The competition between the ferromagnetic exchange interaction and anti-symmetric Dzyaloshinskii-Moriya interaction can stabilize a helical phase or support the formation of skyrmions. In thin films of chiral magnets, the current density can be large enough to unpin the helical phase and reveal its nontrivial dynamics. We theoretically study the dynamics of the helical phase under spin-transfer torques that reveal distinct orientation processes, driven by topological defects in the bulk or induced by edges, limited by instabilities at higher currents. Our experiments confirm the possibility of on-demand switching the helical orientation by current pulses. This helical orientation might serve as a novel order parameter in future spintronics applications.
We study theoretically the dynamics of the spin textures, i.e., Skyrmion crystal (SkX) and spiral structure (SS), in two-dimensional helical magnets under external current. By numerically solving the Landau-Lifshitz-Gilbert equation, it is found that (i) the critical current density of the motion is much lower for SkX compared with SS in agreement with the recent experiment, (ii) there is no intrinsic pinning effect for SkX and the deformation of the internal structure of Skyrmion reduces the pinning effect dramatically, (iii) the Bragg intensity of SkX shows strong time-dependence as can be o…
We theoretically show that in a crystal with a helical lattice structure, orbital and spin magnetizations along a helical axis are induced by an electric current along the helical axis. We propose a simple tight-binding model for calculations, and the results can be generalized to any helical crystals. The induced magnetizations are opposite for right-handed and left-handed helices. The current-induced spin magnetization along the helical axis comes from a radial spin texture on the Fermi surface. This is in sharp contrast to Rashba systems where the induced spin magnetization is perpendicular…
In a variety of rare-earth based compounds singlet superconductivity coexists with helical magnetism. Here we demonstrate that surfaces of these systems should generically host a finite density of zero-energy Majorana modes. In the limit of vanishing disorder, these modes lead to a divergent contribution to zero-energy density of states and to zero-temperature entropy proportional to the sample surface area. When confined to a wire geometry, a discrete number of Majorana modes can be isolated. The relatively large characteristic energy scales for superconductivity and magnetism, compared to ot…
The theory of elasticity and pinning of domain walls in helical magnets is presented. Domain walls perpendicular to the helical axis show non-local elasticity and are marginally pinned by local disorder. Weak anisotropy combined with magnetic dilution leads however to a non-local bulk pinning effect. Domain walls with other orientations include generically vortex arrays, similar to type-II superconductors. Their pinning force is calculated as a function of wall orientation, pitch angle and impurity concentration. It is shown that metastable domains can vary between needle and pancake like shap…
We consider the effects of electron scattering off a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance is a non-monotonous function of the voltage with several extrema.
The interaction of a magnetic insulator with the helical electronic edge of a two-dimensional topological insulator has been shown to lead to many interesting phenomena. One of these is that for a suitable orientation of the magnetic anisotropy axis, the exchange coupling to an easy-plane magnet has no effect on DC electrical transport through a helical edge, despite the fact that it opens a gap in the spectrum of the helical edge [Meng {\em et al.}, Phys.\ Rev.\ B {\bf 90}, 205403 (2014)]. Here, we theoretically consider such a magnet embedded in an interferometer, consisting of a pair of hel…
The current through a helical edge state of a quantum-spin-Hall insulator may be fully transmitted through a magnetically gapped region due to a combination of spin-transfer torque and spin pumping [Meng {\em et al.}, Phys. Rev. B {\bf 90}, 205403 (2014)]. Using a scattering approach, we here argue that in such a system the current is effectively carried by electrons with energies below the magnet-induced gap and well below the Fermi energy. This has striking consequences, such as the absence of shot noise, an exponential suppression of thermal noise, and an obstruction of thermal transport. F…
A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interac…
Optical field interacting with a topologically protected one-dimensional helical state is shown to support a one-dimensional plasmon-polariton that is characterized by a non-linear dispersion. In a two-dimensional Dirac magnet these electro-optical excitations are confined to domain walls, thus, offering a possibility to manipulate quantum optical states by altering magnetic domain configurations. An exact spectral equation for such a topological plasmon-polariton is derived.
Helical magnets which violated space inversion symmetry have rather peculiar topological defects. In isotropic helical magnets with exchange and Dzyaloshinskii-Moriya interactions there are only three types of linear defects: $\pmπ$ and $2π$-disclinations. Weak crystal anysotropy suppresses linear defects on large scale. Instead planar defects appear: domain walls that separate domains with different preferential directions of helical wave vectors. The appearance of such domain walls in the bulk helical magnets and some of their properties were predicted in the work \cite{Li 2012}. In a recent…
Conformation dependent circular current is investigated in a single handed helical geometry in presence of magnetic flux $ϕ$ within a Hartree-Fock mean field approach. The helical model is described by a set of non-planar rings connected by some vertical bonds where each ring is formed by introducing a non-zero hopping between the atoms $a$ and $b$ as shown in Fig.1. By stretching and compressing the geometry, circular current can be regulated significantly and thus the system can be exploited to design current controlled device at the nano-scale level. The proximity effect between the atomic …
The indirect exchange interaction between magnetic impurities located in the bulk of a two-dimensional topological insulator decays exponentially with the distance. The indirect exchange interaction for magnetic impurities mediated by the helical states at the edge of the topological insulator demonstrates behaviour which is typical for the Ruderman-Kittel-Kasuya-Yosida interaction in a one-dimensional metal. We have shown that interference between the bulk and edge states in the two-dimensional topological insulator results in existence of the unusual contribution to the indirect exchange int…
We study the kinetic magnetoelectric effect (current-induced magnetization including both the orbital and spin contributions) in three-dimensional conductors, specializing to the case of p-doped trigonal tellurium. We include both intrinsic and extrinsic contributions to the effect, which stem from the band structure of the crystal, and from disorder scattering, respectively. Specifically, we determine the dependence of the kinetic magnetoelectric response on the hole doping in tellurium, and show that the intrinsic and extrinsic effects dominate for low and high levels of doping, respectively…
Nontrivial topology of interfaces separating anti-chiral phases in helical magnets result in new effects as they interact with spin polarized current. These interfces or vortex walls consist of a one dimensional array of vortex lines. Topological Hall effect comes as a natural expectation. Also Lenz's law will result in a new damping mechanism in these systems. We study the dynamics of these wall interacting with electric current and use fundamental electromagntic laws to calculate this effect. On the other hand discrete nature of these walls affects their pinning and result in low depinning c…
We study current carrying helical edge states in a two-dimensional topological insulator coupled to an environment of localized spins, i.e. a spin bath. The localized spins mediate elastic spin-flip scattering between the helical edge states, and we show how this induces a spin-bath magnetization for a finite current through the edge states. The magnetization appears near the boundaries of the topological insulator, while the bulk remains unmagnetized, and it reaches its maximal value in the high bias regime. Furthermore, the helical edge states remain ballistic in steady state, if no addition…
Novel types of barrel-shaped chiral skyrmions can exist as isolated topological defects or as bound states in magnetic nanolayers with intrinsic and surface/interface induced chirality. The equilibrium parameters of chiral modulations calculated as functions of applied fields, layer thicknesses, and values of surface and volume uniaxial anisotropies allow to find optimal parameters for skyrmionic states in magnetic nanolayers. Our findings also show that in cholesteric cells with homeotropic anchoring smooth skyrmionic textures can be induced as an intriguing alternative to common disclination…
We develop an effective medium theory for electromagnetic wave propagation through gapless non-uniform systems with dynamic chiral magnetic effect. The theory allows to calculate macroscopic-disorder-induced corrections to the values of optical, as well as chiral magnetic conductivities. In particular, we show that spatial fluctuations of optical conductivity induce corrections to the effective value of the chiral magnetic conductivity. Experimentally, these corrections can be observed as sharp features in the Faraday rotation angle near frequencies that correspond to the bulk plasmon resonanc…
Helical symmetry of massive Dirac fermions is broken explicitly in the presence of electric and magnetic fields. Here we present two equations for the divergence of helical and axial-vector currents following the Jackiw-Johnson approach to the anomaly of the neutral axial vector current. We discover the contribution from the helical symmetry breaking is attributed to the occupancy of the two states at the top of the valence band and the bottom of the conduction band. The explicit symmetry breaking fully cancels the anomalous correction from the quantum fluctuation in the band gap. The chiral a…
We analyze the Ruderman-Kettel-Kasuya-Yosida(RKKY) interaction between magnetic impurities embedded in the helical metal on the surface of three-dimensional topological insulators. Apart from the conventional RKKY terms, the spin-momentum locking of conduction electrons also leads to a significant Dzyaloshinskii-Moriya (DM) interaction between impurity spins. For a chain of magnetic impurities, the DM term can result in single-handed spin helix on the surface. The handedness of spin helix is locked with the sign of Fermi velocity of the emergent Dirac fermions on the surface. We also show the …
Three-dimensional topological solitons attract a great deal of interest in fields ranging from particle physics to cosmology but remain experimentally elusive in solid-state magnets. Here we numerically predict magnetic heliknotons, an embodiment of such nonzero-Hopf-index solitons localized in all spatial dimensions while embedded in a helical or conical background of chiral magnets. We describe conditions under which heliknotons emerge as metastable or ground-state localized nonsingular structures with fascinating knots of magnetization field in widely studied materials. We demonstrate magne…
In the presence of the fluid helicity $\boldsymbol{v} \cdot \boldsymbolω$, the magnetic field induces an electric current of the form $\boldsymbol{j} = C_{\rm HME} (\boldsymbol{v} \cdot \boldsymbolω) \boldsymbol{B}$. This is the helical magnetic effect (HME). We show that for massless Dirac fermions with charge $e=1$, the transport coefficient $C_{\rm HME}$ is fixed by the chiral anomaly coefficient $C=1/(2π^2)$ as $C_{\rm HME} = C/2$ independently of interactions. We show the conjecture that the coefficient of the magnetovorticity coupling for the local vector charge, $n = C_{B ω} \boldsymbol…
