Recently, the intrinsic magnetic topological insulator MnBi2Te4 has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect (QAHE), axion insulator state, high-Chern-number and high-temperature Chern insulator states. One key issue in this field is to effectively manipulate these states and control topological phase transitions. Here, by systematic angle-dependent transport measurements, we reveal a magnetization-tuned topological quantum phase transition from Chern insulator to magnetic insulator with gapped Dirac surface states in MnBi2Te4 devices. Specifically, as the magnetic field is tilted away from the out-of-plane direction by around 40-60 degrees, the Hall resistance deviates from the quantization value and a colossal, anisotropic magnetoresistance is detected. The theoretical analyses based on modified Landauer-Buttiker formalism show that the field-tilt-driven switching from ferromagnetic state to canted antiferromagnetic state induces a topological quantum phase transition from Chern insulator to magnetic insulator with gapped Dirac surface states in MnBi2Te4 devices. Our work provides an efficient means for modulating topological quantum states and topological quantum phase transitions.
The interplay between band topology and magnetic order could generate a variety of time-reversal-breaking gapped topological phases with exotic topological quantization phenomena, such as quantum anomalous Hall (QAH) insulators and axion insulators (AxI). Here by combining analytic models and first-principles calculations, we predict QAH and AxI phases can be realized in thin film of an intrinsic antiferromagnetic van der Waal material Mn$_2$Bi$_2$Te$_5$. The phase transition between QAH and AxI is tuned by the layer magnetization, which would provide a promising platform for chiral supercondu…
Using the Green functions method we study transport properties of surface electrons in topological insulators in the presence of a correlated random exchange field. Such an exchange field may be due to random magnetization with correlated fluctuations. We determine the relaxation time due to scattering from the magnetization fluctuations and from other structural defects. Then we calculate the longitudinal charge conductivity taking into account the contribution due to vertex correction.
The magnetoelectric effect predicted in topological insulators makes heterostructures that combine magnetic materials and such insulators promising candidates for spintronics applications. Here, we theoretically consider a setup that exhibits two well-separated interfaces between a topological insulator and a ferromagnetic insulator. We show that there is a topological magnetic dipole-dipole interaction stemming from long-range Coulomb interactions. We analytically derive the magnetization dynamics at the two interfaces and discuss how the long-range coupling can be applied to non-locally indu…
The phenomenological theory for "topological" Hall effect (THE) is proposed. The theory can be used for qualitative analysis of THE in the medium with arbitrary magnetization distribution. In the paper the cylindrical particle with "vortex" magnetization is considered. The hysteresis loop of THE is qualitatively different comparing to abnormal Hall effect. The estimation of THE magnitude in the "vortex" particle is made. For Co particle with 100 nm diameter the THE exceeds normal and abnormal Hall effects until an external magnetic field less than 200 Oe.
We report a continuous phase transition between quantum-anomalous-Hall and trivial-insulator phases in a magnetic topological insulator upon magnetization rotation. The Hall conductivity transits from one plateau of quantized Hall conductivity $e^2/h$ to the other plateau of zero Hall conductivity. The transition curves taken at various temperatures cross almost at a single point, exemplifying the critical behavior of the transition. The slope of the transition curves follows a power-law temperature dependence with a critical exponent of $-0.61$. This suggests a common underlying origin in the…
Topological insulators (TIs) with spin momentum locked topological surface states (TSS) are expected to exhibit a giant spin-orbit torque (SOT) in the TI/ferromagnet systems. To date, the TI SOT driven magnetization switching is solely reported in a Cr doped TI at 1.9 K. Here, we directly show giant SOT driven magnetization switching in a Bi2Se3/NiFe heterostructure at room temperature captured using a magneto-optic Kerr effect microscope. We identify a large charge to spin conversion efficiency of ~1-1.75 in the thin TI films, where the TSS is dominant. In addition, we find the current densit…
Spin-orbit torque (SOT) magnetization switching of ferromagnets with large perpendicular magnetic anisotropy has a great potential for the next-generation non-volatile magnetoresistive random-access memory (MRAM). It requires a high-performance pure spin current source with a large spin Hall angle and high electrical conductivity, which can be fabricated by a mass production technique. In this work, we demonstrate ultrahigh efficient and robust SOT magnetization switching in all-sputtered BiSb topological insulator - perpendicularly magnetized Co/Pt multilayers. Despite fabricated by the indus…
Diameter-modulated nanowires offer an important paradigm to design the magnetization response of 3D magnetic nanostructures by engineering the domain wall pinning. With the aim to understand its nature and to control the process, we analyze the magnetization response in FeCo modulated polycrystalline two-segment nanowires varying the minor diameter. Our modelling indicates a very complex behavior with a strong dependence on the disorder distribution and an important role of topologically non-trivial magnetization structures. We demonstrate that modulated nanowires with a small diameter differe…
We theoretically investigate the phase of the de Haas - van Alphen oscillations in topological line-node semimetals. In these semimetals the chemical potential of charge carriers can essentially depend on the magnetic field, and this dependence changes the phase of the oscillations as compared to the phase in a three-dimensional metal with a band-contact line. Our results elucidate recent experimental data on the Berry phase for certain electron orbits in ZrSiS, ZrSiTe, and ZrSiSe.
Using an approximate expression for the Landau levels of the electrons located near a nodal line of a topological line-node semimetal, we obtain formulas for the magnetization of this semimetal at an arbitrary shape of its line. It is also shown that the dependence of the chemical potential on the magnetic field can be strong in these materials, and this dependence can essentially influence the de Haas - van Alphen oscillations. The obtained results are applied to the rhombohedral graphite which is one of the line-node semimetals. For this material, we find temperature and magnetic field depen…
The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolution of electronic states induced by lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a $\bm{k}$ resolved Born effective charge, and identify another contribution from the phonon-modified electronic …
The origins of the spin-orbit torque (SOT) at ferromagnet/topological insulator (FM/TI) interfaces are incompletely understood. Theory has overwhelmingly focussed on the Edelstein effect due to the surface states in the presence of a scalar scattering potential. We investigate here the contribution to the SOT due to extrinsic spin-orbit scattering of the surface states, focusing on the case of an out-of-plane magnetization. We show that spin-orbit scattering brings about a sizable renormalization of the field-like SOT, which exceeds 20$\%$ at larger strengths of the extrinsic spin-orbit parame…
Using field-angle, temperature, and back-gate-voltage dependence of the weak anti-localization (WAL) and universal conductance fluctuations of thin Bi1.5Sb0.5Te1.7Se1.3 topological-insulator single crystals, in combination with gate-tuned Hall resistivity measurements, we reliably separated the surface conduction of the topological nature from both the bulk conduction and topologically trivial surface conduction. We minimized the bulk conduction in the crystals and back-gate tuned the Fermi level to the topological bottom-surface band while keeping the top surface insensitive to back-gating wi…
The dependence on temperature of the spin magnetization of a two-dimensional electron gas at filling factor unity is studied. Using classical Monte Carlo simulations we analyze the effect that the equivalence between topological and electrical charge has on the the behavior of the magnetization. We find that at intermediate temperatures the spin polarization increases in a thirty per cent due to the Hartree interaction between charge fluctuations.
Precise estimation of spin Hall angle as well as successful maximization of spin-orbit torque (SOT) form a basis of electronic control of magnetic properties with spintronic functionality. Until now, current-nonlinear Hall effect, or second harmonic Hall voltage has been utilized as one of the methods for estimating spin Hall angle, which is attributed to the magnetization oscillation by SOT. Here, we argue the second harmonic Hall voltage in magnetic/nonmagnetic topological insulator (TI) heterostructures, Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_3$/(Bi$_{1-y}$Sb$_y$)$_2$Te$_3$. From the angular, …
Applying electric or magnetic fields is widely used to not only create and manipulate topological states but also facilitate their observations in experiments. In this work, we show by first-principles calculations and topological analysis that the time-reversal (TR) symmetry-broken quantum spin Hall (QSH) state emerges in a two-dimensional ferromagnetic MnBi$_4$Te$_7$ monolayer. This TR-symmetry broken QSH phase possesses a highly tunable nontrivial band gap under an external electric field (or tuning interlayer distance). Furthermore, based on the Wannier-function-based tight-binding approac…
We report that the irreversible magnetization switching process in ferromagnetic nanoparticles is governed by the formation and dynamics of topological point-defects in the form of hedgehog-antihedgehog pairs. After nucleation, these pairs rapidly separate with speeds exceeding domain wall velocities, and they generate an emergent electric field of solenoidal character and substantial magnitude.
We report the observation of efficient charge-to-spin conversion in the three-dimensional topological insulator (TI) Bi2Se3 and Ag bilayer by the spin-torque ferromagnetic resonance technique. The spin orbit torque ratio in the Bi2Se3/Ag/CoFeB heterostructure shows a significant enhancement as the Ag thickness increases to ~2 nm and reaches a value of 0.5 for 5 nm Ag, which is ~3 times higher than that of Bi2Se3/CoFeB at room temperature. The observation reveals the interfacial effect of Bi2Se3/Ag exceeds that of the topological surface states (TSS) in the Bi2Se3 layer and plays a dominant rol…
We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination. This interaction is strongly crystal face dependent and can generate chiral states along edges between crystal facets even for a uniform magnetization. While magnetization parallel to quintuple layers shifts the momentum of Dirac point, perpendicular magnetization lifts the Kramers degeneracy at any Dirac points except on the side face where the spectrum remains gapless and the Hall conductivity switches sign. Chiral states can be found at an…
We study supercurrent and proximity vortices in a Josephson junction made of disordered surface states of a three-dimensional topological insulator with a proximity induced in-plane helical magnetization. In a regime where the rotation period of helical magnetization is larger than the junction width, we find supercurrent 0-π crossovers as a function of junction thickness, magnetization strength, and parameters inherent to the helical modulation and surface states. The supercurrent reversals are associated with proximity induced vortices, nucleated along the junction width, where the number of…
We study dynamics of the magnetization coupled to the surface Dirac fermions of a three di- mensional topological insulator. By solving the Landau-Lifshitz-Gilbert equation in the presence of charge current, we find current induced magnetization dynamics and discuss the possibility of mag- netization reversal. The torque from the current injection depends on the transmission probability through the ferromagnet and shows nontrivial dependence on the exchange coupling. The mag- netization dynamics is a direct manifestation of the inverse spin-galvanic effect and hence another ferromagnet is unne…
Electric-field control of magnetization dynamics is fundamentally and technologically important for future spintronic devices. Here, based on electric-field control of both magnetic anisotropy and spin--orbit torque, two distinct methods are presented for switching the magnetization in topological insulator (TI)/magnetic-TI hybrid systems. The magnetic anisotropy energy in magnetic TIs is formulated analytically as a function of the Fermi energy, and it is confirmed that the out-of-plane magnetization is always favored for the partially occupied surface band. Also proposed is a transistor-like…
The discovery of quantum spin Hall materials with huge bulk gaps in experiment, such as bismuthene, provides a versatile platform for topological devices. We propose a topological quantum dot (QD) device in bismuthene ribbon in which two planar magnetization areas separate the sample into a QD and two leads. At zero temperature, peaks of differential conductance emerge, demonstrating the discrete energy levels from the confined topological edge states. The key parameters of the QD, the tunneling coupling strength with the leads and the discrete energy levels, can be controlled by the planar ma…
Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a low symmetry permalloy microstructure is obtained by X-ray vector magnetic tomography and analysed in detail in terms of topological charges and emergent fields. A central asymmetric domain wall with a complex 3D structure is observed in which magnetization chirality transitions are mediated by Bloch points arranged in several dipoles and a triplet. The ideal…
We theoretically study the magnetization dynamics of a thin ferromagnetic film exchange-coupled with a surface of a strong three-dimensional topological insulator. We focus on the role of electronic zero modes imprinted by domain walls (DW's) or other topological textures in the magnetic film. Thermodynamically reciprocal hydrodynamic equations of motion are derived for the DW responding to electronic spin torques, on the one hand, and fictitious electromotive forces in the electronic chiral mode fomented by the DW, on the other. An experimental realization illustrating this physics is propose…
We theoretically study the spin and charge generation along with the electron transport on a disordered surface of a doped three-dimensional topological insulator/magnetic insulator junction by using Green's function techniques. We find that the spin and charge current are induced by not only local but also nonlocal magnetization dynamics through nonmagnetic impurity scattering on the disordered surface of the doped topological insulator. We also clarify that the spin current as well as charge density are induced by spatially inhomogeneous magnetization dynamics, and the spin current diffusive…
Established forms of electromagnetic coupling are usually conservative (in insulators) or dissipative (in metals and semiconductors). Here we point out the possibility of nondissipative electric driving of magnetization dynamics, if the valence electronic states have nontrivial topology in the combined space of crystal momentum and magnetization configuration. We provide a hybrid insulator system to demonstrate that the topology-based nonconservative electrical generalized force is capable of supporting sustained magnetization motion in the presence of Gilbert damping, with quantized and stead…
We demonstrate that the metallic topological surface states wrap on all sides the 3D topological crystalline insulator SnTe. This is achieved by studying oscillatory quantum magneto-transport and magnetization at tilted magnetic fields which enables us to observe simultaneous contributions from neighbouring sample sides. Taking into account pinning of the Fermi energy by the SnTe reservoir we successfully describe theoretically the de Haas-van Alphen oscillations of magnetization. The determined π-Berry phase of surface states confirms their Dirac fermion character. We independently observe os…
We investigate theoretically the dynamics of magnetization coupled to the surface Dirac fermions of a three dimensional topological insulator, by deriving the Landau-Lifshitz-Gilbert (LLG) equation in the presence of charge current. Both the inverse spin-Galvanic effect and the Gilbert damping coefficient $α$ are related to the two-dimensional diagonal conductivity $σ_{xx}$ of the Dirac fermion, while the Berry phase of the ferromagnetic moment to the Hall conductivity $σ_{xy}$. The spin transfer torque and the so-called $β$-terms are shown to be negligibly small. Anomalous behaviors in variou…
The Dirac-like surface states of the topological insulators (TIs) are protected by time reversal symmetry (TRS) and exhibit a host of novel properties. Introducing magnetism into TI, which breaks the TRS, is expected to create exotic topological magnetoelectric effects. A particularly intriguing phenomenon in this case is the magnetic field dependence of electrical resistance, or magnetoresistance (MR). The intricate interplay between topological protection and broken-TRS may lead to highly unconventional MR behaviour that can find unique applications in magnetic sensing and data storage. Howe…
We report angular-dependent spin-wave spectroscopy on kagome artificial spin ice made of large arrays of interconnected Ni80Fe20 nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic in-plane angular dependencies. Micromagnetic simulations allow us to interpret characteristic resonances of a two-step magnetization reversal of the nanomagnets. The dynamic properties are consistent with topological defects that are provoked via a magnetic field applied at specific angles. Simulations that we performed on previously investigated kagome artif…
A general expression for the orbital magnetization of a Floquet system is derived. The expression holds for a clean system, and is valid for any driving protocol, and arbitrary occupation of the bands. The orbital magnetization is shown to be large not only for Chern insulators, but also for anomalous phases where the Chern number does not fully account for the topology. In addition, the orbital magnetization is shown to take significant values both for a thermal equilibrium occupation of the Floquet bands, and for occupations determined by a quantum quench from an initial state with zero orbi…
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…
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 …
Under suitable conditions, some twisted graphene multilayers and transition-metal dichalcogenides become Chern insulators, exhibiting the anomalous quantum Hall effect and orbital magnetization due to spontaneous valley polarization. We study interaction of a Chern insulator with circularly polarized light. The interaction energy contains an antisymmetric term that couples to the helicity of incident light. For a two-band Chern insulator, this term is expressed as an integral involving the Berry curvature of the system. Taking advantage of this interaction, we propose an experimental protocol …
The anomalous Hall effect (AHE) is studied on the surface of a 3D magnetic topological insulator. By applying a modified semi-classical framework, all three contributions to the AHE, the intrinsic Berry phase curvature effect, the side-jump effect and the skew scattering effects are systematically treated, and analytical expressions for the conductivities are obtained in terms of the Fermi level, the spatial orientation of the surface magnetization and the concentration of magnetic and non-magnetic impurities. We demonstrate that the AHE can change sign by altering the orientation of the surfa…
The magneto-transport and magnetization measurements of Sb1.90Cu0.10Te3 were performed at different temperatures and different fields. Magneto-transport measurement at high field indicates the coexistence of both bulk and surface states. The magnetization shows the induced antiferromagnetic ordering with Cu doping and the observed quantum oscillation in it indicates that magnetization in Sb1.90Cu0.10Te3 is the bulk property. The non linearity in Hall data suggests the existence of anomalous and topological Hall effect. The anomalous and topological Hall effect (THE) from measured hall data of …
Based on first-principles calculations, we find novel valley-polarized quantum anomalous Hall (VP-QAH) phases with a large gap-0.19 eV at an appropriate buckled angle and tunable topological phase transitions driven by the spontaneous magnetization within a half-hydrogenated Bi honeycomb monolayer. Depending on the magnetization orientation, four different phases can emerge, i.e., two VP-QAH phases, ferromagnetic insulating and metallic states. When the magnetization is reversed from the +$\mathbf{z}$ to -$\mathbf{z}$ directions, accompanying with a sign change in the Chern number (from -1 to …
We theoretically study the magnetoresistance (MR) of two-dimensional massless Dirac electrons as found on the surface of three-dimensional topological insulators (3D TIs) that is capped by a ferromagnetic insulator (FI). We calculate charge and spin transport by Kubo and Boltzmann theories, taking into account the ladder-vertex correction and the in-scattering due to normal and magnetic disorder. The induced exchange splitting is found to generate an electric conductivity that depends on the magnetization orientation, but its form is very different from both the anisotropic and spin Hall MR. T…
Magnetic lateral multilayers have been fabricated on weak perpendicular magnetic anisotropy amorphous Nd-Co films in order to perform a systematic study on the conditions for controlled nucleation of topological defects within their magnetic stripe domain pattern. A lateral thickness modulation of period $w$ is defined on the nanostructured samples that, in turn, induces a lateral modulation of both magnetic stripe domain periods $λ$ and average in-plane magnetization component $M_{inplane}$. Depending on lateral multilayer period and in-plane applied field, thin and thick regions switch indep…
We study the magnetoelectric coupling at the surface of a topological insulator. We are in particular interested in the surface current induced by a static Zeeman/exchange field. This surface current can be related to the orbital magnetization of the system. For an insulator with zero Chern number, the orbital magnetization is independent of the details at the boundary. With the appearance of surface states in the topological insulator, it is not immediately obvious if the response is not affected by the conditions at the surface. We investigate this question using exact diagonalization to a l…
An approach to the electrostatic control of $90^{\circ}$ magnetization rotation in the hybrid structures composed of topological insulators (TIs) and adjacent ferromagnetic insulators (FMI) is proposed and studied. The concept is based on TI electron energy variation with in-plane to put-of plane FMI magnetization turn. The calculations explicitly expose the effect of free energy variability in the form of the electrically controlled uniaxial magnetic anisotropy, which depends on proximate exchange interaction and TI surface electron density. Combining with inherent anisotropy, the magnetizati…
We show that a spontaneous strain and spontaneous magnetization can arise in the doped topological insulators with a two-component superconducting vector order parameter. The details of the effects crucially depend on the symmetry of the superconducting order parameter, whether it is nematic or chiral. The transition from the nematic state to the chiral one can be performed by application of a magnetic field while the transition from the chiral state to the nematic one is tuned by the external strain. These transitions associated with a jump of the magnetic susceptibility and mechanical stiffn…
Results are presented for Floquet systems in two spatial dimensions where the Floquet driving breaks an effective time reversal symmetry. The driving protocol also induces flat bands that correspond to anomalous Floquet phases where the Chern number is zero and yet chiral edge modes exist. Analytic expressions for the edge modes, Berry curvature, and the orbital magnetization are derived for the flat bands. Results are also presented for the static Haldane model for parameters when the bands are flat. Floquet driving of the same model is shown to give rise to Chern insulators as well as anomal…
We report broadband spin-wave spectroscopy on kagome artificial spin ice (ASI) made of large arrays of interconnected Ni$_{80}$Fe$_{20}$ nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic magnetic field dependencies. Making use of micromagnetic simulations, we identify resonances that reflect the spin-solid-state and monopole-antimonopole pairs on Dirac strings. The latter resonances allow for the generation of highly-charged vertices in ASIs via microwave assisted switching. Our findings open further perspectives for fundamental studi…
We calculate the magnetization of the helical metallic surface states of a topological insulator. We account for the presence of a small sub-dominant Schr{ö}dinger piece in the Hamiltonian in addition to the dominant Dirac contribution. This breaks particle-hole symmetry. The cross-section of the upper Dirac cone narrows while that of the lower cone broadens. The sawtooth pattern seen in the magnetization of the pure Dirac limit as a function of chemical potential ($μ$) is shifted; but, the quantization of the Hall plateaus remains half integral. This is verified by taking the derivative of th…
