The two-dimensional electron gas in a bilayer graphene in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N=0 at integer filling factors $ν\in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $ν=-1,3$, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias where \textit{electric} dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that by further increasing the bias at these two filling factors, the two-dimensional electron gas goes first through a Skyrmion crystal state and then into an helical state where the pseudospins rotate in space. The pseudospin textures in both the Skyrmion and helical states are due to the presence of a Dzyaloshinskii-Moriya interaction in the effective pseudospin Hamiltonian when orbital coherence is present in the ground state. We study in detail the electronic structure of the helical and Skyrmion crystal states as well as their collective excitations and then compute their electromagnetic absorption.
We study spin effects of quantum wires formed in bilayer graphene by electrostatic confinement. With a proper choice of the confinement direction, we show that in the presence of magnetic field, spin-orbit interaction induced by curvature, and intervalley scattering, bound states emerge that are helical. The localization length of these helical states can be modulated by the gate voltage which enables the control of the tunnel coupling between two parallel wires. Allowing for proximity effect via an s-wave superconductor, we show that the helical modes give rise to Majorana fermions in bilayer…
We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60 degree over a large energetic range in one of the valleys, and down to -60 degree in the other. In a Y-junctio…
A quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering d…
In the presence of a finite interlayer displacement field bilayer graphene has an energy gap that is dependent on stacking and largest for the stable AB and BA stacking arrangements. When the relative orientations between layers are twisted through a small angle to form a moir$\mathrm{\acute{e}}$ pattern, the local stacking arrangement changes slowly. We show that for non-zero displacement fields the low-energy physics of twisted bilayers is captured by a phenomenological helical network model that describes electrons localized on domain walls separating regions with approximate AB and BA stac…
In minimally twisted bilayer graphene, a moir{é} pattern consisting of AB and BA stacking regions separated by domain walls forms. These domain walls are predicted to support counterpropogating topologically protected helical (TPH) edge states when the AB and BA regions are gapped. We fabricate designer moir{é} crystals with wavelengths longer than 50 nm and demonstrate the emergence of TPH states on the domain wall network by scanning tunneling spectroscopy measurements. We observe a double-line profile of the TPH states on the domain walls, only occurring when the AB and BA regions are gappe…
We measure microwave photocurrent in devices made from InAs/GaInSb bilayers where both insulating bulk state and conducting edge state were observed in the inverted-band regime, consistent with the theoretical prediction for a quantum spin Hall (QSH) insulator. It has been theoretically proposed that microwave photocurrent could be a unique probe in studying the properties of QSH edge states. To distinguish possible photoresponse between bulk state and helical edge state, we prepare Hall bar and Corbino disk from the same wafer. Results show that the Corbino disk samples have a negligible phot…
We experimentally investigate spin-polarized electron transport between a permalloy ferromagnet and the edge of a two-dimensional electron system with band inversion, realized in a narrow, 8~nm wide HgTe quantum well. In zero magnetic field, we observe strong asymmetry of the edge potential distribution with respect to the ferromagnetic ground lead. This result indicates, that the helical edge channel, specific for the structures with band inversion even at the conductive bulk, is strongly coupled to the ferromagnetic side contact, possibly due to the effects of proximity magnetization. It all…
The coupling between angular (twisting) and longitudinal modulations arising near the ordering temperature of noncentrosymmetric ferromagnets strongly influences the structure of skyrmion states and their evolution in an applied magnetic field. In the precursor states of cubic helimagnets, a continuous transformation of skyrmion lattices into the saturated state is replaced by the first-order processes accompanied by the formation of multidomain states. Recently the effects imposed by dominant longitudinal modulations have been reported in bulk MnSi and FeGe. Similar phenomena can be observed …
A twisted graphene bilayer exhibits a triangular Moiré pattern in the local stacking, that smoothly alternates between the three basic types AA', AB' and BA'. Under an interlayer bias U, the latter two types develop a spectral gap, characterised by opposite valley Chern numbers. We show that for large enough Moiré periods and bias, these regions become depleted electronically, and topologically protected helical modes appear at their boundaries. This gives rise to a delocalised topological network of the Chalker-Coddington type, composed of valley current vortices. This network can be tailored…
We calculate the conductance of a two-dimensional bilayer with inverted electron-hole bands, to study the sensitivity of the quantum spin Hall insulator (with helical edge conduction) to the combination of electrostatic disorder and a perpendicular magnetic field. The characteristic breakdown field for helical edge conduction splits into two fields with increasing disorder, a field $B_{c}$ for the transition into a quantum Hall insulator (supporting chiral edge conduction) and a smaller field $B'_{c}$ for the transition to bulk conduction in a quasi-metallic regime. The spatial separation of t…
We study spin dependent transport through a magnetic bilayer graphene nanojunction configured as two dimensional normal/ferromagnetic/normal structure where the gate-voltage is applied on the layers of ferromagnetic graphene. Based on the fourband Hamiltonian, conductance is calculated by using Landauer Butikker formula at zero temperature. For parallel configuration of the ferromagnetic layers of bilayer graphene, the energy band structure is metallic and spin polarization reaches to its maximum value close to the resonant states, while for antiparallel configuration, the nanojunction behaves…
An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.
We describe a new phase transition of the bilayer quantum Hall ferromagnet at filling fraction $ν= 1$. In the presence of static disorder (modeled by a periodic potential), bosonic $S=1/2$ spinons can undergo a superfluid-insulator transition while preserving the ferromagnetic order. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Physical consequences for charge and counterflow conductivity, and for interlayer tunneling conductance in the presence of quenched disorder are discussed.
Evidence of orbital Hall current induced correlation in second harmonic response of longitudinal and transverse voltage in light metal-ferromagnet bilayers
We derive a kinetic equation for the electrons moving on the surface of a three-dimensional topological insulator. Due to the helical nature of the excitations backward scattering is suppressed in the collision integral, and the spin dynamics is entirely constrained by that of the charge. We further analyze the tunneling between the helical and a conventional metal or ferromagnet. We find that the tunnel resistance strongly depends on the angle between the magnetization in the ferromagnet and the current in the helical metal. A nonmagnetic layer on top of the helical metal amplifies the curren…
We study the spin and charge currents flowing at the interface of an itinerant ferromagnet with a topological spin-triplet superconductor having different number of time-reversal-invariant Majorana helical modes. Depending on the number of helical modes, the capacity of carrying spin and charge currents is shown to be directly related to the amplitude and orientation of the ferromagnetic magnetization with respect to the superconducting $\vec{d}$-vector. Differently from the one-helical mode spin-triplet superconductor, we find that the presence of a finite amount of electronic hybridization w…
We measure electrically detected ferromagnetic resonance in microdevices patterned from ultra-thin Co/Pt bilayers. Spin pumping and rectification voltages are observed and distinguished via their angular dependence. The spin-pumping voltage shows an unexpected increase as the cobalt thickness is reduced below 2 nm. This enhancement allows more efficient conversion of spin to charge current and motivates a theory modelling the dependence of impurity scattering on surface roughness.
Inelastic light scattering measurements of low-lying collective excitations of electron double layers in the quantum Hall state at total filling nu_T=1 reveal a deep magnetoroton in the dispersion of charge-density excitations across the tunneling gap. The roton softens and sharpens markedly when the phase boundary for transitions to highly correlated compressible states is approached. The findings are interpreted with Hartree-Fock evaluations that link soft magnetorotons to enhanced excitonic Coulomb interactions and to quantum phase transitions in the ferromagnetic bilayers.
We have previously reported ferromagnetism evinced by a large hysteretic anomalous Hall effect in twisted bilayer graphene (tBLG). Subsequent measurements of a quantized Hall resistance and small longitudinal resistance confirmed that this magnetic state is a Chern insulator. Here we report that, when tilting the sample in an external magnetic field, the ferromagnetism is highly anisotropic. Because spin-orbit coupling is negligible in graphene such anisotropy is unlikely to come from spin, but rather favors theories in which the ferromagnetism is orbital. We know of no other case in which fer…
Bilayer electron-hole systems with unequal electron and hole densities are expected to have exciton condensate ground states with spontaneous spin-polarization in both conduction and valence bands. In the absence of spin-orbit and electron-hole exchange interactions there is no coupling between the spin-orientations in the two quantum wells. In this article we show that Rashba spin-orbit interactions lead to unconventional magnetic anisotropies, whose strength we estimate, and to ordered states with unusual quasiparticle spectra.
We have measured the magneto-resistance of freely suspended high-mobility bilayer graphene. For magnetic fields $B>1$ T we observe the opening of a field induced gap at the charge neutrality point characterized by a diverging resistance. For higher fields the eight-fold degenerated lowest Landau level lifts completely. Both the sequence of this symmetry breaking and the strong transition of the gap-size point to a ferromagnetic nature of the insulating phase developing at the charge neutrality point.
The spectral functions of the pseudospin correlation functions in the bilayer quantum Hall system at ν=1 are investigated numerically, where the pseudospin describes the layer degrees of freedom. In the pseudospin-ferromagnetic phase, the lowest-energy excitation branch is closely connected with the ground state through the fluctuations of pseudospin S_y and S_z, and it plays a significant role on the tunneling properties in this system. For the system with very small tunneling amplitude and layer separation smaller than the critical one, the system-size dependence of calculated spectral funct…
We systematically measured the DC voltage V_ISH induced by spin pumping together with the inverse spin Hall effect in ferromagnet/platinum bilayer films. In all our samples, comprising ferromagnetic 3d transition metals, Heusler compounds, ferrite spinel oxides, and magnetic semiconductors, V_ISH invariably has the same polarity. V_ISH furthermore scales with the magnetization precession cone angle with a universal prefactor, irrespective of the magnetic properties, the charge carrier transport mechanism or type. These findings quantitatively corroborate the present theoretical understanding o…
Topological insulators (TIs) are a novel class of materials with nontrivial surface or edge states. Time-reversal symmetry (TRS) protected TIs are characterized by the Z2 topological invariant and their helical property becomes lost in an applied magnetic field. Currently there exist extensive efforts searching for TIs that are protected by symmetries other than TRS. Here we show, a topological phase characterized by a spin Chern topological invariant is realized in an inverted electron-hole bilayer engineered from indium arsenide-gallium antimonide (InAs/GaSb) semiconductors which retains rob…
Ferromagnetic transitions between quantum Hall states with different polarization at a fixed filling factor can be studied by varying the ratio of cyclotron and Zeeman energies in tilted magnetic field experiments. However, an ability to locally control such transitions at a fixed magnetic field would open a range of attractive applications, e.g. formation of a reconfigurable network of one-dimensional helical domain walls in a two-dimensional plane. Coupled to a superconductor, such domain walls can support non-Abelian excitation. In this article we report development of heterostructures wher…
Topological insulators, along with Chern insulators and Quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the time-reversal invariant helical edge-modes in bilayer graphene/monolayer WSe$_2$-based heterostructures -- a phase generally considered as a precursor to the field of generic topological insulators. Our observation of this elusive phase depended crucially on our ability to create mesoscopic devices comprising both a moiré superlattice potential and strong spin-orbit coupli…
We theoretically show that the three-dimensional (3D) topological insulator (TI)/thin-film ferromagnetic metal (FMM) bilayer structure is possible to be a quantum anomalous Hall (QAH) insulator with a wide global band gap. Studying the band structure and the weight distributions of eigenstates, we demonstrate that the attachment of a metallic thin-film on the 3DTI can shift the topologically non-trivial state into the metal layers due to the hybridization of bands around the original Dirac point. By introducing the magnetic exchange interaction in the thin-film layers, we compute the anomalous…
We present harmonic transverse voltage measurements of current-induced thermoelectric and spin-orbit torque (SOT) effects in ferromagnet/normal metal bilayers, in which thermal gradients produced by Joule heating and SOT coexist and give rise to ac transverse signals with comparable symmetry and magnitude. Based on the symmetry and field-dependence of the transverse resistance, we develop a consistent method to separate thermoelectric and SOT measurements. By addressing first ferromagnet/light metal bilayers with negligible spin-orbit coupling, we show that in-plane current injection induces a…
Spin-helical states, which arise in quasi-one-dimensional (1D) channels with spin-orbital (SO) coupling, underpin efforts to realize topologically-protected quantum bits based on Majorana modes in semiconductor nanowires. Detecting helical states is challenging due to non-idealities present in real devices. Here we show by means of tight-binding calculations that by using ferromagnetic contacts it is possible to detect helical modes with high sensitivity even in the presence of realistic device effects, such as quantum interference. This is possible because of the spin-selective transmission p…
Coherent spin-dependent transport through a junction containing of Normal/Ferromagnetic/Normal bilayer graphene nanoribbon with zigzag edges is investigated by using Landauer formalism. In a more realistic set-up, the exchange field is induced by two ferromagnetic insulator strips deposited on the ribbon edges while a perpendicular electric field is applied by the top gated electrodes. Our results show that, for antiparallel configuration, a band gap is opened giving rise a semiconducting behavior, while for parallel configuration, the band structure has no band gap. As a result, a giant magne…
Graphene-based materials show promise for spintronic applications due to their potentially large spin coherence length. On the other hand, because of their small intrinsic spin-orbit interaction, an external magnetic source is desirable in order to perform spin manipulation. Because of the flat nature of graphene, the proximity interaction with a ferromagnetic insulator (FI) surface seems a natural way to introduce magnetic properties into graphene. Exploiting the peculiar electronic properties of bilayer graphene coupled with FIs, we show that it is possible to devise very efficient gate-tuna…
The recent report on the observation of soft magnetorotons in the dispersion of charge-density excitations across the tunneling gap in coupled bilayers at total Landau level filling factor $ν_T=1$ is reviewed. The inelastic light scattering experiments take advantage of the breakdown of wave-vector conservation that occurs under resonant excitation. The results offer evidence that in the quantum Hall state there is a roton that softens and sharpens markedly when the phase boundary for transitions to highly-correlated compressible states is approached. These findings are interpreted with Hartre…
We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations, and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion, and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a no…
Using a semiclassical approach that simultaneously incorporates the spin Hall effect (SHE), spin diffusion, quantum well states, and interface spin-orbit coupling (SOC), we address the interplay of these mechanisms as the origin of the in-plane current induced spin torque observed in the normal metal/ferromagnetic metal bilayer thin films. Focusing on the bilayers with a ferromagnet much thinner than its spin diffusion length, such as Pt/Co with $\sim 10$nm thickness, our approach addresses simultaneously the two contributions to the spin torque, namely the spin-transfer torque (SHE-STT) due t…
We present a microscopic theory of ground-state spectral function of bilayer quantum Hall systems that includes interactions between Hartree-Fock quasiparticles and quantum fluctuations of the order parameter field. The collective modes in these systems are properly described only when fluctuations in direct and exchange particle-hole channels are taken into account. Using an auxiliary field functional integral approach, we present a generalization of the random phase approximation \emph{for quasiparticle self-energy} which captures fluctuations in both channels. We discuss its relationship to…
We realized point contact spectroscopy experiment on ferromagnet/superconductor bilayers. Differential conductance curves show several features that we explained within Bogoliubov-de Gennes formalism considering the presence of two interfaces in the normal-metal-tip/ferromagnet/superconductor device. We demonstrate that such configuration is suitable as local probe of the spin polarization and thickness of ferromagnetic layer, directly on bilayer areas. This is due to the high sensitivity of the Andreev surface states to the physical properties of the ferromagnetic interlayer.
We study theoretically the magnetic screening properties of thin, diffusive superconductor/ferromagnet bilayers subject to a perpendicular magnetic field. We find that the effective penetration depth characterizing the magnetic response oscillates with the thickness of the ferromagnetic layer on the scale of the ferromagnetic coherence length.
A "squeezed-vacuum" state considered in quantum optics is shown to be realized in the ground-state wavefunction for the bilayer quantum Hall system at the total Landau level filling of $ν=1/m$ (m: odd integer). This is derived in the boson approximation, where a particle-hole pair creation across the symmetric-antisymmetric gap, $Δ_{SAS}$, is regarded as a boson. In terms of the pseudospin describing the layers, the state is a spin-squeezed state, where the degree of squeezing is controlled by the layer separation and $Δ_{SAS}$. An exciton condensation, which amounts to a rotated spin-squeezed…
We study spin transport in a fully hBN encapsulated monolayer-graphene van der Waals (vdW) heterostructure, at room temperature. A top-layer of bilayer-hBN is used as a tunnel barrier for spin-injection and detection in graphene with ferromagnetic cobalt electrodes. We report surprisingly large and bias induced (differential) spin-injection (detection) polarizations up to 50% (135%) at a positive voltage bias of +0.6 V, as well as sign inverted polarizations up to -70% (-60%) at a reverse bias of -0.4 V. This demonstrates the potential of bilayer-hBN tunnel barriers for practical graphene spin…
Topological insulators (TIs) and graphene present two unique classes of materials which are characterized by spin polarized (helical) and non-polarized Dirac-cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in TIs. Here, we report the experimental observation of the renormalized quasi-particle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 subst…
It is well-known that the ground state of homogeneous superconducting systems with spin-orbit coupling (SOC) in the presence of the Zeeman field is the so-called helical state, which is characterized by the phase modulation of the order parameter, but zero supercurrent density. In this work we investigate the realization of the helical state in a hybrid system with spatially separated superconductivity and exchange field by considering S/F bilayer on top of a 3D topological insulator. This system is characterized by strong spin-momentum locking and, consequently, provides the most favorable co…
Helical Edge Transport in the ν= 0 Quantum Hall Ferromagnetic State of an Organic Dirac Fermion System
University of Tokyo（东京大学）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；National Institute for Materials Science（国立材料科学研究所）；Ewha Womans University（梨花女子大学）
The rich phase diagram of quantum spin-ladder systems has attracted much attention in the theoretical literature. The progress in experimental realisations of this fascinating physics however has been much slower. While materials with a ladder-like structure exist, one always has coupling between the ladders to muddy the waters. In addition, such materials exhibit limited (if any) tunability in terms of the magnetic exchange parameters, and experimental probing of the different phases is a great challenge. In this work, we show that a realisation of spin-ladder physics can occur in an engineer…
We analyze the enhancement of the superconducting critical temperature of superconducting/ferromagnetic bilayers due to the appearance of localized superconducting states in the vicinity of magnetic domain walls in the ferromagnet. We consider the case when the main mechanism of the superconductivity destruction via the proximity effect is the exchange field. We demonstrate that the influence of the domain walls on the superconducting properties of the bilayer may be quite strong if the domain wall thickness is of the order of superconducting coherence length.
Superconductor/ferromagnet bilayers are known to exhibit nontrivial dependence of the critical temperature T_c on the thickness d_f of the ferromagnetic layer. We develop a general method for investigation of T_c as a function of the bilayer's parameters. It is shown that interference of quasiparticles makes T_c(d_f) a nonmonotonic function. The results are in good agreement with experiment. Our method also applies to multilayered structures.
We compute the phase diagram of a biased graphene bilayer. The existence of a ferromagnetic phase is discussed with respect both to carrier density and temperature. We find that the ferromagnetic transition is first order, lowering the value of $U$ relatively to the usual Stoner criterion. We show that in the ferromagnetic phase the two planes have unequal magnetization and that the electronic density is hole like in one plane and electron like in the other.
Topological insulators (TIs) are a unique class of materials characterized by a surface (edge) Dirac cone state of helical Dirac fermions in the middle of bulk (surface) gap. When the thickness (width) of TIs is reduced, however, interaction between the surface (edge) states will open a gap removing the Dirac cone. Using density function theory calculation, we demonstrate the creation of helical Dirac fermions from interfacing two gapped TI films, a single bilayer Bi grown on a single quintuple layer Bi2Se3 or Bi2Te3. The theoretical prediction is directly confirmed by experiment. We further s…
We investigate the effect of eddy currents on ferromagnetic resonance (FMR) in ferromagnet-normal metal (FM/NM) bilayer structures. Eddy-current effects are usually neglected for NM layer thicknesses below the microwave (MW) skin depth (approx. 800 nm for Au at 10 GHz). However, we show that in much thinner NM layers (10-100 nm of Au or Cu) they induce a phase shift in the FMR excitation when the MW driving field has a component perpendicular to the sample plane. This results in a strong asymmetry of the measured absorption lines. In contrast to typical eddy-current effects, the asymmetry is l…
We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$ν=2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.
The phase diagram of a biased graphene bilayer is computed and the existence of a ferromagnetic phase is discussed both in the critical on-site interaction $U_{c}$ versus doping density and versus temperature. We show that in the ferromagnetic phase the two planes have unequal magnetization and that the electronic density is hole like in one plane and electron like in the other. We give evidence for a \emph{first-order} phase transition between paramagnetic and ferromagnetic phases induced by doping at zero temperature.
The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor $ν$=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at $ν$=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic f…
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $θ\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also…
We propose an experimental scheme to determine the spin-transfer torque efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from the measurement of the longitudinal magnetoresistace. Solving a diffusive spin-transport theory with appropriate boundary conditions gives an analytical formula of the longitudinal charge current density. The longitudinal charge current has a term that is proportional to the square of the spin-transfer torque efficiency and that also depends on the ratio of the film thickness to the spin diffusion length of the ferromagnet. Extracting this cont…
We present a microscopic study of the interlayer spacing d versus in-plane magnetic field $B_\parallel$ phase diagram for bilayer quantum Hall (QH) pseudo-ferromagnets. In addition to the interlayer charge balanced commensurate and incommensurate states analyzed previously, we address the corresponding interlayer charge unbalanced "canted" QH states. We predict a large anomaly in the bilayer capacitance at the canting transition and the formation of dipole stripe domains with periods exceeding 1 micron in the canted state.
The natures of the ground state in a $ν_{\rm T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the Halperin's (1,1,1) state is not relevant in the incompressible regime near the incompressible to compressible transition point in which the Josephson-like effect was observed. The two-particle correlation function shows the deflated correlation hole at this regime. An effective model that can give a good approximation to the ground state is proposed. A connecti…
A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional …
We consider the zero-filled quantum-Hall ferromagnetic state of bilayer graphene subject to a kink-like perpendicular electric field, which generates domain walls in the electronic state and low-energy collective modes confined to move along them. In particular, it is shown that two pairs of collective helical modes are formed at opposite sides of the kink, each pair consisting of modes with identical helicities. We derive an effective field-theoretical model of these modes in terms of two weakly coupled anisotropic quantum spin-ladders, with parameters tunable through control of the electric …
