We derive compact analytical expressions for the coupled spin-charge susceptibility of a clean helical metal at the surface of a three dimensional topological insulator (TI). These expressions lead to unconventional non-collinear RKKY interactions between two impurity magnetic moments placed on the surface of a TI, and predict the generation of electric currents by time-dependent magnetic moments. We determine the influence of gate and bias voltages on the interlayer exchange coupling between two single-domain ferromagnetic monolayers deposited on top of a TI.
We study the dynamical interplay between ferroelectricity and magnetism in a multiferroic with a helical magnetic order. We show that the dynamical exchange-striction induces a biquadratic interaction between the spins and transverse phonons resulting in quantum fluctuations of the spontaneous ferroelectric polarization $\mathbf{P}$ in the ferroelectric phase. The hybridization between the spin wave and the fluctuation of the electric polarization leads to low-lying transverse phonon modes. Those are perpendicular to $\mathbf{P}$ and to the helical spins at small wave vector but then turn para…
Materials with optical activity can rotate the polarization plane of transmitted light. The most typical example is the natural optical activity, which has the symmetry property of changing sign after space inversion but being invariant to time inversion. Faraday rotation exhibits the opposite: it is invariant to space inversion but changes sign after time reversal. Here, we demonstrate that in a magnetoelectric material, another type of polarization rotation is possible. This effect is investigated in magnetoelectric YbAl3(BO3)4 under the viewpoint of time and space inversion symmetry argumen…
Topological insulators (TIs) in three space dimensions can be characterized by a quantized magnetoelectric coefficient. However, this coupling does not have experimentally observable consequences in the presence of time-reversal symmetry, because the contributions of both bulk and surface states cancel each other. Instead, the characteristic response of a TI is a nonlinear magnetoelectric effect. Field theoretic aspects of the nonlinear magnetoelectric response and numerical calculations for experimentally relevant geometries are discussed. Distinct from this effect, the magnetoelectric coupli…
By an electrical-pump--optical-probe technique we show that the electric-field-induced reversal of the magnetic order parameter in multiferroic MnWO$_4$ occurs on the time scale of milliseconds and maintains a rigid coupling of the magnetization to the magnetically induced electric polarization. The temporal progression of the spatially resolved domain structure was imaged with nanosecond resolution by optical second harmonic generation and compared to the quasi-static domain reversal. A qualitative model gives an estimate of why the magnetoelectric order-parameter reversal in the magnetically…
Insulating helimagnetic Cu2OSeO3 shows sizeable magnetoelectric effects in its skyrmion phase. Using magnetization measurements, magneto-current analysis and dielectric spectroscopy, we provide a thorough investigation of magnetoelectric coupling, polarization and dielectric constants of the ordered magnetic and polar phases of single-crystalline Cu2OSeO3 in external magnetic fields up to 150 mT and at temperatures below 60 K. From these measurements we construct a detailed phase diagram. Especially, the skyrmion phase and the metamagnetic transition of helical to conical spin order are charac…
Magnetoelectric coupling in helical multiferroics allows to steer spin order with electric fields. Here we show theoretically that in a helical multiferroic chain quantum information processing as well as quantum phases are highly sensitive to electric (E) field. Applying E-field, the quantum state transfer fidelity can be increased and made directionally dependent. We also show that E field transforms the spin-density-wave/nematic or multipolar phases of frustrated ferromagnetic spin-1/2 chain in chiral phase with a strong magnetoelectric coupling. We find sharp reorganization of the entangle…
Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk theta term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional theta/pi. We show that fractional theta/pi is only possible in a gapped time reversal invariant system of bosons or f…
We analyze the coupling between the ferroelectric and magnetic order parameters in the magnetoelectric multiferroic BiFeO_3 using density functional theory within the local spin density approximation and the LSDA+U method. We show that weak ferromagnetism of the Dzyaloshinskii-Moriya type occurs in this material, and we analyze the coupling between the resulting magnetization and the structural distortions. We explore the possibility of electric-field-induced magnetization reversal and show that, although it is unlikely to be realized in BiFeO_3, it is not in general impossible. Finally we out…
The magnetic properties of the high temperature alpha form of the CaCr2O4 compound have been investigated for the first time by magnetic susceptibility, specific heat and powder neutron diffraction. The system undergoes a unique magnetic phase transition at 43K to a long range order incommensurate helical phase with magnetic propagation vector k=(0,0.3317(2),0). The magnetic model proposed from neutron diffraction data shows that the plane of rotation of the spins is perpendicular to the wave-vector, and that the magnetic modulation is consistent with two modes belonging to distinct irreducibl…
We establish quasi-two-dimensional thin films of iron-based superconductors (FeSCs) as a new high-temperature platform for hosting intrinsic time-reversal-invariant helical topological superconductivity (TSC). Based on the combination of Dirac surface state and bulk extended $s$-wave pairing, our theory should be directly applicable to a large class of experimentally established FeSCs, opening a new TSC paradigm. In particular, an applied electric field serves as a "topological switch" for helical Majorana edge modes in FeSC thin films, allowing for an experimentally feasible design of gate-co…
We have discovered strong magnetoelectric (ME) effects in the single chiral-helical magnetic state of single-crystalline langasite Ba3NbFe3Si2O14 that is crystallographically chiral. The ferroelectric polarization, predominantly aligned along the a axis below the Neel temperature of ~27 K, changes in a highly non-linear fashion in the presence of in-plane magnetic fields (H) perpendicular to the a axis (H//b*). This ME effect as well as smaller ME effects in other directions exhibit no poling dependence, suggesting the presence of a self-formed single ME domain. In addition, these ME effects a…
We develop a theory for manipulating the effective band structure of interacting helical edge states realized on the boundary of two-dimensional time-reversal symmetric topological insulators. For sufficiently strong interaction, an interacting edge band gap develops, spontaneously breaking time-reversal symmetry on the edge. The resulting spin texture, as well as the energy of the the time-reversal breaking gaps, can be tuned by an external moiré potential (i.e., a superlattice potential). Remarkably, we establish that by tuning the strength and period of the potential, the interacting gaps c…
Controlling magnetism using voltage is highly desired for applications, but remains challenging due to fundamental contradiction between polarity and magnetism. Here we propose a mechanism to manipulate magnetic domain walls in ferrimagnetic or ferromagnetic multiferroics using electric field. Different from those studies based on static domain-level couplings, here the magnetoelectric coupling relies on the collaborative spin dynamics around domain walls. Accompanying the reversal of spin chirality driven by polarization switching, a "rolling-downhill"-like motion of domain wall is achieved a…
We perform a combined experimental and theoretical study of a magnetic-field ($B$) induced evolution of magnetic and ferroelectric properties in an antiferromagnetic material Pb(TiO)Cu$_4$(PO$_4$)$_4$, whose structure is characterized by a staggered array of Cu$_4$O$_{12}$ magnetic units with convex geometry known as square cupola. Our experiments show a $B$-induced phase transition from a previously reported low-$B$ linear magnetoelectric phase to a new high-$B$ magnetoelectric phase, which accompanies a 90$^\circ$ flop of electric polarization and gigantic magnetodielectric effect. Moreover,…
The magnetic and ferroelectric properties of the multiferroic system Mn$_{1-x}$Co$_x$WO$_4$ (x=0.135, 0.15, and 0.17) are studied in magnetic fields $H_c$ oriented along the monoclinic $c$-axis. Mn$_{0.85}$Co$_{0.15}$WO$_4$, which is right at the phase boundary between two helical spin structures, exhibits a spontaneous sign change of the ferroelectric polarization when cooled in fields $H_c>$ 25 kOe. The origin of the ferroelectric polarization is studied and two magnetic exchange interactions contributing to the polarization are identified. In Mn$_{0.85}$Co$_{0.15}$WO$_4$ domains of the char…
The chirality-dependent magnetoelectric properties of Neel-type domain walls in iron garnet films is observed. The electrically driven magnetic domain wall motion changes the direction to the opposite with the reversal of electric polarity of the probe and with the chirality switching of the domain wall from clockwise to counterclockwise. This proves that the origin of the electric field induced micromagnetic structure transformation is inhomogeneous magnetoelectric interaction.
Helical metals realized at the surfaces of topological insulators have recently attracted wide attention due to their potential applications in spintronics. In this paper we propose to realize helical metals through the application of THz light on common two-dimensional semiconductors and discuss their observable properties. We show that the application of circularly polarized light enables coherent manipulation of magnetization. Moreover, for a range of chemical potentials the system behaves as a helical metal, exhibiting a large anomalous Hall conductivity and associated magnetoelectric effe…
Magnetic skyrmions are localized nanometric spin textures with quantized winding numbers as the topological invariant. Rapidly increasing attention has been paid to the investigations of skyrmions since their experimental discovery in 2009, due both to the fundamental properties and the promising potential in spintronics based applications. However, controlled creation of skyrmions remains a pivotal challenge towards technological applications. Here, we report that skyrmions can be created locally by electric field in the magnetoelectric helimagnet Cu$\mathsf{_2}$OSeO$\mathsf{_3}$. Using Loren…
Biquadratic {\it antisymmetric} exchange terms of the form $ - [C_{ij} e^α_{ij}({\bf s}_i\times{\bf s}_j)_z]^2$, where ${\bf e}_{ij}$ is the unit vector connecting sites $i$ and $j$ and $α= x,y$, due partially to magnetoelectric coupling effects, are shown to be responsible for the spin-flop helical phase in CuFeO$_2$ at low magnetic field and temperature. Usual biquadratic {\it symmetric} exchange, likely due to magnetoelastic coupling, is found to support the stability of axial magnetic states at higher fields in this nearly-Heisenberg like stacked triangular antiferromagnet. A model Hamilto…
Chiral magnetic textures with non-trivial topology are known as skyrmions, and due to their unique properties they are promising in novel magnetic storage applications. While the electric manipulation of either isolated skyrmions or a whole skyrmion lattice have been intensively reported, the electric effects on skyrmion clusters remain scarce. In magnetoelectric compound Cu$_2$OSeO$_3$, a skyrmion cluster can be created near the helical-skyrmion phase boundary. Here, we report the in situ electric field writing/erasing of skyrmions in such a skyrmion cluster. Our real space/time image data ob…
We investigate a dynamical magnetoelectric effect due to a magnetic resonance in helical spin structures through the coupling between magnetization and electric polarization via a spin current mechanism. We show that the magnon has both the dynamical magnetic moment $ΔM^ω$ and the electric moment $ΔP^ω$ ($\perp ΔM^ω$), i.e., a dynamical toroidal moment, under external magnetic fields, and thus it is named the {\em toroidalmagnon}. The toroidalmagnon exists in most conical spin structures owing to the generality of the spin current mechanism. In the absorption of electromagnetic waves, the toro…
We have revisited the magnetic structure of manganese phosphorus trisulfide MnPS3 using neutron diffrac- tion and polarimetry. MnPS3 undergoes a transition toward a collinear antiferromagnetic order at 78 K. The resulting magnetic point-group breaks both the time reversal and the space inversion thus allowing a linear magnetoelectric coupling. Neutron polarimetry was subsequently used to prove that this coupling provides a way to manipulate the antiferromagnetic domains simply by cooling the sample under crossed magnetic and electrical fields, in agreement with the nondiagonal form of the magn…
Violation of time reversal and spatial inversion symmetries has profound consequences for elementary particles and cosmology. Spontaneous breaking of these symmetries at phase transitions gives rise to unconventional physical phenomena in condensed matter systems, such as ferroelectricity induced by magnetic spirals, electromagnons, non-reciprocal propagation of light and spin waves, and the linear magnetoelectric (ME) effect - the electric polarization proportional to the applied magnetic field and the magnetization induced by the electric field. Here, we report the experimental study of the …
We use Dirac quantization of flux to study fractional charges and axion angles θin interacting topological insulators with gapless surface modes protected by time-reversal symmetry. In interacting topological insulators, there are two types of fractional axion angle due to conventional odd and nontrivial even flux quantization at the boundary. On even flux quantization in a gapped time reversal invariant system, we show that there is a halved quarter fractional quantum Hall effect on the surface with Hall conductance of p/4q e2/2h with p and q odd integers. The gapless surface modes can be cha…
Magnetization can be induced by an electric field in systems without inversion symmetry $\mathcal{P}$ and time-reversal symmetry $\mathcal{T}$. This phenomenon is called the magnetoelectric (ME) effect. The spin ME effect has been actively studied in multiferroics. The orbital ME effect also exists and has been mainly discussed in topological insulators at zero temperature. In this paper, we study the intrinsic orbital ME response in metals at finite temperature using the Kubo formula. The intrinsic response originates from the Fermi sea and does not depend on the dissipation. Especially in sy…
Magnetoelectric phenomena are intimately linked to relativistic effects and also require the material to break spatial inversion symmetry and time reversal invariance. Magnetoelectric coupling can substantially affect light-matter interaction and lead to non-reciprocal light propagation. Here, we confirm on a fully experimental basis, without invoking either symmetry-based or material-specific assumptions, that the optical magnetoelectric effect in materials with non-parallel magnetization ($\boldsymbol{M}$) and electric polarization ($\boldsymbol{P}$) generates a trilinear term in the refract…
By extending our general spin-current model to non-centrosymmetric spin dimers and performing density functional calculations, we investigate the causes for the helical magnetic order and the origin of the giant ferroelectric polarization of CaMn7O12. The giant ferroelectric polarization is proposed to be caused by the symmetric exchange striction due to the canting of the Mn4+ spin arising from its strong Dzyaloshinskii-Moriya (DM) interaction. Our study suggests that CaMn7O12 may exhibit a novel magnetoelectric coupling mechanism in which the magnitude of the polarization is governed by the …
The helical edge states of time-reversal invariant two-dimensional topological insulators are protected against backscattering in idealized models. In more realistic scenarios with a shallow confining potential at the sample boundary, additional strongly interacting edge states may arise, that could interfere with the topological protection of edge conduction. We find that interaction effects within the reconstructed edges are well described by the Luttinger liquid model. While interactions between this Luttinger liquid and the helical edge states can in principle give rise to dynamical spin p…
We present a theory of magnetoelectric magnon-photon coupling in cavities hosting noncentrosymmetric magnets. Analogously to nonreciprocal phenomena in multiferroics, the magnetoelectric coupling is time-reversal and inversion asymmetric. This asymmetry establishes a means for exceptional tunability of magnon-photon coupling, which can be switched on and off by reversing the magnetization direction. Taking the multiferroic skyrmion-host Cu$_2$OSeO$_3$ with ultralow magnetic damping as an example, we reveal the electrical activity of skyrmion eigenmodes and propose it for magnon-photon splittin…
Electrically controllable valence-conduction band reversals in helical trilayer graphene
Weizmann Institute of Science（魏茨曼科学研究所）；Massachusetts Institute of Technology（麻省理工学院）；University of Texas at Dallas（德克萨斯大学达拉斯分校）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；National Institute for Materials Science（国立材料研究所）
We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance $G_0$ of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature $T_K$ for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global $U(1)$ symmetry. This symmetry can be broken by an anisotropic exchange couplin…
We present spin transport studies on a low-field, room-temperature magnetoelectric multiferroic polycrystalline $\text{Sr}_{3}\text{Co}_{2}\text{Fe}_{24}\text{O}_{41}$ (SCFO)|Pt heterostructure wherein a highly tunable transverse conical magnetic phase is responsible for static and dynamic magnetoelectric coupling. We measured angular dependence of spin Hall magnetoresistance (SMR) at constant magnetic fields ($H$) in the range of 50 to 100 kOe. Application of field below the critical value (2.5 kOe), yielded negative SMR and the $H$-evolution of normalized SMR exhibited a negative gradient. F…
We formulate the lattice version of the three-dimensional SU(2) Landau level problem with time reversal invariance. By taking a Landau-type gauge, the system is reduced into the one-dimensional SU(2) Harper equation characterized by a periodic spin-dependent gauge potential. The surface spectra indicate the spatial separation of helical states with opposite eigenvalues of the lattice helicty operator. The band topology is investigated from both the analysis of the boundary helical Fermi surfaces and the calculation of the Z2-index based on the bulk wavefunctions. The transition between a 3D we…
We have performed synchrotron radiation X-ray and neutron diffraction measurements on magnetoelectric multiferroic CuFe1-xAlxO2 (x=0.0155), which has a proper helical magnetic structure with incommensurate propagation wave vector in the ferroelectric phase. The present measurements revealed that the ferroelectric phase is accompanied by lattice modulation with a wave number 2q, where q is the magnetic modulation wave number. We have calculated the Fourier spectrum of the spatial modulations in the local electric polarization using a microscopic model proposed by Arima [T. Arima, J. Phys. Soc. …
The single helical Fermi surface on the surface state of three-dimensional topological insulator Bi2Se3 is constrained by the time-reversal invariant bulk topology to possess a spin-singlet superconducting pairing symmetry. In fact, the Cu-doped, and pressure-tuned superconducting Bi2Se3 show no evidence of the time reversal symmetry breaking. We report on the detection of the time reversal symmetry (TRS) breaking in the topological superconductor Sr0.1Bi2Se3 , probed by zero-field (ZF) μSR measurements. The TRS breaking provides strong evidence for the existence of spin-triplet pairing state.…
Thermodynamic properties of the helical spins with magnetoelectric coupling is simulated by Monte Carlo algorithm. It is shown that the spin-spin correlations are affected by the thermal fluctuations and the electric field. Results for the temperature-dependence of ferroelectric polarization and the susceptibility are also presented in connection with the multiferroic phase transition.
Due to the lack of both parity and time reversal symmetries, the Rashba superconductors CePt_3Si, CeRhSi_3, and CeIrSi_3, in the presence of a magnetic field, are unstable to helical (single plane-wave) order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field-temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-q phase, in which both the magnitude and the phase of the order parameter are spatially varying. We find t…
We report our combined experimental and theoretical study of magnetoelectric properties of an antiferromagnet Sr(TiO)Cu$_4$(PO$_4$)$_4$, in comparison with the isostructurals Ba(TiO)Cu$_4$(PO$_4$)$_4$ and Pb(TiO)Cu$_4$(PO$_4$)$_4$. The family of compounds commonly possesses a low-symmetric magnetic unit called the square cupola, which is a source of magnetoelectric responses associated with the magnetic multipoles activated under simultaneous breaking of spatial inversion and time reversal symmetries. Measuring the full magnetization curves and the magnetic-field profiles of dielectric constan…
One-dimensional (1D) electron systems in the presence of Coulomb interaction are described by Luttinger liquid theory. The strength of Coulomb interaction in the Luttinger liquid, as parameterized by the Luttinger parameter K, is in general difficult to measure. This is because K is usually hidden in powerlaw dependencies of observables as a function of temperature or applied bias. We propose a dynamical way to measure K on the basis of an electronic time-of-flight experiment. We argue that the helical Luttinger liquid at the edge of a 2D topological insulator constitutes a preeminently suited…
We demonstrate the possibility to induce and control peculiar spin textures in a helical Luttinger liquid, by means of a time-dependent magnetic scatterer. The presence of a perturbation that breaks the time-reversal symmetry opens a gap in the spectrum, inducing single-particle backscattering and a peculiar spin response. We show that in the weak backscattering regime asymmetric spin textures emerge at the left and right side of the scatterer, whose spatial oscillations are controlled by the ratio between the magnetization frequency and the Fermi energy and by the electron interaction. This p…
We study the time reversal (T) symmetry breaking of 2d helical fermi liquid, with application to the edge states of 3d topological band insulators with only one two-component Dirac fermion at finite chemical potential, as well as other systems with spin-orbit coupling. The T-breaking Ising order parameter is not over-damped and the theory is different from the ordinary Hertz-Millis theory for order parameters at zero momentum. We argue that the T-breaking phase transition is an 3d Ising transition, and the quasiparticles are well-defined in the quantum critical regime.
We study the localization-driven correlated states among two isolated dirty interacting helical edges as realized at the boundaries of two-dimensional $\mathbb{Z}_2$ topological insulators. We show that an interplay of time-reversal symmetric disorder and strong interedge interactions generically drives the entire system to a gapless localized state, preempting all other intraedge instabilities. For weaker interactions, an antisymmetric interlocked fluid, causing a negative perfect drag, can emerge from dirty edges with different densities. We also find that the interlocked fluid states of hel…
We develop a theory of finite-temperature momentum-resolved tunneling spectroscopy (MRTS) for disordered, interacting two-dimensional topological-insulator edges. The MRTS complements conventional electrical transport measurement in characterizing the properties of the helical Luttinger liquid edges. Using standard bosonization technique, we study low-energy spectral function and the MRTS tunneling current, providing a detailed description controlled by disorder, interaction, and temperature, taking into account Rashba spin orbit coupling, interedge interaction and distinct edge velocities. Ou…
Recently, Kaminski et al. have reported that time reversal symmetry is broken in the pseudogap phase in the high temperature superconducting material Bi_2Sr_2CaCu_2O_{2+δ} (Bi-2212). Here we examine the role of translationally invariant broken time reversal states on d_{x^2-y^2} superconductors. In particular, we determine the change in the superconducting order parameter structure. We find that the broken time reversal pseudogap state that is consistent with the experiment of Kaminski et al., gives rise to a novel mixed singlet-triplet pairing d+ip phase. This d+ip state is shown to give rise…
