Meron Pair Research Articles

Electrical engineering of topological magnetism in two-dimensional heterobilayers

The emergence of topological magnetism in two-dimensional (2D) van der Waals (vdW) magnetic materials and their heterostructures is an essential ingredient for next-generation information technology devices. Here, we demonstrate the all-electric switching of the topological nature of individual magnetic objects emerging in 2D vdW heterobilayers. We show from the first principles that an external electric field modifies the vdW gap between CrTe2 and (Rh, Ti)Te2 layers and alters the underlying magnetic interactions. This enables switching between ferromagnetic skyrmions and meron pairs in the CrTe2/RhTe2 heterobilayer while it enhances the stability of frustrated antiferromagnetic merons in the CrTe2/TiTe2 heterobilayer. We envision that the electrical engineering of distinct topological magnetic solitons in a single device could pave the way for novel energy-efficient mechanisms to store and transmit information with applications in spintronics.

Research progress in the magnetic domain wall topology

Topological magnetic skyrmions, as information units, possess distinct advantages such as high reliability, enhanced integration, and low energy consumption. These novel topological characteristics offer critical material and technological support for the rapid development of information technology, 5G communication, and big data. However, the application of magnetic skyrmions in practical devices is severely impeded by certain limitations, including their stability dependence on magnetic field and the deflection caused by the skyrmion Hall effect under electric current. Consequently, exploring new topological magnetic domain structures and material systems suitable for application becomes a pivotal area of research. This paper primarily focuses on experimental studies utilizing high-resolution Lorentz transmission electron microscopy for <i>in situ</i> real-space observation and manipulation of topological merons and skyrmions inside the magnetic domain wall, confirming the theoretical prediction of magnetic domain wall skyrmions in 2013. We has firstly achieved topological meron chains inside the domain walls by using the spin reorientation transition in two-dimensional van der Waals Fe<sub>5–<i>x</i></sub>GeTe<sub>2</sub> magnets, and systematically studied the dynamic behavior of domain wall topological magnetic domain structures under external electric and magnetic fields, filling the blanks in this research area. The important and special roles of magnetic domain walls are revealed at the same time. Then the GdFeCo amorphous ferrimagnetic thin film was designed and prepared based on the summarized mechanism with the domain wall meron pairs successfully reproduced. Moreover, the reversible topological transformation from domain wall meron pair to domain wall skyrmions has also been realized without external magnetic field during spin reorientation transformation as temperature changing. The results of micromagnetic simulation and electric experiments on the topological domains in domain walls would provided a strong basis and support for the future research.

Emergence of Stable Meron Quartets in Twisted Magnets.

The investigation of twist engineering in easy-axis magnetic systems has revealed remarkable potential for generating topological spin textures. Implementing twist engineering in easy-plane magnets, we introduce a novel approach to achieving fractional topological spin textures, such as merons. Through atomistic spin simulations on twisted bilayer magnets, we demonstrate the formation of a stable double Meron pair, which we refer to as the "Meron Quartet" (MQ). Unlike a single pair, the merons within the MQ exhibit exceptional stability against pair annihilation due to the protective localization mechanism induced by the twist that prevents collision of the Meron cores. Furthermore, we showcase that the stability of the MQ can be enhanced by adjusting the twist angle, resulting in an increased resistance to external perturbations such as external magnetic fields. Our findings highlight the twisted magnet as a promising platform for achieving merons as stable magnetic quasiparticles in van der Waals magnets.

Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet.

The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N=-1/2 and antimeron with N=1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N=-1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.

Multiferroicity in a Two-Dimensional Non-van der Waals Crystal of AgCr2X4 (X = S or Se).

Two-dimensional (2D) intrinsic multiferroics have long been pursued not only for their potential technological applications but also as model systems for studying emergent quantum phenomena and coupling mechanisms between various order parameters in low-dimensional space. However, the realization of 2D multiferroics is still a challenge. In this paper, we reveal that 2D AgCr2X4 (X = S or Se) crystals, which have been synthesized from the non-van der Waals (non-vdW) AgCrX2 bulk phase, are type I half-metallic/metallic multiferroics in which ferroelectricity and ferromagnetism coexist. The off-centering displacement of the Ag ion introduces out-of-plane polarization, and the magnetism originates from the interactions between Cr atoms. Remarkably, AgCr2Se4 shows topologically nontrivial spin textures, such as Meron pairs and Néel-type skyrmions, under suitable temperatures and magnetic fields. Our findings demonstrate that 2D multiferroics can be achieved from non-vdW materials and in turn open a new avenue for 2D multiferroics.

Field-free topological behavior in the magnetic domain wall of ferrimagnetic GdFeCo

Exploring and controlling topological textures such as merons and skyrmions has attracted enormous interests from the perspective of fundamental research and spintronic applications. It has been predicted theoretically and proved experimentally that the lattice form of topological meron-skyrmion transformation can be realized with the requirement of external magnetic fields in chiral ferromagnets. However, such topological transition behavior has yet to be verified in other materials. Here, we report real-space observation of magnetic topology transformation between meron pairs and skyrmions in the localized domain wall of ferrimagnetic GdFeCo films without the need of magnetic fields. The topological transformation in the domain wall of ferrimagnet is introduced by temperature-induced spin reorientation transition (SRT) and the underlying mechanism is revealed by micromagnetic simulations. The convenient electric-controlling topology transformation and driving motion along the confined domain wall is further anticipated, which will enable advanced application in magnetic devices.

Meron-like topological spin defects in monolayer CrCl3

Noncollinear spin textures in low-dimensional magnetic systems have been studied for decades because of their extraordinary properties and promising applications derived from the chirality and topological nature. However, material realizations of topological spin states are still limited. Employing first-principles and Monte Carlo simulations, we propose that monolayer chromium trichloride (CrCl3) can be a promising candidate for observing the vortex/antivortex type of topological defects, so-called merons. The numbers of vortices and antivortices are found to be the same, maintaining an overall integer topological unit. By perturbing with external magnetic fields, we show the robustness of these meron pairs and reveal a rich phase space to tune the hybridization between the ferromagnetic order and meron-like defects. The signatures of topological excitations under external magnetic field also provide crucial information for experimental justifications. Our study predicts that two-dimensional magnets with weak spin-orbit coupling can be a promising family for realizing meron-like spin textures.

Creation and annihilation of topological meron pairs in in-plane magnetized films

Merons which are topologically equivalent to one-half of skyrmions can exist only in pairs or groups in two-dimensional (2D) ferromagnetic (FM) systems. The recent discovery of meron lattice in chiral magnet Co8Zn9Mn3 raises the immediate challenging question that whether a single meron pair, which is the most fundamental topological structure in any 2D meron systems, can be created and stabilized in a continuous FM film? Utilizing winding number conservation, we develop a new method to create and stabilize a single pair of merons in a continuous Py film by local vortex imprinting from a Co disk. By observing the created meron pair directly within a magnetic field, we determine its topological structure unambiguously and explore the topological effect in its creation and annihilation processes. Our work opens a pathway towards developing and controlling topological structures in general magnetic systems without the restriction of perpendicular anisotropy and Dzyaloshinskii–Moriya interaction.

Multiply quantized and fractional skyrmions in a binary dipolar Bose-Einstein condensate under rotation

We consider a binary dipolar Bose-Einstein condensate with repulsive contact and dipolar interactions under rotation. Our results show that the interplay among short-range interaction, long-range interaction, and rotation can give rise to a rich variety of topological configurations, including giant skyrmions with multiply topological charges and skyrmion-vortex lattices. In particular, we find that for fixed rotation frequencies, tuning the short- and long-range interactions can derive novel ground-state phases, such as a meron pair composed of two fractional skyrmions and a skyrmion with topological charge $Q=2$ centered in giant skyrmions.

Switching of chiral magnetic skyrmions by picosecond magnetic field pulses via transient topological states.

Magnetic chiral skyrmions are vortex like spin structures that appear as stable or meta-stable states in magnetic materials due to the interplay between the symmetric and antisymmetric exchange interactions, applied magnetic field and/or uniaxial anisotropy. Their small size and internal stability make them prospective objects for data storage but for this, the controlled switching between skyrmion states of opposite polarity and topological charge is essential. Here we present a study of magnetic skyrmion switching by an applied magnetic field pulse based on a discrete model of classical spins and atomistic spin dynamics. We found a finite range of coupling parameters corresponding to the coexistence of two degenerate isolated skyrmions characterized by mutually inverted spin structures with opposite polarity and topological charge. We demonstrate how for a wide range of material parameters a short inclined magnetic field pulse can initiate the reliable switching between these states at GHz rates. Detailed analysis of the switching mechanism revealed the complex path of the system accompanied with the excitation of a chiral-achiral meron pair and the formation of an achiral skyrmion.

Half-skyrmion and vortex-antivortex pairs in spinor condensates

We propose a simple experimental scheme to generate spin textures in the ground state of interacting ultracold bosonic atoms loaded in a two-dimensional harmonic trap. Our scheme is based on two co-propagating Laguerre-Gauss laser beams illuminating the atoms and coupling two of their internal ground state Zeeman sublevels. Using a Gross-Pitaevskii description, we show that the ground state of the atomic system has different topological properties depending on the interaction strength and the laser beam intensity. A half-skyrmion state develops at low interactions while a meron pair develops at large interactions.

Topology and Origin of Effective Spin Meron Pairs in Ferromagnetic Multilayer Elements

We report on pairs of converging-diverging spin vortices in Co/Rh/NiFe trilayer disks. The lateral magnetization distribution of these effective spin merons is directly imaged by means of element-selective x-ray microscopy. By this method, both the divergence and circulation states of the individual layers are identified to be antisymmetric. Reversal measurements on corresponding continuous films reveal that biquadratic interlayer exchange coupling is the cause for the effective meron pair formation. Moreover, their three-dimensional magnetization structure is determined by micromagnetic simulations. Interestingly, the magnetic induction aligns along a flux-closing torus. This toroidal topology enforces a symmetry break, which links the core polarities to the divergence configuration.

Gauge-invariant magnetic monopole dominance in quark confinement

We show that a gauge-invariant magnetic monopole can be defined in Yang-Mills theory without matter fields, using a non-Abelian Stokes theorem and change of field variables a la Cho-Faddeev-Niemi, instead of using the Abelian projection. In fact, we give a first exact solution representing a magnetic monopole loop due to a meron pair with the non-trivial Pontryagin index. In addition, we summarize remarkable results of numerical simulations based on a new formulation of Yang-Mills theory: “Abelian” dominance and magnetic monopole dominance in the string tension. Finally, we discuss a novel feature in the case of SU ( 3 ) gauge group.

Skyrmion and bimeron excitations in bilayer quantum Hall systems

Charged excitations are topological solitons (skyrmions) in quantum Hall systems. They are CP 3 skyrmions in the bilayer system, where the underlying symmetry is SU(4). We present a microscopic formulation of CP 3 skyrmions in a system where the electron density is imbalanced between the two layers. A skyrmion is constructed by dressing a cloud of SU(4) isospins around an electron or a hole, and it carries the same charge as an electron or a hole at the filling factor ν = 1 . When the parallel magnetic field penetrates between the two layers, it deforms a skyrmion into a bimeron (a pair of merons). Each meron carries a fractional charge. We calculate the activation energy and show that it decreases rapidly as the parallel magnetic field increases near the balanced point.

Magnetic monopole loops supported by a meron pair as the quark confiner

Magnetic monopole loops supported by a meron pair as the quark confiner

Magnetic monopole loops supported by a meron pair as the quark confiner

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two-meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen, and Gross suggested long ago.

VORTICES IN MULTICOMPONENT BOSE–EINSTEIN CONDENSATES

We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.

Vortex Molecules in Coherently Coupled Two-Component Bose-Einstein Condensates

A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and one in the other are connected by a domain wall of the relative phase, constituting a "vortex molecule," which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.

A NOVEL MERON-INDUCED PSEUDOSPIN WAVE IN THE BILAYER QUANTUM HALL COHERENT STATE AND THE RESIDUAL ZERO-BIAS PEAK IN TUNNELING CONDUCTANCE

In the bilayer quantum Hall coherent state for νT deviating slightly from unity, we show that, instead of the global order parameter, the periodic domain structure accompanying the charged meron pairs spontaneously breaks the pseudospin U(1) rotational symmetry. 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, which can be distinct from the pseudopsin Goldstone feature in a high bias voltage range.

Monopole and vortex content of a meron pair

We investigate the monopole and vortex content of a meron pair by calculating the points at which the transformation to the Laplacian Center Gauge is ill-defined and by studying the behavior of Wilson loops. These techniques reveal complementary aspects of the vortex and monopole structure, including the presence of closed monopole lines and closed vortex surfaces joining the two merons, and evidence for intersecting vortex surfaces at each meron.