructures can break the symmetry of MnPSe3 and induce the spin splitting. Here, we simulate the MnPSe3/GeC vdW heterostructure and investigate the effects of the stacking and interlayer coupling effect on both spin and valley splitting. The excitation mode of valley excitons is greatly related to the stacking of heterostructures. The interlayer excitons can only be formed in one of the configurations with C3 symmetry according to optical selection transition rule. The interlayer coupling effect is modulated by changing interlayer distance. With vertical compressive strain (−20%), the spin and valley splitting higher than 50 meV and 30 meV can be obtained in MnPSe3/GeC vdW heterostructures, respectively. This study suggests that the stacking and vertical strain are both efficient approaches to modulate the spin and valley splitting through the interlayer coupling effect in the vdW heterostructures.

Ab initio prediction of anomalous Hall effect in antiferromagnetic CaCrO3

While the anomalous Hall effect takes place typically in ferromagnets with finite magnetization, large anomalous Hall conductivity in noncollinear antiferromagnetic systems has been recently observed and attracted much attention. In this paper, we predict the anomalous Hall effect in perovskite ${\mathrm{CaCrO}}_{3}$ as a representative of collinear antiferromagnetic materials. Our result shows that the $C$-type antiferromagnetic ordering generates the sizable anomalous Hall conductivity. Based on symmetry analyses, we show that the antiferromagnetic order parameter belongs to the same irreducible representation as the ferromagnetic order parameter in the nonsymmorphic space group, allowing the nonvanishing Berry curvatures in $k$ space. By performing first-principles density-functional theory calculations, we find that the Berry-curvature ``hot spots'' lie along the gapped nodal lines where spin-orbit coupling induces the spin splitting of Cr-$3d$ bands near the Fermi energy and enhances the anomalous Hall effect in ${\mathrm{CaCrO}}_{3}$.

Room-temperature magnetoresistance in a single-layer composite film based on noncollinear antiferromagnetic Mn3Sn

The recently discovered room-temperature magnetoresistance in all-antiferromagnetic tunnel junctions is promising for highly integrated ultrafast memory applications. Here, we report a room-temperature magnetoresistance effect in a single-layer composite film consisting of noncollinear antiferromagnetic Mn3Sn and nonmagnetic Ag. A room-temperature butterfly like magnetoresistance of ∼0.3% is obtained for the Mn3Sn–Ag composite film, which is induced by the giant magnetoresistance effect governed by the magnetic octupole induced momentum space spin splitting in the noncollinear antiferromagnet Mn3Sn. Moreover, compared to the complicated multilayer all-antiferromagnetic tunnel junction structures, the simple fabrication process of single-layer composite films in this work could facilitate the application of antiferromagnetic magnetoresistance devices.

Dispersive cavity-mediated quantum gate between driven dot-donor nuclear spins

Nuclear spins show exceptionally long coherence times but the underlying good isolation from their environment is a challenge when it comes to controlling nuclear spin qubits. A particular difficulty, not only for nuclear spin qubits, is the realization of two-qubit gates between distant qubits. Recently, strong coupling between an electron spin and microwave resonator photons as well as a microwave resonator mediated coupling between two electron spins both in the resonant and the dispersive regime have been reported and, thus, a microwave resonator mediated electron spin two-qubit gate seems to be in reach. Inspired by these findings, we theoretically investigate the interaction of a microwave resonator with a hybrid quantum dot-donor (QDD) system consisting of a gate-defined Si QD and a laterally displaced $^{31}\mathrm{P}$ phosphorous donor atom implanted in the Si host material. We find that driving the QDD system allows to compensate the frequency mismatch between the donor nuclear spin splitting in the MHz regime and typical superconducting resonator frequencies in the GHz regime, and also enables an effective nuclear spin-photon coupling. While we expect this coupling to be weak, we predict that coupling the nuclear spins of two distant QDD systems dispersively to the microwave resonator allows the implementation of a resonator-mediated nuclear spin two-qubit $\sqrt{i\mathrm{SWAP}}$ gate with a gate fidelity approaching $90%$.