The surface states of three-dimensional topological insulators exhibit a helical spin texture with spin locked to momentum. To date, however, the direct all-electrical detection of the helical spin texture has remained elusive owing to the lack of necessary spin-sensitive measurements. We here provide a general theory for spin polarized transports of helical Dirac electrons through spin-polarized scanning tunneling microscopy (STM). It is found that different from conventional magnetic materials, the tunneling conductance through the TI surface acquires an extra component determined by the in-plane spin texture, exclusively associated with spin momentum locking. Importantly, this extra conductance unconventionally depends on the spatial azimuthal angle of the magnetized STM tip, which is never carried out in previous STM theory. By magnetically doping to break the symmetry of rotation and time reversal of the TI surface, we find that the measurement of the spatial resolved conductance can reconstruct the helical structure of spin texture. Furthermore, one can extract the SML angle if the in-plane magnetization is induced purely by the spin-orbit coupling of surface Dirac elections. Our theory offers an alternative way, rather than using angle resolved photoemission spectroscopy, to electrical identify the helical spin texture on TI surfaces.
Recent experiments by Gutiérrez $\textit{et al.}$ [Nature Phys. $\textbf{12}$, 950 (2016)] on a graphene-copper superlattice have revealed an unusual Kekulé bond texture in the honeycomb lattice --- a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called "Kek-Y" texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field $B$ the valley degeneracy of the $B$-dependent Landau levels is removed by the valley-momentum locking --- but a …
Recently, orbital-textures have been found in Rashba and topological insulator (TI) surface states as a result of the spin-orbit coupling (SOC). Here, we predict a $p_x/p_y$ orbital texture, in linear dispersive Dirac bands, arising at the K/K' points of $χ$-$h_0$ borophene chiral monolayer. Combining first-principles calculations with effective hamiltonians, we show that the orbital pseudospin has its direction locked with the momentum in a similar way as TIs' spin-textures. Additionally, considering a layer pseudospin degree of freedom, this lattice allows stackings of layers with equivalent…
Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since electrical reading of chiral attributes is highly non-trivial with conventional current perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from extensive first-principles simulations and multiple scattering expansion the emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly efficient all-electrical readout of the chirality and helicity of re…
The viability of past, current and future devices for information technology hinges on their sensitivity to the presence of impurities. The latter can lead to resistivity anomalies, the so-called Kondo effect, reshape extrinsically Hall effects or reduce the efficiency of magnetoresistance effects essential in spintronics. Here we demonstrate that atomic defects enable highly efficient all-electrical detection of spin-swirling textures, in particular magnetic skyrmions, which are promising bits candidates in future spintronics devices. Impurities amplify the bare transport signal and can alter…
We investigate how the ability of the vortex oscillation mode of a spin-torque nano-oscillator to lock to an external microwave signal is modified when it is coupled to another oscillator. We show experimentally that mutual electrical coupling can lead to locking range enhancements of a factor 1.64. Furthermore, we analyze the evolution of the locking range as a function of the coupling strength through experiments and numerical simulations. By uncovering the mechanisms at stake in the locking range enhancement, our results will be useful for designing spin-torque nano-oscillators arrays with …
In spin-orbit coupled crystals, symmetries can protect multifold degeneracies with large Chern numbers and Brillouin zone spanning topological surface states. In this work, we explore the extent to which the nontrivial topology of chiral multifold fermions impacts the spin texture of bulk states. To do so, we formulate a definition of spin-momentum locking in terms of reduced density matrices. Using tools from the theory of topological quantum chemistry, we show how the reduced density matrix can be determined from the knowledge of the basis orbitals and band representation forming the multifo…
We study correlations and magnetic textures of localized spins, doped in three-dimensional Dirac semimetals. An effective field theory for magnetic moments is constructed by integrating out the fermionic degrees of freedom. The spin correlation shows a strong anisotropy, originating from spin-momentum locking of Dirac electrons, in addition to the conventional Heisenberg-like ferromagnetic correlation. The anisotropic spin correlation allows topologically nontrivial magnetic excitation textures such as a transient hedgehog state, as well as the ferromagnetic ground state. The spin-wave dispers…
The unique feature of surface states in topological insulators is the so-called "spin-momentum locking", which means that electron spin is oriented along a fixed direction for a given momentum and forms a texture in the momentum space. In this work, we study spin textures of two typical topological insulators in Hg-Based Chalcogenides, namely HgTe and HgS, based on both the first principles calculation and the eight band Kane model. We find opposite helicities of spin textures between these two materials, originating from the opposite signs of spin-orbit couplings. Furthermore, we reveal that …
In this study, we report first experimental evidence of spin-momentum locking in the topological phonons in an inhomogeneously strained Si thin film. The spin-momentum locking in the topological phonons lead to a longitudinal spin texture or spatially inhomogeneous spin distribution in the freestanding sample structure. The spin texture was uncovered using location dependent Hall effect and planar Hall effect measurement. The charge carrier density and anomalous Hall resistance showed a linear behavior along the length of the sample. Similarly, the planar Hall resistance related with the spin …
We consider the energy spectrum and the spin-parity structure of the eigenstates for a quantum dot made of a strong topological insulator. Using the effective low-energy theory in a finite-length cylinder geometry, numerical calculations show that even at the lowest energy scales, the spin direction in a topologically protected surface mode is not locked to the surface. We find "zero-momentum" modes, and subgap states localized near the "caps" of the dot. Both the energy spectrum and the spin texture of the eigenstates are basically reproduced from an analytical surface Dirac fermion descripti…
While some of the most elegant applications of topological insulators, such as quantum anomalous Hall effect, require the preservation of Dirac surface states in the presence of time-reversal symmetry breaking, other phenomena such as spin-charge conversion rather rely on the ability for these surface states to imprint their spin texture on adjacent magnetic layers. In this work, we investigate the spin-momentum locking of the surface states of a wide range of monolayer transition metals (3$d$-TM) deposited on top of Bi$_{2}$Se$_{3}$ topological insulators using first principles calculations. …
We formulate an energy-storage concept based on the free energy associated with metastable magnetic configurations. Despite the active, magnetic region of the battery being electrically insulating, it can sustain effective hydrodynamics of spin textures, whose conservation law is governed by topology. To illustrate the key physics and potential functionality, we focus here on the simplest quasi-one-dimensional case of planar winding of the magnetic order parameter. The energy is stored in the metastable winding number, which can be injected electrically by an appropriately tailored spin torque…
We consider a hybrid structure consisting of superconducting or normal leads with a combined ferromagnet-3D topological insulator interlayer. We compare responses of a Josephson junction and a normal junction to magnetic texture dynamics. In both cases the electromotive force resulting from the magnetization dynamics generates a voltage between the junction leads. For an open circuit this voltage is the same for normal and superconducting leads and allows for electrical detection of magnetization dynamics and a structure of a given magnetic texture. However, under the applied current the elect…
The spin orientation of electronic wavefunctions in crystals is an internal degree of freedom, typically insensitive to electrical knobs. We argue from a general symmetry analysis and a $\vec k \cdot \vec p$ perspective, that monolayer 1T'-WTe$_2$ possesses a gate-activated canted spin texture that produces an electrically tunable bulk band quantum geometry. In particular, we find that due to its out-of-plane asymmetry, an applied out-of-plane electric field breaks inversion symmetry to induce both in-plane and out-of-plane electric dipoles. These in-turn generate spin-orbit coupling to lift t…
The magnetoelectric effects in the surface states of the 3D TI are extremely strong due to the full spin-momentum locking. Here the microscopic theory of S/3D TI bilayer structures in terms of quasiclassical Green's functions is developed. On the basis of the developed formalism it is shown that the DOS in the S/TI bilayer manifests giant magnetoelectric behavior and, as a result, S/3D TI heterostructures can work as non-magnetic fully electrically controllable spin filters. It is shown that due to the full spin-momentum locking the amplitudes of the odd-frequency singlet and triplet component…
We have designed three-dimensional models of topological insulator thin films, showing a tunability of the odd number of Dirac cones on opposite surfaces driven by the atomic-scale geometry at the boundaries. This enables creation of a single Dirac cone at the $Γ$-point as well as possible suppression of quantum tunneling between Dirac states at opposite surfaces (and gap formation), when opposite surfaces are geometrically differentiated. The spin texture of surface states was found to change from a spin-momentum-locking symmetry to a progressive loss in surface spin polarization upon the int…
Electron spin-momentum locking together with background magnetic textures can significantly alter the electron transport properties. We theoretically investigate the electron transport at the interface between a topological insulator and a magnetic insulator with magnetic skyrmions on the top. In contrast to the conventional topological Hall effect in normal metals, the skyrmions yield an additional contribution to the anomalous Hall conductivity even in the absence of in-plane magnetic texture, arising from the phase factor characteristic to Dirac electrons acquired at skyrmion boundary.
We theoretically study electrical responses of magnetization in Weyl semimetals. The Weyl semimetal is a new class of topological semimetals, possessing hedgehog type spin textures in momentum space. Because of this peculiar spin texture, an interplay of electron transport and spin dynamics might provide new method to electrical control of magnetization. In this paper, we consider the magnetically doped Weyl semimetals, and systematically study current- and charge-induced spin torque exerted on the local magnetization in three-dimensional Dirac-Weyl metals. We determine all current-induced spi…
Surface states of three-dimensional topological insulators exhibit the phenomenon of spin-momentum locking, whereby the orientation of an electron spin is determined by its momentum. Probing the spin texture of these states is of critical importance for the realization of topological insulator devices, however the main technique available so far is the spin- and angle-resolved photoemission spectroscopy. Here we reveal a close link between the spin texture and a new kind of magneto-resistance, which depends on the relative orientation of the current with respect to the magnetic field as well a…
Coupling degrees of freedom of distinct nature plays a critical role in numerous physical phenomena. The recent emergence of layered materials provides a laboratory for studying the interplay between internal quantum degrees of freedom of electrons. Here, we report experimental signatures of new coupling phenomena connecting real spin with layer pseudospins in bilayer WSe2. In polarization-resolved photoluminescence measurements, we observe large spin orientation of neutral and charged excitons generated by both circularly and linearly polarized light, with a splitting of the trion spectrum in…
Topological insulator is a new state of matter which exhibits exotic surface electronic properties. Determining the spin texture of this class of material is of paramount importance for understanding its topological order and can lead to potential applications in spintronics. Here, we have investigated the nature of the surface state of the topological insulator with hexagonal warping subjected to an off-resonant circularly polarized light. The resulting electronic ground state exhibits a novel feature of spin texture breaking the conventional spin-momentum locking present on a topological ins…
A three-dimensional topological insulator manifests gapless surface modes, described by two-dimensional Dirac equation. We study magnetic textures, such as domain walls and vortices, in a ferromagnetic thin film deposited on a three-dimensional topological insulator. It is shown that these textures can be electrically charged, ascribed to the proximity effect with the Dirac surface states. We derive a general relation between the electric and the magnetic charges. As a physical consequence, we discuss domain wall motion driven by an applied electric field, which promises magnetic devices with …
The surface of a topological insulator hosts Dirac electronic states with the spin-momentum locking, which constrains spin orientation perpendicular to electron momentum. As a result, collective plasma excitations in the interacting Dirac liquid manifest themselves as coupled charge- and spin-waves. Here we demonstrate that the presence of the spin component enables effective coupling between plasma waves and spin waves at interfaces between the surface of a topological insulator and insulating magnet. Moreover, the helical nature of spin-momentum locking textures provides the phase winding in…
The recently discovered interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) in multilayers with perpendicular magnetic anisotropy favors the canting of spins in the in-plane direction and could thus enable new exciting spin textures such as Hopfions in continuous multilayer films. A key requirement is to control the IL-DMI and so in this study, the influence of an electric current on the IL-DMI is investigated by out-of-plane hysteresis loops of the anomalous Hall effect under applied in-plane magnetic fields. The direction of the in-plane field is varied to obtain a full azimuthal dependenc…
We present a new switching mechanism that utilizes the proximity coupling between the surface spin texture of a Weyl semimetal and a superconductor, in a Weyl semimetal/superconductor/Weyl semimetal trilayer heterostructure. We show that the superconductivity in the middle layer can be fully suppressed by the surface spin texture of the Weyl semimetals in the presence of an external magnetic field, but it can be recovered again by only changing the field direction. The restoration of the middle-layer superconductivity indicates a sharp transition to a low-resistance state. This sharp switching…
Topological insulators represent a new quantum state of matter that are insulating in the bulk but metallic on the edge or surface. In the Dirac surface state, it is well-established that the electron spin is locked with the crystal momentum. Here we report a new phenomenon of the spin texture locking with the orbital texture in a topological insulator Bi2Se3. We observe light-polarization-dependent spin texture of both the upper and lower Dirac cones that constitutes strong evidence of the orbital-dependent spin texture in Bi2Se3. The different spin texture detected in variable polarization g…
We demonstrate that the spin orientation of an electron propagating in a one-dimensional nanostructure with Rashba spin-orbit (SO) coupling can be manipulated on demand by changing the geometry of the nanosystem. Shape deformations that result in a non-uniform curvature give rise to complex three-dimensional spin textures in space. We employ the paradigmatic example of an elliptically deformed quantum ring to unveil the way to get an all-geometrical and all-electrical control of the spin orientation. The resulting spin textures exhibit a tunable topological character with windings around the r…
Momentum-space topology of electrons under strong spin-orbit coupling contributes to the electrically induced torques exerting on magnetic textures insensitively to disorder or thermal fluctuation. We present a direct connection between band topology and the torques by classifying the whole torques phenomenologically. As well as the intrinsic anomalous Hall effect, the torques also emerge intrinsically from the anomalous velocity of electrons regardless of a nonequilibrium transport current. We especially point out the intrinsic contribution arising exclusively in magnetic textures, which we c…
Antiferromagnetic spintronics is an emerging area of quantum technologies that leverage the coupling between spin and orbital degrees of freedom in exotic materials. Spin-orbit interactions allow spin or angular momentum to be injected via electrical stimuli to manipulate the spin texture of a material, enabling the storage of information and energy. In general, the physical process is intrinsically local: spin is carried by an electrical current, imparted into the magnetic system, and the spin texture then rotates. The collective excitations of complex spin textures have rarely been utilized …
We explore the second order bilinear magnetoelectric resistance (BMER) effect in the d-electron-based two-dimensional electron gas (2DEG) at the SrTiO3 (111) surface. We find an evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the six-fold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin-texture…
Topological magnon modes are expected to be useful for novel applications such as robust information propagation, since they are immune to backscattering and robust against disorder. Although there are several of theoretical proposals for topological magnon modes and growing experimental efforts for realizing them by now, it is still desirable to add complementary insights on this important phenomenon. Here, we propose a new scheme to achieve topological magnon where only nearest-neighbour exchange couplings on honeycomb lattice are necessary. In both ferromagnets and antiferromagnets, tuning …
Spin Hall oscillators (SHO) are promising candidates for the generation, detection and amplification of high frequency signals, that are tunable through a wide range of operating frequencies. They offer to be read out electrically, magnetically and optically in combination with a simple bilayer design. Here, we experimentally study the spatial dependence and spectral properties of auto-oscillations in SHO devices based on Pt(7 nm)/\ Ni$_{\mathrm{80}}$Fe$_{\mathrm{20}}$(5 nm) tapered nanowires. Using Brillouin light scattering microscopy, we observe two individual self-localized spin-wave bulle…
Partially filled Landau levels host competing orders, with electron solids prevailing close to integer fillings before giving way to fractional quantum Hall liquids as the Landau level fills. Here, we report the observation of an electron solid with noncolinear spin texture in monolayer graphene, consistent with solidification of skyrmions---topological spin textures characterized by quantized electrical charge. In electrical transport, electron solids reveal themselves through a rapid metal-insulator transition in the bulk electrical conductivity as the temperature is lowered, accompanied by …
The Rashba-Dresselhaus effect is the splitting of doubly degenerate band extrema in semiconductors, accompanied by the emergence of counter-rotating spin textures and spin-momentum locking. Here we investigate how this effect is modified by lattice vibrations. We show that, in centrosymmetric non-magnetic crystals, for which a bulk Rashba-Dresselhaus effect is symmetry-forbidden, electron-phonon interactions can induce a phonon-assisted, dynamic Rashba-Dresselhaus spin splitting in the presence of an out-of-equilibrium phonon population. In particular, we show how Rashba, Dresselhaus, or Weyl …
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. The spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner.
Strong dependence of the Josephson energy on the magnetization orientation in Josephson junctions with ferromagnetic interlayers and spin-orbit coupling opens a way to control magnetization by Josephson current or Josephson phase. Here we investigate the perspectives of magnetization control in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions on the surface of a 3D topological insulator hosting Dirac quasiparticles. Due to the spin-momentum locking of these Dirac quasiparticles a strong dependence of the Josephson current-phase relation on the magnetization orientation is …
Spin momentum locking is a key feature of the topological surface state, which plays an important role in spintronics. The electrical detection of current-induced spin polarization protected by the spin momentum locking in non-magnetic systems provides a new platform for developing spintronics while previous studies were mostly based on magnetic materials. In this study, the spin transport measurement of Dirac semimetal Cd3As2 was studied by the three-terminal geometry, and a hysteresis loop signal with high resistance and low resistance state was observed. The hysteresis was reversed by rever…
A topological insulator is characterized by spin-momentum locking on its boundary. The spin momentum locking on the surface of a three dimensional topological insulator leads to the existence of a non-trivial Berry's phase which leads to exotic transport phenomena on topological surfaces. Using spin-sensitive probes (Mott polarimetry), we observe the spin-momentum coupling and uncover the chiral nature of surface electrons in TlBiSe2. We demonstrate that the surface electrons in TlBiSe2 collectively carry a quantum Berry's phase of $π$ and a definite chirality ($η$ = -1, left-handed) associate…
For the IV-VI semiconductor family we derive an exact relation between the microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl topological surface state wave function, thus obtaining a fully microscopic surface state. We find that the balance of spin-orbit interaction and crystal field in the bulk, and the band bending at the surface, can profoundly influence the surface state spin-momentum locking. As a manifestation of this we predict that the spin texture of the $M$-point Dirac cones of SnTe can be tuned through an unexpectedly rich sequence of spin textures -- warp…
Dynamics of coupled spin-torque oscillators can be exploited for non-Boolean information processing. However, the feasibility of coupling large number of STOs with energy-efficiency and sufficient robustness towards parameter-variation and thermal-noise, may be critical for such computing applications. In this work, the impacts of parameter-variation and thermal-noise on two different coupling mechanisms for STOs, namely, magnetic-coupling and electrical-coupling are analyzed. Magnetic coupling is simulated using dipolar-field interactions. For electricalcoupling we employed global RF-injectio…
We theoretically investigate the effects of tunable magnetic fringe fields generated by arrays of switchable magnetic junctions (MJs) on the quantum states of an underlying two-dimensional (2D) system formed in a semiconductor quantum well. The magnetic landscape generated by the MJ-array can be reconfigured on the nanometer scale by electrically switching the magnetic state of individual MJs. The interaction between the spin of the carriers and the fringe fields generates effective spin-dependent potentials acting like quantum dots (barriers) for carriers with spin parallel (antiparallel) to …
