Significant Spin-orbit Coupling Research Articles

Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr2RuO4

Even-parity interorbital spin-triplet pairing emerges as an intriguing candidate in multiorbital superconductors with significant Hund's and spin-orbit coupling. Within such a state, the pairing is dominated by the intraband pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the name, shadowed triplet. With atomic spin-orbit coupling, it was shown that this pairing exhibits an anisotropic $s$-wave character, while higher angular momentum pairing symmetries such as $d$- or $g$-wave have been proposed based on phenomenological analyses in candidate systems. A natural question is then whether higher angular momentum pairings may arise with this form of spin-triplet pairing. Here, we examine the interplay between spin-orbit coupling and the electronic dispersions in correlated metals and demonstrate how they can be realized. We apply this idea to Sr$_{2}$RuO$_{4}$ and determine the competition among different pairing states as multiple spin-orbit coupling parameters are tuned. The presence of both $d$- and $g$-wave pairings, including a $d+ig$ state, are found when momentum-dependent spin-orbit coupling with $d$-wave character is increased. Implications of the theory and future directions are also discussed.

Magnon modes as a joint effect of surface ferromagnetism and spin–orbit coupling in CoSi chiral topological semimetal

CoSi single crystal is a known realization of a chiral topological semimetal with simultaneously broken mirror and inversion symmetries. In addition to the symmetry-induced spin–orbit coupling, surface ferromagnetism is known in nominally diamagnetic CoSi structures, which appears due to the distorted bonds and ordered vacancies near the surface. We experimentally investigate electron transport through a thin CoSi flake at high current density. Surprisingly, we demonstrate dV/dI(I) curves which are qualitatively similar to ones for ferromagnetic multilayers with characteristic dV/dI magnon peaks and unconventional magnetic field evolution of the peaks’ positions. We understand these observations as a result of current-induced spin polarization due to the significant spin–orbit coupling in CoSi. Scattering of non-equilibrium spin-polarized carriers within the surface ferromagnetic layer is responsible for the precessing spin-wave excitations, so the observed magnon modes are the joint effect of surface ferromagnetism and spin–orbit coupling in a CoSi chiral topological semimetal. Thus, thin CoSi flakes behave as magnetic conductors with broken inversion symmetry, which is important for different spintronic phenomena.

Massive Dirac fermions and strong Shubnikov–de Haas oscillations in single crystals of the topological insulator Bi2Se3 doped with Sm and Fe

Topological insulators (TIs) are emergent materials with unique band structure, which allow the study of quantum effect in solids, as well as contribute to high-performance quantum devices. To achieve the better performance of TIs, here, we present a codoping strategy using synergistic rare-earth (RE) Sm and transition-metal Fe dopants in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ single crystals, which combine the advantages of both a transition-metal-doped TI [high ferromagnetic ordering temperature and observed quantum anomalous Hall effect (QAHE)], and a RE doped TI (large magnetic moments and significant spin-orbit coupling). In the as-grown single crystals, clear evidences of ferromagnetic ordering were observed. The angle-resolve photoemission spectroscopy indicates the ferromagnetism opens a \ensuremath{\sim}44 meV band gap at the surface Dirac point. Moreover, the mobility of the carriers at 3 K is $\ensuremath{\sim}7400\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{Vs}$, and we thus observed an ultra-strong Shubnikov--de Haas oscillation in the longitudinal resistivity, as well as the Hall steps in transverse resistivity 14 T. Our transport and angular-resolved photoemission spectroscopy results suggest that the RE and transition metal codoping in the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ system is a promising avenue to implement the QAHE, as well as harnessing the massive Dirac fermion in electrical devices.

Heisenberg and anisotropic exchange interactions in magnetic materials with correlated electronic structure and significant spin-orbit coupling

The Dzyaloshinskii-Moriya (DM) interaction, as well as symmetric anisotropic exchange, are important ingredients for stabilizing topologically non-trivial magnetic textures, such as, e.g., skyrmions, merons and hopfions. These types of textures are currently in focus from a fundamental science perspective and they are also discussed in the context of future spintronics information technology. While the theoretical understanding of the Heisenberg exchange interactions is well developed, it is still a challenge to access, from first principles theory, the DM interaction as well as the symmetric anisotropic exchange, which both require a fully-relativistic treatment of the electronic structure, in magnetic systems where substantial electron-electron correlations are present. Here, we present results of a theoretical framework which allows to compute these interactions in any given system and demonstrate its performance for several selected cases, for both bulk and low-dimensional systems. We address several representative cases, including the bulk systems CoPt and FePt, the B20 compounds MnSi and FeGe as well as the low-dimensional transition metal bilayers Co/Pt(111) and Mn/W(001). The effect of electron-electron correlations is analyzed using dynamical mean-field theory on the level of the spin-polarized $T$-matrix + fluctuating exchange (SPTF) approximation, as regards the strength and character of the isotropic (Heisenberg) and anisotropic (DM) interactions in relation to the underlying electronic structure. Our method can be combined with more advanced techniques for treating correlations, e.g., quantum Monte Carlo and exact diagonalization methods for the impurity solver of dynamical mean-field theory. We find that correlation-induced changes of the DM interaction can be rather significant, with up to five-fold modifications in the most distinctive case.

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

Phase Transitions and Water Splitting Applications of 2D Transition Metal Dichalcogenides and Metal Phosphorous Trichalcogenides.

2D layered materials turn out to be the most attractive hotspot in materials for their unique physical and chemical properties. A special class of 2D layered material refers to materials exhibiting phase transition based on environment variables. Among these materials, transition metal dichalcogenides (TMDs) act as a promising alternative for their unique combination of atomic‐scale thickness, direct bandgap, significant spin–orbit coupling and prominent electronic and mechanical properties, enabling them to be applied for fundamental studies as catalyst materials. Metal phosphorous trichalcogenides (MPTs), as another potential catalytic 2D phase transition material, have been employed for their unusual intercalation behavior and electrochemical properties, which act as a secondary electrode in lithium batteries. The preparation of 2D TMD and MPT materials has been extensively conducted by engineering their intrinsic structures at the atomic scale. In this study, advanced synthesis methods of preparing 2D TMD and MPT materials are tested, and their properties are investigated, with stress placed on their phase transition. The surge of this type of report is associated with water‐splitting catalysis and other catalytic purposes. This study aims to be a guideline to explore the mentioned 2D TMD and MPT materials for their catalytic applications.

Room-temperature Magnetoresistance in Hybrid Halide Perovskites: Effect of Spin-Orbit Coupling

Hybrid halide perovskites have emerged as promising materials for spintronics research due to their significant and tunable spin-orbit coupling (SOC). However, experimental findings that can discern the correlation between spintronic properties and SOC are rare. Here, we report the observation of room-temperature magnetoresistance (MR) and discuss the influence of chemical modification, hence SOC, in lead-based hybrid halide perovskites. Suppression of current under magnetic field (B) in perovskite thin films is explained in terms of field-modulated spin-mixing activity. We find that the MR increases upon replacement of ${\mathrm{I}}^{\ensuremath{-}}$ with ${\mathrm{Br}}^{\ensuremath{-}}$ and ${\mathrm{Cl}}^{\ensuremath{-}}$. The internal magnetic field parameter, i.e., HWHM of MR(B) reduces as we replace ${\mathrm{I}}^{\ensuremath{-}}$ by ${\mathrm{Br}}^{\ensuremath{-}}$ and ${\mathrm{Cl}}^{\ensuremath{-}}$ evidencing SOC is indeed weakened on substituting ${\mathrm{I}}^{\ensuremath{-}}$ with lighter halogen ions. Moreover, we analyze the effect of organic cation exchange by replacing ${\mathrm{MA}}^{+}$ with ${\mathrm{FA}}^{+}$ but no drastic change in MR response is observed. Our results successfully establish the crucial role played by SOC on MR for the development of spintronic devices, based on hybrid halide perovskites.

Giant photogalvanic effect and second-harmonic generation in magnetic axion insulators

The second-order nonlinear optical (NLO) processes, such as photogalvanic effect and second-order harmonic generation (SHG), play crucial roles in probing and controlling light-matter interactions for energy and device applications. Combining quantum perturbation theory and first-principles simulations, we predict a giant injection-current photogalvanic effect and SHG in a family of emerging axion insulators, the even septuple layers of $\mathrm{MnB}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{4}$ (MBT) materials. Their amplitudes of photocurrent and SHG are about 1--2 orders of magnitude larger than those of proper ferroelectrics and antiferromagnetic $\mathrm{Cr}{\mathrm{I}}_{3}$. Moreover, unlike the widely studied injection current observed under circularly polarized light, the injection photocurrent of MBT only emerges under linearly polarized light, making it suitable for device applications. These unique characters are from a combination effect of parity-time symmetry and significant spin-orbit coupling. Our predicted enhanced NLOs are valuable for characterizing subtle magnetic orders and shed light on infrared photodetecting and photovoltaic applications based on magnetic topological materials.

Non-collinear Order and Spin–Orbit Coupling in Sr3ZnIrO6

Sr$_{3}$ZnIrO$_{6}$ is an effective spin one-half Mott insulating iridate belonging to a family of magnets which includes a number of quasi-one dimensional systems as well as materials exhibiting three dimensional order. Here we present the results of an extensive investigation into the magnetism including heat capacity, a.c. susceptibility, muon spin rotation ($\mu$SR), neutron diffraction and inelastic neutron scattering on the same sample. It is established that the material exhibits a transition at about $17$ K into a three-dimensional antiferromagnetic structure with propagation vector $\boldsymbol{k}=(0,\frac{1}{2},1)$ in the hexagonal setting of R$\bar{3}$c and non-collinear moments of $0.87$$\mu_B$ on Ir$^{4+}$ ions. Further we have observed a well defined powder averaged spin wave spectrum with zone boundary energy of $\sim 5$ meV at $5$ K. We stress that a theoretical analysis shows that the observed non-collinear magnetic structure arises from anisotropic inter- and intra- chain exchange which has its origin in significant spin-orbit coupling. The model can satisfactorily explain the observed spin wave excitations.

Mononuclear High‐spin Octahedral Cobalt(II) Complex with Positive Axial Magnetic Anisotropy: Synthesis, Crystal Structure, and DFT Studies

This article outlines the magnetic features of a new six–coordinate high‐spin cobalt(II) complex cis‐[CoII(tmphen)2(NCS)2] (1) achieved via the reactions of cobalt(II) thiocyanate with 3,4,7,8‐tetramethyl‐1,10‐phenanthroline. The complex 1 was thoroughly characterized by different analytical and spectroscopic techniques and further confirmed by single X‐ray crystal diffraction pattern. Complex 1 is a neutral molecule and adopt highly distorted six‐coordinate CoN6 octahedral coordination sphere surrounded by two thiocyanate N atoms in cis locations and the equatorial plane is occupied by two imine N atoms from the two tmphen ligand while the remaining two imine N atoms reside in the axial positions. Magnetic susceptibility data of complex 1 revealed that the χΜT values decrease significantly to a value of 1.49 cm3·K·mol–1 at 2.0 K on decreasing temperatures below 100 K, mainly ascribed to the significant spin–orbit coupling (SOC) of six‐coordinate CoII ions. Furthermore, a field‐dependence measurement was performed at 2 K, which shows a positive curvature up to 27 kOe, while it becomes linear up to 2.01 NμB, which authenticated the fact that only the lowest Kramers doublet of ground state is appreciably populated.

Transport-induced suppression of nuclear field fluctuations in multi-quantum-dot systems

Magnetic noise from randomly fluctuating nuclear spin ensembles is the dominating source of decoherence for many multi-quantum-dot multielectron spin qubits. Here we investigate in detail the effect of a DC electric current on the coupled electron-nuclear spin dynamics in double and triple quantum dots tuned to the regime of Pauli spin blockade. We consider both systems with and without significant spin-orbit coupling and find that in all cases the flow of electrons can induce a process of dynamical nuclear spin polarization that effectively suppresses the nuclear polarization gradients over neighboring dots. Since exactly these gradients are the components of the nuclear fields that act harmfully in the qubit subspace, we believe that this presents a straightforward way to extend coherence times in multielectron spin qubits by at least one order of magnitude.

Low Schottky barrier contacts to 2H-MoS2 by Sn electrodes

The semiconductor MoS2 has attracted much attention owing to its sizable energy bandgap, significant spin–orbit coupling, and quantum effects such as the valley Hall effect and gate-induced superconductivity. However, in electronic devices, the energy bandgap usually gives rise to the formation of Schottky barriers at the interface to the contact metal, which may render devices intended for quantum transport inapplicable at low temperature. Therefore, the fabrication of Ohmic contacts operational at low temperature is crucial. Yet, it currently remains a substantial challenge to produce low resistive contacts with a simple process. We manifest that low temperature Ohmic contacts to mono- and few-layer MoS2 can be achieved with Tin (Sn) as the contact metal. Sn is directly evaporated onto MoS2, and hence, this establishes a much easier fabrication method than tunneling barriers, for example. We provide detailed device characterization, extract Schottky barrier heights, demonstrate multiterminal measurements, and propose a possible explanation: strain induced deformation of MoS2 imposed by Sn.

Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems

We demonstrate the emergence of the non-Abelian geometric potentials and thus the three-dimensional (3D) spin-orbit coupling (SOC) for ultracold atoms without using the laser beams. This is achieved by subjecting an atom to a periodic perturbation which is the product of a position-dependent Hermitian operator $\hat{V}\left(\mathbf{r}\right)$ and a fast oscillating periodic function $f\left(\omega t\right)$ with a zero average. To have a significant spin-orbit coupling (SOC), we analyze a situation where the characteristic energy of the periodic driving is not necessarily small compared to the driving energy $\hbar\omega$. Applying a unitary transformation to eliminate the original periodic perturbation, we arrive at a non-Abelian (non-commuting) vector potential term describing the 3D SOC. The general formalism is illustrated by analyzing the motion of an atom in a spatially inhomogeneous magnetic field oscillating in time. A cylindrically symmetric magnetic field provides the SOC involving the coupling between the spin $\mathbf{F}$ and all three components of the orbital angular momentum (OAM) $\mathbf{L}$. In particular, the spherically symmetric monopole-type synthetic magnetic field $\mathbf{B}\propto\mathbf{r}$ generates the 3D SOC of the $\mathbf{L}\cdot \mathbf{F}$ form, which resembles the fine-structure interaction of hydrodgen atom. However, the strength of the SOC here goes as $1/r^{2}$ for larger distances, instead of $1/r^3$ as in atomic fine structure. Such a longer-ranged SOC significantly affects not only the lower states of the trapped atom, but also the higher ones. Furthermore, by properly tailoring the external trapping potential, the ground state of the system can occur at finite OAM, while the ground state of hydrogen atom has zero OAM.

Quasiparticle interference and symmetry of superconducting order parameter in strongly electron-doped iron-based superconductors

Motivated by recent experimental reports of significant spin–orbit coupling (SOC) and a sign-changing order-parameter in the Li1−xFex(OHFe)1−yZnySe superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states—s-wave, d-wave and helical p-wave—can have a fully gapped density of states consistent with angle-resolved photoemission spectroscopy experiments and, due to SOC, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity A1g (s-wave) and B2g (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.

High electron mobility with significant spin-orbit coupling in rock-salt YbO epitaxial thin film

We studied the optical and electrical properties of ytterbium monoxide (YbO) epitaxial thin films with unusual Yb2+ (4f145d0) valence grown by the pulsed laser deposition method. The narrow bandgap of 0.25 eV and the large crystal field splitting of 5d orbitals in YbO determined from absorption spectra were consistent with the chemical trends of ytterbium monochalcogenides (YbChs). Electrical resistivity was tunable upon electron doping via introduction of oxygen vacancies. Electron mobility at room temperature increased up to ∼13 cm2 V−1 s−1 with increasing electron carrier density. The heavily electron-doped YbO showed weak antilocalization at low temperature, suggesting significant spin-orbit coupling owing to the heavy Yb nucleus.

A Co(II)-Hydrazone Schiff Base Single Ion Magnet Exhibiting Field Induced Slow Relaxation Dynamics

An octahedral Co(II) complex with N′-(2-hydroxybenzylidene)acetohydrazide Schiff base ligand [HL] forms a 3D supramolecular assembly supported by non-coordinating ClO4− ions and H2O molecules. Individual spin centres are non-interacting and give rise to significant spin-orbit coupling, resulting in field induced slow magnetisation relaxation; which is characteristic of Single Ion Magnet (SIM) behaviour.

Possible Origin of the Absence of Magnetic Order in LiOsO3: Spin–Orbit Coupling Controlled Ground State

LiOsO3 is the first experimentally confirmed polar metal with ferroelectric‐like distortion. One puzzling experimental fact is its paramagnetic state down to very low temperature with negligible magnetic moment, which is anomalous considering its 5d3 electron configuration since other osmium oxides (e.g., NaOsO3) with 5d3 Os ions are magnetic. Here the magnetic and electronic properties of LiOsO3 are re‐investigated carefully using the first‐principles density functional theory. The calculations reveal that the magnetic state of LiOsO3 can be completely suppressed by the spin–orbit coupling. The subtle balance between significant spin–orbit coupling and weak Hubbard U of 5d electrons can explain both the nonmagnetic LiOsO3 and magnetic NaOsO3. This work provides a reasonable understanding of the long‐standing puzzle of magnetism in some osmium oxides.

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k·p method

A systematic numerical investigation of spin-orbit fields in the conduction bands of III-V semiconductor nanowires is performed. Zinc-blende InSb nanowires are considered along [001], [011], and [111] directions, while wurtzite InAs nanowires are studied along [0001] and [10$\overline{1}$0] or [11$\overline{2}$0] directions. Realistic multiband $\vec{k} \cdot \vec{p}\,$ Hamiltonians are solved by using plane-wave expansions of real-space parameters. In all cases the linear and cubic spin-orbit coupling parameters are extracted for nanowire widths from 30 to 100 nm. Typical spin-orbit energies are on the $\mu$eV scale, except for InAs wurtzite nanowires grown along [10$\overline{1}$0] or [11$\overline{2}$0], in which the spin-orbit energy is about meV, largely independent of the wire diameter. Significant spin-orbit coupling is obtained by applying a transverse electric field, causing the Rashba effect. For an electric field of about 4 mV/nm the obtained spin-orbit energies are about 1 meV for both materials in all investigated growth directions. The most favorable system, in which the spin-orbit effects are maximal, are InAs WZ nanowires grown along [1010] or [11$\overline{2}$0], since here spin-orbit energies are giant (meV) already in the absence of electric field. The least favorable are InAs WZ nanowires grown along [0001], since here even the electric field does not increase the spin-orbit energies beyond 0.1 meV. The presented results should be useful for investigations of optical orientation, spin transport, weak localization, and superconducting proximity effects in semiconductor nanowires.

Spin-dependent magneto-thermopower of narrow-gap lead chalcogenide quantum wells

A semi-classical analysis of magneto-thermopower behaviour, namely, the Seebeck and Nernst effect (NE) in quantum wells of IV-VI lead salts with significant extrinsic Rashba spin-orbit coupling (RSOC) is performed in this report. In addition to the spin-dependent Seebeck effect that has been observed before, we also theoretically predict a similar spin-delineated behavior for its magneto-thermal analog, the spin-dependent NE. The choice of lead salts follows from a two-fold advantage they offer, in part, to their superior thermoelectric properties, especially PbTe, while their low band gaps and high spin-orbit coupling make them ideal candidates to study RSOC governed effects in nanostructures. The calculations show a larger longitudinal magneto-thermopower for the spin-up electrons while the transverse components are nearly identical. In contrast, for a magnetic field free case, the related power factor calculations reveal a significantly higher contribution from the spin-down ensemble and suffer a reduction with an increase in the electron density. We also discuss qualitatively the limitations of the semi-classical approach for the extreme case of a high magnetic field and allude to the observed thermopower behaviour when the quantum Hall regime is operational. Finally, techniques to modulate the thermopower are briefly outlined.

Room-temperature superparamagnetism due to giant magnetic anisotropy in MoS defected single-layer MoS2

Room-temperature superparamagnetism due to a large magnetic anisotropy energy (MAE) of a single atom magnet has always been a prerequisite for nanoscale magnetic devices. Realization of two dimensional (2D) materials such as single-layer (SL) MoS2, has provided new platforms for exploring magnetic effects, which is important for both fundamental research and for industrial applications. Here, we use density functional theory (DFT) to show that the antisite defect (MoS) in SL MoS2 is magnetic in nature with a magnetic moment μ of ∼2 and, remarkably, exhibits an exceptionally large atomic scale MAE of ∼500 meV. Our calculations reveal that this giant anisotropy is the joint effect of strong crystal field and significant spin–orbit coupling (SOC). In addition, the magnetic moment μ can be tuned between 1 and 3 by varying the Fermi energy , which can be achieved either by changing the gate voltage or by chemical doping. We also show that MAE can be raised to ∼1 eV with n-type doping of the MoS2:MoS sample. Our systematic investigations deepen our understanding of spin-related phenomena in SL MoS2 and could provide a route to nanoscale spintronic devices.