Finite Spin-orbit Coupling Research Articles

Boosting the Edelstein effect of two-dimensional electron gases by ferromagnetic exchange

Strontium titanate (SrTiO3) two-dimensional electron gases (2DEGs) have broken spatial inversion symmetry and possess a finite Rashba spin-orbit coupling. This enables the interconversion of charge and spin currents through the direct and inverse Edelstein effects, with record efficiencies at low temperature but more modest effects at room temperature. Here, we show that making these 2DEGs ferromagnetic enhances the conversion efficiency by nearly one order of magnitude. Starting from the experimental band structure of nonmagnetic SrTiO3 2DEGs, we mimic magnetic exchange coupling by introducing an out-of-plane Zeeman term in a tight-binding model. We then calculate the band structure and spin textures for increasing internal magnetic fields and compute the Edelstein effect using a semiclassical Boltzmann approach. We find that the conversion efficiency first increases strongly with increasing magnetic field, then shows a maximum, and finally decreases. This field dependence is caused by the competition of the exchange coupling with the effective Rashba interaction. While the magnetic field enhances the splitting of band pairs (both in momentum and in spin expectation value), it also weakens the in-plane Rashba-type spin texture. The former mechanism increases the Edelstein effect, and the latter reduces it. Published by the American Physical Society 2024

Robust half-metallicity and topological properties in square-net potassium manganese chalcogenides

Combining ab initio and model Hamiltonian approaches, we investigate the electronic, magnetic, and topological properties of potassium manganese chalcogenides that host square nets of Mn and chalcogen atoms. Our analysis establishes these compounds to be robust half-metallic ferromagnets. The origin of ferromagnetism in these compounds is found to be based on a kinetic energy-driven double-exchange mechanism, first proposed for ${\mathrm{Sr}}_{2}{\mathrm{FeMoO}}_{6}$, a double-perovskite compound. The presence of finite spin-orbit coupling at chalcogen sites triggers nontrivial topology of the chalcogen-derived bands at the conducting channel, dominating the electronic structure close to the Fermi level. This puts the studied compounds in the class of topological half-metals with appreciable values of anomalous Hall conductivity, opening up the application possibility in topological quantum spintronics. Cleavability of these layered compounds makes the situation further promising.

Spin–orbit coupling controlling the superconducting dome of artificial superlattices of quantum wells

While it is known that a resonant amplification of Tc in two-gap superconductors can be driven by using the Fano–Feshbach resonance tuning the chemical potential near a Lifshitz transition, little is known on tuning the Tc resonance by cooperative interplay of the Rashba spin–orbit coupling (RSOC) joint with phonon mediated (e-ph) pairing at selected k-space spots. Here, we present first-principles quantum calculation of superconductivity in an artificial heterostructure of metallic quantum wells with 3 nm period where quantum size effects give two-gap superconductivity with RSOC controlled by the internal electric field at the interface between the nanoscale metallic layers intercalated by insulating spacer layers. The key results of this work show that fundamental quantum mechanics effects including RSCO at the nanoscale [Mazziotti et al., Phys. Rev. B, 103, 024523 (2021)] provide key tools in applied physics for quantitative material design of unconventional high temperature superconductors at ambient pressure. We discuss the superconducting domes where Tc is a function of either the Lifshitz parameter (η) measuring the distance from the topological Lifshitz transition for the appearing of a new small Fermi surface due to quantum size effects with finite spin–orbit coupling and the variable e-ph coupling g in the appearing second Fermi surface linked with the energy softening of the cut off ω0.

Anomalous Hall effect in the coplanar antiferromagnetic coloring-triangular lattice

We study the anomalous Hall effect on the antiferromagnetic coloring-triangular lattice with a coplanar magnetic configuration in the presence of a spin-orbit interaction. The effect of the spin-orbit coupling is included at an effective level as a rotation of the electronic spin as the electrons hop from site to site. Our result reveals that a finite Hall conductivity in the planar ${120}^{\ensuremath{\circ}}$ structure takes place if a finite spin-orbit coupling is present. A quantized Hall conductivity occurs at global band gaps resulting from the topologically nontrivial band structure.

Phase diagram of graphene in the presence of spin-orbit coupling and electron-electron interaction

We theoretically investigate in this work the interplay between the intrinsic spin-orbit coupling (SOC) and electron-electron interaction on the magnetism in the graphene honeycomb lattice. Particularly, a phase diagram is here explored and studied by Kane-Mele-Hubbard (KMH) model combined with mean-field theory and self-consistent algorithm. Results show that the graphene undergoes a phase transition from the gapless semi-metal to topological band insulator (TBI) at a finite SOC and weak Coulomb energy U, and another transition from the TBI to antiferromagnetic ordered insulator at stronger Coulomb energy U observed as well. Moreover, our calculations also point out the prior developing orientation of magnetic moments in the in-plane direction driven by the SOC rather than that in the out-of-plane direction without the SOC.

Two types of dark solitons in a spin-orbit-coupled Fermi gas

Dark solitons in quantum fluids are well known nonlinear excitations that are usually characterized by a single length scale associated with the underlying background fluid. We show that in the presence of spin-orbit coupling and a linear Zeeman field, superfluid Fermi gases support two different types of nonlinear excitations featured by corresponding length scales related to the existence of two Fermi surfaces. Only one of these types, which occurs for finite spin-orbit coupling and a Zeeman field, survives to the topological phase transition, and is therefore capable to sustain Majorana zero modes. At the point of the emergence of this soliton for varying the Zeeman field, the associated Andreev bound states present a minigap that vanishes for practical purposes, in spite of lacking the reality condition of Majorana modes.

Metal/ SrTiO3 two-dimensional electron gases for spin-to-charge conversion

SrTiO$_3$-based two-dimensional electron gases (2DEGs) can be formed through the deposition of epitaxial oxides like LaAlO$_3$ or of reactive metals such as Al. Such 2DEGs possess a finite Rashba spin-orbit coupling that has recently been harnessed to interconvert charge and spin currents through the direct and inverse Edelstein and spin Hall effects. Here we compare the formation and properties of 2DEGs generated in SrTiO$_3$ by the growth of Al, Ta and Y ultrathin films by magnetron sputtering. By combining in situ and ex situ X-ray photoelectron spectroscopy (XPS) we gain insight into the reduction of the SrTiO$_3$ and the appearance of Ti$^{3+}$ states associated with 2DEG formation, its reoxidation by exposure to the air, and the transformation of the metal into its binary oxides. We extract the carrier densities through magnetotransport and compare them with the XPS data. Finally, working with samples covered by an extra layer of NiFe, we perform spin-pumping ferromagnetic resonance experiments and investigate spin-charge conversion as a function of gate voltage. We identify trends in the data across the different sample systems and discuss them as a function of the carrier density and the transparency of the metal oxide tunnel barrier.

All‐Electrical Magnon Transport Experiments in Magnetically Ordered Insulators

Angular momentum transport is one of the cornerstones of spintronics. Spin angular momentum is not only transported by mobile charge carriers but also by the quantized excitations of the magnetic lattice in magnetically ordered systems. In this regard, magnetically ordered insulators (MOIs) provide a platform for magnon spin transport experiments without additional contributions from spin currents carried by mobile electrons. In combination with charge‐to‐spin current conversion processes in conductors with finite spin–orbit coupling, it is possible to realize all‐electrical magnon transport schemes in thin‐film heterostructures. Herein, an insight into such experiments and recent breakthroughs achieved is provided. Special attention is given to charge‐current‐based manipulation via an adjacent normal metal of magnon transport in MOIs in terms of spin‐transfer torque. Moreover, the influence of two magnon modes with opposite spin in antiferromagnetic insulators on all‐electrical magnon transport experiments is discussed.

Erratum: Z2 characterization for three-dimensional multiband Hubbard models [Phys. Rev. Research 2 , 013299 (2020)

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spin-orbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surface originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, non-trivially linked nodal line semimetals and circuit-based quantum simulators.

Complete polarization of electronic spins in OLEDs

At low temperatures and high magnetic fields, electron and hole spins in an organic light-emitting diode become polarized so that recombination preferentially forms molecular triplet excited-state species. For low device currents, magnetoelectroluminescence perfectly follows Boltzmann activation, implying a virtually complete polarization outcome. As the current increases, the magnetoelectroluminescence effect is reduced because spin polarization is suppressed by the reduction in carrier residence time within the device. Under these conditions, an additional field-dependent process affecting the spin-dependent recombination emerges, possibly related to the build-up of triplet excitons and their interaction with free charge carriers. Suppression of the EL alone does not prove electronic spin polarization. We therefore probe changes in the spin statistics of recombination directly in a dual singlet-triplet emitting material, which shows a concomitant rise in phosphorescence intensity as fluorescence is suppressed. Finite spin-orbit coupling in these materials gives rise to a microscopic distribution in effective g-factors of electrons and holes, Δg, i.e., a distribution in Larmor frequencies. This Δg effect in the pair, which mixes singlet and triplet, further suppresses singlet-exciton formation at high fields in addition to thermal spin polarization of the individual carriers.

Anisotropic Berry phase in the Dirac nodal-line semimetal ZrSiS: The effect of spin-orbit coupling

The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the $k$ space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the $c$ axis and magnetic field rotating in the $ab$ plane. The extremal orbits identified through the field orientation dependence of the QOs interlock with the nodal line, leading to a nonzero Berry phase. Most importantly, the Berry phase shows a significant dependence on the magnetic field orientation, which we argue to be due to the finite spin-orbit coupling gap. Our results demonstrate the importance of the spin-orbit coupling and the nodal-line dispersion in understanding the quantum transport of NLSMs.

Electronic Band Topology of Monoclinic MoS2 Monolayer: Study Based on Elementary Band Representations for Layer Groups

A monoclinic monolayer is demonstrated to be a topological semimetal (spinless), or zero‐gap semiconductor (spinful, without spin–orbit coupling), or topologically trivial insulator (finite spin–orbit coupling). The latter contradicts a previous prediction that exhibits quantum‐spin Hall (QSH) effect, and the reported value of ‐invariant, calculated from inversion‐parity values at four Brillouin‐zone high‐symmetry points. Namely, as the electronic states of two of these points are double degenerate and transform according to irreducible representations carrying no parity, the band topology of is investigated using elementary band representations (EBRs) for layer groups (LGs). Novel subroutines, which output EBRs and Wilson loop operators for low‐dimensional systems, are incorporated into POLSym code. Based on the calculated band structure decomposition onto EBRs of the relevant symmetry group and Wilson loop eigen‐spectra, it is revealed that valence‐band Wannier functions do not break the symmetry, and that Wannier centers are localized within a unit cell. Moreover, the QSH state is proved to be not realizable within ‐phase group‐VI transition‐metal dichalcogenides, because EBRs for the relevant symmetry groups are topologically trivial. However, it is predicted that among compounds that form other monoclinic structure, with symmorphic LG symmetry, there may exist topologically nontrivial phases, including the QSH state.

Real-space Berry curvature of itinerant electron systems with spin-orbit interaction

By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $\gamma$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid for SU(2) invariant systems, $\gamma=\Omega/2$, where $\Omega$ is the solid angle subtended by the local magnetic moments enclosed by the loop. The general form of $\gamma$ demonstrates that collinear and coplanar magnetic textures can also induce a Berry phase different from 0 or $\pi$, smoothly connecting the result for SU(2) invariant systems with the well-known result of Karplus and Luttinger for collinear ferromagnets with finite SOC. By taking the continuum limit of the theory, we also derive the corresponding generalized form of the real space Berry curvature. The new expression is a generalization of the scalar spin chirality, which is presented in an explicitly covariant form. We finally show how these simple concepts can be used to understand the origin of the spontaneous topological Hall effect that has been recently reported in collinear and coplanar antiferromagnetic phases of correlated materials.

Orbital transmutation and the electronic spectrum of FeSe in the nematic phase

We consider the electronic spectrum near $M=(\pi,\pi)$ in the nematic phase of FeSe ($T<T_{{\rm nem}}$) and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the $M$ point. These have been identified as having $xz$ and $yz$ orbital character well below $T_{{\rm nem}}$, but remain split at $T>T_{{\rm nem}}$, in apparent contradiction to the fact that in the tetragonal phase the $xz$ and $yz$ orbitals are degenerate. Here we present two scenarios which can describe the data. In both scenarios, hybridization terms present in the tetragonal phase leads to an orbital transmutation, a change in the dominant orbital character of some of the bands, between $T > T_{\rm nem}$ and $T \ll T_{\rm nem}$. The first scenario relies on the spin-orbit coupling at the $M$ point. We show that a finite spin-orbit coupling gives rise to orbital transmutation, in which one of the modes, identified as $xz$ ($yz)$ at $T \ll T_{{\rm nem}}$, becomes predominantly $xy$ at $T > T_{{\rm nem}}$ and hence does not merge with the predominantly $yz$ ($xz$) mode. The second scenario, complementary to the first, takes into consideration the fact that both ARPES and STM are surface probes. In the bulk, a direct hybridization between the $xz$ and $yz$ orbitals is not allowed at the $M$ point, however, it is permitted on the surface. In the presence of a direct $xz/yz$ hybridization, the orbital character of the $xz/yz$ modes changes from pure $xz$ and pure $yz$ at $T \ll T_{{\rm nem}}$ to $xz \pm yz$ at $T > T_{{\rm nem}}$, i.e., the two modes again have mono-orbital character at low $T$, but do not merge at $T_{{\rm nem}}$. We discuss how these scenarios can be distinguished in polarized ARPES experiments.

Chiral damping, chiral gyromagnetism, and current-induced torques in textured one-dimensional Rashba ferromagnets

We investigate Gilbert damping, spectroscopic gyromagnetic ratio and current-induced torques in the one-dimensional Rashba model with an additional noncollinear magnetic exchange field. We find that the Gilbert damping differs between left-handed and right-handed N\'eel-type magnetic domain walls due to the combination of spatial inversion asymmetry and spin-orbit interaction (SOI), consistent with recent experimental observations of chiral damping. Additionally, we find that also the spectroscopic $g$ factor differs between left-handed and right-handed N\'eel-type domain walls, which we call chiral gyromagnetism. We also investigate the gyromagnetic ratio in the Rashba model with collinear magnetization, where we find that scattering corrections to the $g$ factor vanish for zero SOI, become important for finite spin-orbit coupling, and tend to stabilize the gyromagnetic ratio close to its nonrelativistic value.

Disorder robustness and protection of Majorana bound states in ferromagnetic chains on conventional superconductors

Majorana bound states (MBSs) are well established in the clean limit in chains of ferromagnetically aligned impurities deposited on conventional superconductors with finite spin-orbit coupling. Here we show that these MBSs are very robust against disorder. By performing self-consistent calculations we find that the MBSs are protected as long as the surrounding superconductor show no large signs of inhomogeneity. We also find that longer chains offer more stability against disorder for the MBSs, albeit the minigap decreases, as do increasing strengths of spin-orbit coupling and superconductivity.

Superconducting order parameterπ-phase shift in magnetic impurity wires

It has previously been found that a magnetic impurity in a conventional $s$-wave superconductor can give rise to a local $\pi$-phase shift of the superconducting order parameter. By studying a finite wire of ferromagnetic impurities, we are able to trace the origin of the $\pi$-phase shift to a resonance condition for the Bogoliubov-de Gennes quasiparticle states. When non-resonating states localized at the impurity sites are pulled into the condensate for increasing magnetic strength, the superconducting order parameter is reduced in discrete steps, eventually resulting in a $\pi$-phase shift. We also show that for a finite spin-orbit coupling, the $\pi$-phase shift is preserved and occurs in a large portion of the topologically non-trivial phase.

Unusual nodal behaviors of the superconducting gap in the iron-based superconductor Ba(Fe0.65Ru0.35)2As2 : Effects of spin-orbit coupling

We have investigated the superconducting gap of optimally doped Ba(Fe$_{0.65}$Ru$_{0.35}$)$_2$As$_2$ by angle-resolved photoemission spectroscopy (APRES) using bulk-sensitive 7 eV laser and synchrotron radiation. It was found that the gap is isotropic in the $k_x$-$k_y$ plane both on the electron and hole Fermi surfaces (FSs). The gap magnitudes of two resolved hole FSs show similar $k_z$ dependences and decrease as $k_z$ approaches $\sim$ 2$\pi$/$c$ (i.e., around the Z point) unlike the other Fe-based superconductors reported so far, where the superconducting gap of only one hole FS shows a strong $k_z$ dependence. This unique gap structure can be understood in the scenario that the $d_{z^2}$ orbital character is mixed into both hole FSs due to the finite spin-orbit coupling between almost degenerate FSs and is reproduced by calculations within the random phase approximation including the spin-orbit coupling.

Hund Interaction, Spin-Orbit Coupling, and the Mechanism of Superconductivity in Strongly Hole-Doped Iron Pnictides.

We present a novel mechanism of s-wave pairing in Fe-based superconductors. The mechanism involves holes near d_{xz}/d_{yz} pockets only and is applicable primarily to strongly hole doped materials. We argue that as long as the renormalized Hund's coupling J exceeds the renormalized interorbital Hubbard repulsion U^{'}, any finite spin-orbit coupling gives rise to s-wave superconductivity. This holds even at weak coupling and regardless of the strength of the intraorbital Hubbard repulsion U. The transition temperature grows as the hole density decreases. The pairing gaps are fourfold symmetric, but anisotropic, with the possibility of eight accidental nodes along the larger pocket. The resulting state is consistent with the experiments on KFe_{2}As_{2}.

Currents induced by magnetic impurities in superconductors with spin-orbit coupling.

We show that superconducting currents are generated around magnetic impurities and ferromagnetic islands proximity coupled to superconductors with finite spin-orbit coupling. Using the Ginzburg-Landau theory, T-matrix calculation, as well as self-consistent numerical simulation on a lattice, we find a strong dependence of the current on the direction and magnitude of the magnetic moment. We establish that in the case of point magnetic impurities, the current is carried by the induced Yu-Shiba-Rusinov (YSR) subgap states. In the vicinity of the phase transition, where the YSR states cross at zero energy, the current increases dramatically. Furthermore, we show that the currents are orthogonal to the local spin polarization and, thus, can be probed by measuring the spin-polarized local density of states.