Motivated by the recent observation [Zeissler et al, Nature Comm. 11, 428 (2020)] of enigmatic radius-independent skyrmion Hall angle in chiral magnets, we derive skyrmion Hall angle based on the recent solution of skyrmions characterized by the sole length scale determined with the Dzyaloshinskii-Moriya interaction strength and applied magnetic field. We find that the skyrmion Hall angle is independent of input current density and the length-scale which determines the radius of a skyrmion.This is corroborated with the single length-scale dependent skyrmion profile which is the solution of the Euler equation of polar angle representing magnetization. Although the magnitude of Hall angle may change with the change of profile (shape) of the skyrmion, it remains unchanged for a particular profile. With the application of tunable current along mutually perpendicular directions, this property enables us to propose an experimental setup by which the transverse motion of a skyrmion can be restricted so that the skyrmion can only traverse longitudinally. We further find the length-scale and input-current density independent Hall angles for merons where their transverse motion will be opposite depending on whether the spin at their centers are up or down, in agreement with an experiment.
Meron-mediated phase transitions in quasi-two-dimensional chiral magnets with easy-plane anisotropy: successive transformation of the hexagonal skyrmion lattice into the square lattice and into the tilted FM state
The recent experimental confirmation of a transformation between meron and skyrmion topological spin textures in the chiral magnet Co$_8$Zn$_9$Mn$_3$ [S.-Z. Lin et al., Phys. Rev. B 91, 224407 (2015); X. Z. Yu et al., Nature 564, 95 (2018)] confirms that the skyrmion crystals discovered in 2009 [S. Mühlbauer et al., Science 323, 915 (2009)] are just the tip of the iceberg. Crystals of topological textures, including skyrmions, merons, vortices, and monopoles, can be stabilized by combining simple physical ingredients, such as lattice symmetry, frustration, and spin anisotropy. The current chal…
We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures particularly of the skyrmions, showing an excellent agreement with experiments and first-principle stud…
Fe$_{5-x}$GeTe$_2$ is a centrosymmetric, layered van der Waals (vdW) ferromagnet that displays Curie temperatures $T_c$ (270-330 K) that are within the useful range for spintronic applications. However, little is known about the interplay between its topological spin textures (e.g., merons, skyrmions) with technologically relevant transport properties such as the topological Hall effect (THE), or topological thermal transport. Here, we show via high-resolution Lorentz transmission electron microscopy that merons and anti-meron pairs coexist with Néel skyrmions in Fe$_{5-x}$GeTe$_2$ over a wide…
We argue that topological meron excitations, which are in a strong coupling phase (bound in pairs) in infinite quantum Hall ferromagnets, become deconfined in finite size quantum Hall systems. Although effectively for larger systems meron energy grows with the size of the system, when gyromagnetic ratio is small meron becomes the lowest lying state of a quantum Hall droplet. This comes as a consequence of the many-body correlations built in the meron construction that minimize the interaction energy. We demonstrate this by using mean field ansatzes for meron wave function. The ansatzes will en…
We study the equilibrium phase diagram of ultrathin chiral magnets with easy-plane anisotropy $A$. The vast triangular skyrmion lattice phase that is stabilized by an external magnetic field evolves continuously as a function of increasing $A$ into a regime in which nearest-neighbor skyrmions start overlapping with each other. This overlap leads to a continuous reduction of the skyrmion number from its quantized value $Q=1$ and to the emergence of antivortices at the center of the triangles formed by nearest-neighbor skyrmions. The antivortices also carry a small "skyrmion number" $Q_A \ll 1$ …
We study annihilation mechanisms of small first- and second-order skyrmions and antiskyrmions on the frustrated $J_1-J_2-J_3$ square lattice with broken inversion symmetry (DMI). We find that annihilation happens via the injection of the opposite topological charge in the form of meron or antimeron nucleation. Overall, the exchange frustration generates a complex energy landscape with not only many (meta)stable and unstable local energy solutions, but also many possible paths connecting them. Whenever possible, we compute the activation energy and attempt frequency for the annihilation of isol…
Polar skyrmions are predicted to emerge from the interplay of elastic, electrostatic and gradient energies, in contrast to the key role of the anti-symmetric Dzyalozhinskii-Moriya interaction in magnetic skyrmions. With the discovery of topologically-stable polar skyrmions, it is of both fundamental and practical interest to understand the microscopic nature and the possibility of temperature- and strain-driven phase transitions in ensembles of such polar skyrmions. Here, we explore the reversible transition from a skyrmion state (topological charge of -1) to a two-dimensional, tetratic lattic…
During the last years, topologically protected collective modes of the magnetization have called much attention. Among these, skyrmions and merons have been the object of intense study. In particular, topological skyrmions are objects with an integer skyrmion number $Q$ while merons have a half-integer skyrmion charge $q$. In this work, we consider a $Q=1$ skyrmion, composed by a meron and an antimeron (bimeron), displacing in a ferromagnetic racetrack, disputing a long-distance competition with its more famous counterpart, the typical $Q=1$ cylindrically symmetrical skyrmion. Both types of to…
We study meron quasiparticle excitations in the ν= 1 quantum Hall bilayer. Considering the well known single meron state, we introduce its effective form, valid in the longdistance limit. That enables us to propose two (and more) meron states in the same limit. Further, establishing a plasma analogy of the (111) ground state, we find the impurities that play the role of merons and derive meron charge distributions. Using the introduced meron constructions in generalized (mixed) ground states and corresponding plasmas for arbitrary distance between the layers, we calculate the interaction betwe…
Quantum Hall bilayer phase diagram with respect to interlayer distance bears a remarkable similarity with phase diagrams of strongly correlated systems as a function of doping, with magnetic ordering on the one end and Fermi-liquid-like behaviour on the other. Moreover, it has been suggested [PRL 101, 176803 (2008)] that a BCS correlated state of composite fermions with p-wave pairing may exist in the intermediate region. In the same region, an exact diagonalization study in the torus geometry [PRB 69, 045319 (2004)] pointed out the existence of state(s) with pseudospin spiraling order. Here w…
Merons and skyrmions are classical topological solitons. However, they will become quantum mechanical objects when their sizes are of the order of nanometers. Recently, quantum computation based on nanoscale skyrmions was proposed. Here, we propose to use a nanoscale meron in a magnetic nanodisk as a qubit, where the up and down directions of the core spin are assigned to be the qubit states $|0\rangle$ and $|1\rangle$. First, we show numerically that a meron with the radius containing only $7$ spins can be stabilized in a ferromagnetic nanodisk classically. Then, we show theoretically that un…
In this paper we report calculations of some pseudospin textures for bilayer quantum hall systems with filling factor $ ν=1$. The textures we study are isolated single meron solutions. Meron solutions have already been studied at great length by others by minimising the microscopic Hamiltonian between microscopic trial wavefunctions. Our approach is somewhat different. We calculate them by numerically solving the nonlinear integro -differential equations arising from extremisation of the effective action for pseudospin textures. Our results can be viewed as augmenting earlier results and provi…
In the bilayer quantum Hall coherent state for $ν_T$ deviating slightly from one, we show that, instead of the global order parameter, the spontaneous breaking of the pseudospin U(1) rotational symmetry is reflected by the periodic domain structure accompanying with the charged meron pairs. The motion of meron pairs induces a novel pseudospin wave. The long range order of the periodic domains in a low bias voltage range leads to the residual zero-bias peak in the tunneling conductance even when the pseudopsin Goldstone feature in a high bias voltage range can be distinct from it.
In order to address many of the challenges and bottlenecks currently experienced by traditional charge based technologies, various alternatives are being actively explored to provide potential solutions of device miniaturization and scaling in the more-than-MOORE era. Amongst these alternatives, spintronics physics and devices have recently attracted a rapidly increasing interest by exploiting the additional degree of electron's spins. For example, magnetic domain-wall racetrack-memory and logic devices have been realized via manipulating domain-wall motion. As compared to domain-wall based de…
We analyze the transport properties of bilayer quantum Hall systems at total filling factor $ν=1$ in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries, cu…
We develop a nonperturbative approach to the quantum Hall bilayer (QHB) at ν=1 using trial wave functions. We predict phases of the QHB for arbitrary distance d and, our approach, in a dual picture, naturally introduces a new kind of quasiparticles - neutral fermions. Neutral fermion is a composite of two merons of the same vorticity and opposite charge. For small d (i.e. in the superfluid phase), neutral fermions appear as dipoles. At larger d dipoles dissociate into the phase of the two decoupled Fermi-liquid-like states. This scenario is relevant for the experimental situation where impurit…
Recent advances in the physics of current-driven antiferromagnetic skyrmions have observed the absence of a Magnus force. We outline the symmetry reasons for this phenomenon, and show that this cancellation will fail in the case of spin polarized currents. Pairing micromagnetic simulations with semiclassical spin wave transport theory, we demonstrate that skyrmions produce a spin-polarized transverse magnon current, and that spin-polarized magnon currents can in turn produce transverse motion of antiferromagnetic skyrmions. We examine qualitative differences in the frequency dependence of the …
The non-monotonic behavior of the NMR signal linewidth in the 2D quantum Hall system is explained in terms of the interplay between skyrmions localization, due to the influence of disorder, and the non-trivial temperature dependent skyrmion dynamics.
We investigate the skyrmion formation process in nano-structured FeGe Hall-bar devices by measurements of topological Hall effect, which extracts the winding number of a spin texture as an emergent magnetic field. Step-wise profiles of topological Hall resistivity are observed in the course of varying the applied magnetic field, which arise from instantaneous changes in the magnetic nano-structure such as creation, annihilation, and jittering motion of skyrmions. The discrete changes in topological Hall resistivity demonstrate the quantized nature of emergent magnetic flux inherent in each sky…
In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $ν=1$. Bimerons are excitations corresponding to bound pairs of merons and anti-merons. Bimeron solutions have already been studied at great length by other groups by minimising the microsopic Hamiltonian between microscopic trial wavefunctions. Here we calculate them by numerically solving coupled nonlinear partial differential equations arising from extremisation of the effective action for pseudospin textures. We also calculate the different contributions to the energy of our bime…
Using a particle-based simulation model, we show that quenched disorder creates a drive-dependent skyrmion Hall effect as measured by the change in the ratio $R=V_{\perp}/V_{||}$ of the skyrmion velocity perpendicular ($V_{\perp}$) and parallel ($V_{||}$) to an external drive. $R$ is zero at depinning and increases linearly with increasing drive, in agreement with recent experimental observations. At sufficiently high drives where the skyrmions enter a free flow regime, $R$ saturates to the disorder-free limit. This behavior is robust for a wide range of disorder strengths and intrinsic Hall a…
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 topological Hall effect is used extensively to study chiral spin textures in various materials. However, the factors controlling its magnitude in technologically-relevant thin films remain uncertain. Using variable temperature magnetotransport and real-space magnetic imaging in a series of Ir/Fe/Co/Pt heterostructures, here we report that the chiral spin fluctuations at the phase boundary between isolated skyrmions and a disordered skyrmion lattice result in a power-law enhancement of the topological Hall resistivity by up to three orders of magnitude. Our work reveals the dominant role of…
We investigate quasiparticles in bilayer quantum Hall systems around total filling factor nu =1 by current-pumped and resistively detected NMR. The measured Knight shift reveals that the spin component in the quasiparticle increases continuously with $Δ_{SAS}$. Combined with results for the pseudospin component obtained by activation gap measurements, this demonstrates that both spin and pseudospin are contained in a quasiparticle at intermediate $Δ_{SAS}$, providing evidence for the existence of the spin-pseudospin intermixed SU(4) skyrmion. Nuclear spin relaxation measurements show that the …
The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseud…
We provide unambiguous theoretical evidence for the formation of correlation-induced isolated merons in rotationally-symmetric quantum dots. Our calculations rely on neither the lowest-Landau-level approximation, nor on the maximum-density-droplet approximation, nor on the existence of a spin-polarized state. For experimentally accessible system parameters, unbound merons condense in the ground state at magnetic fields as low as $B^* = 0.2$ T and for as few as N = 3 confined fermions. The four-fold degenerate ground-state at $B^*$ corresponds to four orthogonal merons $\ket{QC}$ characterized …
We numerically examine thermal effects on the skyrmion Hall angle for driven skyrmions interacting with quenched disorder. We identify a creep regime in which motion occurs via intermittent jumps between pinned and flowing states. Here the skyrmion Hall angle is zero since the skyrmions have time to relax into equilibrium positions in the pinning sites, eliminating the side-jump motion induced by the Magnus force. At higher drives we find a crossover to a viscous flow regime where the skyrmion Hall angle is finite and increases with increasing drive or temperature. Our results are in agreement…
Arising from emergent electromagnetic field of magnetic skyrmions due to their nontrivial topology, the skyrmion Hall effect might be a roadblock for practical applications since any longitudinal motions of skyrmions in nanotrack is accompanied by a transverse motion. A direct consequence of such an effect is easy destruction of skyrmions at the nanotrack edges during their fast motions along the nanotrack, despite their topological protection. Here we propose an entirely novel solution of completely inhibiting such skyrmion Hall effect without affecting its topological properties based on a a…
We study properties of some known trial wavefunctions in bilayer quantum Hall systems at the total filling factor $ ν_{T}=1 $. In particular, we find that the properties of a meron wavefunction and a natural "quasi-hole" wave function are dramatically different due to the broken symmetry and the associated Goldstone mode in the bulk. Although the (smallest) meron has localized charge $ 1/2 $ and logarithmically divergent energy, the charge of the quasi-hole excitation extends over the whole system and its energy diverges linearly with the area of the system. This indicates that the natural qua…
Magneto-transport properties have been investigated for epitaxial thin films of B20-type MnSi grown on Si(111) substrates. Both Lorentz transmission electron microscopy (TEM) images and topological Hall effect (THE) clearly point to the robust formation of skyrmions over a wide temperature-magnetic field region. New features distinct from those of bulk MnSi are observed for epitaxial MnSi films: a shorter (nearly half) period of the spin helix and skyrmions, and an opposite sign of THE. These observations suggest versatile features of skyrmion-induced THE beyond the current understanding.
Magnetic skyrmions are topologically stable objects that are made with a bunch of spins tightly arranged in a smooth fashion. Their topological nature provides unusual and complex transport properties, such as the skyrmion Hall effect. Extensive Hall data have further revealed asymmetry between skyrmion and antiskyrmion Hall angles, which cannot be accounted by known mechanisms. Here, we explain this asymmetry by utilizing another universal transport coefficient called `Hall viscosity,' extensively studied in quantum Hall systems. Hall viscosity is modeled in steady-state skyrmions motion by g…
Exploring a classical solution of the non-linear sigma model for a quantum Hall ferromagnet, a skyrmion-magnon effective hamiltonian is obtained via the collective coordinates method. Using the Feynman-Vernon functional integral formalism for this model we find the temperature dependent transport coefficients which characterize a single skyrmion dynamics.
We present a microscopic theory of skyrmions in the monolayer quantum Hall ferromagnet. It is a peculiar feature of the system that the number density and the spin density are entangled intrinsically as dictated by the W$%_{\infty}$ algebra. The skyrmion and antiskyrmion states are constructed as W$_{\infty }$-rotated states of the hole-excited and electron-excited states, respectively. They are spin textures accompanied with density modulation that decreases the Coulomb energy. We calculate their excitation energy as a function of the Zeeman gap and compared the result with experimental data.
A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a $θ$-term determines the spin and statistics of these skyrmions.
It is widely believed that the skyrmion Hall effect, often disruptive for device applications, vanishes for overall topologically trivial structures such as (synthetic) antiferromagnetic skyrmions and skyrmioniums due to a compensation of Magnus forces. In this manuscript, however, we report that in contrast to the case of spin-transfer torque driven skyrmion motion, this notion is generally false for spin-orbit torque driven objects. We show that the skyrmion Hall angle is directly related to their helicity and imposes an unexpected roadblock for developing faster and lower input racetrack me…
We numerically study the interacting quantum Hall skyrmion system based on the Chern-Simons action. By noticing that the action is invariant under global spin rotations in the spin space with respect to the magnetic field direction, we obtain the low-energy effective action for a many skyrmion system. Performing extensive molecular dynamics simulations, we establish the thermodynamic phase diagram for a many skyrmion system.
We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we te…
We discuss the contribution of magnetic Skyrmions to the Hall viscosity and propose a simple way to identify it in experiments. The topological Skyrmion charge density has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In an electrically neutral system, the Skyrmion charge density is directly related to the thermal Hall conductivity. These results are direct consequences of the field theory Ward identities, which relate various physical quantities based on symmetries and have been previously applied to quantum Hall systems.
Electron spin-momentum locking together with background magnetic textures can significantly alter the electron transport properties. We theoretically investigate the electron transport at the interface between a topological insulator and a magnetic insulator with magnetic skyrmions on the top. In contrast to the conventional topological Hall effect in normal metals, the skyrmions yield an additional contribution to the anomalous Hall conductivity even in the absence of in-plane magnetic texture, arising from the phase factor characteristic to Dirac electrons acquired at skyrmion boundary.
We have discussed here the Magnus force acting on the vortices and skyrmions in the quantum Hall systems. We have found that it is generated by the chirality of the system which is associated with the Berry phase and is same for both the cases.
Magnetic skyrmions are whirl-like nano-objects with topological protection. When driven by direct currents (DC), skyrmions move but experience a transverse deflection. This so-called skyrmion Hall effect is often regarded a drawback for memory applications. Herein, we show that this unique effect can also be favorable for spintronic applications: We show that in a racetrack with a broken inversion symmetry, the skyrmion Hall effect allows to translate an alternating current (AC) into a directed motion along the track, like in a ratchet. We analyze several modes of the ratchet mechanism and sho…
Magnetic skyrmions are stable nanosized spin structures that can be displaced at low electrical current densities. Because of these properties, they have been proposed as building blocks of future electronic devices with unprecedentedly high information density and low energy consumption. The electrical detection of skyrmions via the Topological Hall Effect (THE), has so far been demonstrated only at cryogenic temperatures. Here, we report the observation of a skyrmion Topological Hall Effect near room temperature (276 K) in a mesoscopic lamella of FeGe. This region unambiguously coincides wit…
Magnetic skyrmions can be driven by an applied spin-polarized electron current which exerts a spin-transfer torque on the localized spins constituting the skyrmion. However, the longitudinal dynamics is plagued by the skyrmion Hall effect which causes the skyrmions to acquire a transverse velocity component. We show how to use spin-orbit interaction to control the skyrmion Hall angle and how the interplay of spin-transfer and spin-orbit torques can lead to a complete suppression of the transverse motion. Since the spin-orbit torques can be controlled all-electronically by a gate voltage, the s…
Bilayer quantum Hall states at $ν=1$ have been demonstrated to possess a distinguished state with interlayer phase coherence. The state has both excitations of Skyrmion with spin and pseudoSkyrmion with pseudospin. We show that Skyrmion $\leftrightarrow$ pseudoSkyrmion transition arises in the state by changing imbalance between electron densities in both layers; PseudoSkyrmion is realized at balance point, while Skyrmion is realized at large imbalance. The transition can be seen by observing the dependence of activation energies on magnetic field parallel to the layers.
We calculate in an analyical fashion the energies and net spins of skyrmions in fractional quantum Hall systems, based on the suggestion that skyrmion states are spontaneously $L_Z$ and $S_Z$ symmetry-breaking states. The quasihole-skyrmion state with a charge $-e/3$ around $ν$ = 1/3, where the ground state is known as a spin-polarized ferromagnetic state, is found to exist even in high magnetic fields up to about 7 T for GaAs samples.
The well-known Hall effect describes the transverse deflection of charged particles (electrons or holes) in an electric-current carrying conductor under the influence of perpendicular magnetic fields, as a result of the Lorentz force. Similarly, it is intriguing to examine if quasi-particles without an electric charge, but with a topological charge, show related transverse motion. Chiral magnetic skyrmions with a well-defined spin topology resulting in a unit topological charge serve as good candidates to test this hypothesis. In spite of the recent progress made on investigating magnetic skyr…
