Emergent chirality in a polar meron to skyrmion phase transition
Yu-Tsun Shao, Sujit Das, Zijian Hong, Ruijuan Xu, Swathi Chandrika, Fernando Gómez-Ortiz, Pablo García-Fernández, Long-Qing Chen, Harold Y. Hwang, Javier Junque… 展开作者
Yu-Tsun Shao, Sujit Das, Zijian Hong, Ruijuan Xu, Swathi Chandrika, Fernando Gómez-Ortiz, Pablo García-Fernández, Long-Qing Chen, Harold Y. Hwang, Javier Junquera, Lane W. Martin, Ramamoorthy Ramesh, David A. Muller
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 lattice of merons (with topological charge of -1/2) upon varying the temperature and elastic boundary conditions in [(PbTiO3)16/(SrTiO3)16]8 lifted-off membranes. This topological phase transition is accompanied by a change in chirality, from zero-net chirality (in meronic phase) to net-handedness (in skyrmionic phase). To map these changes microscopically required developing new imaging methods. We show how scanning convergent beam electron diffraction provides a robust measure of the local polarization simultaneously with the strain state at sub-nm resolution, while also directly mapping the chirality of each skyrmion. Using this, we demonstrate strain as a crucial order parameter to drive isotropic-to-anisotropic structural transitions of chiral polar skyrmions to non-chiral merons, validated with X-ray reciprocal space mapping and theoretical phase-field simulations. These results revealed by our new measurement methods provide the first illustration of systematic control of rich variety of topological dipole textures by altering the mechanical boundary conditions, which may offer a promising way to control their functionalities in ferroelectric nanodevices using the local and spatial distribution of chirality and order.
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…
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
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" $Q_A \ll 1$ …
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…
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…
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…
Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Neel walls and quantify the DMI induced by the Pd capp…
Magnetic skyrmions are localized chiral spin textures, which offer great promise to store and process information at the nanoscale. In the presence of asymmetric exchange interactions, their chirality, which governs their dynamics, is generally considered as an intrinsic parameter set during the sample deposition. In this work, we experimentally demonstrate that a gate voltage can control this key parameter. We probe the chirality of skyrmions and chiral domain walls by observing the direction of their current-induced motion and show that a gate voltage can reverse it. This local and dynamical…
We present a mechanism for deterministic control of the Bloch chirality in magnetic domain walls and skyrmions, originating from the interplay between an interfacial Dzyaloshinskii$-$Moriya interaction (DMI) and a perpendicular magnetic field. Although conventional interfacial DMI favors chiral Néel skyrmions, it does not break the energetic symmetry of the two Bloch chiralities in mixed Bloch$-$Néel skyrmions. However, the energy barrier to switching between Bloch chiralities does depend on the sense of rotation, which is dictated by the direction of the driving field. Our analytical and micr…
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…
Recent advances on the stabilization and manipulation of chiral magnetization configurations in systems consisting in alternating atomic layers of ferromagnetic and non-magnetic materials hold promise of innovation in spintronics technology. The low dimensionality of the systems promotes spin orbit driven interfacial effects like antisymmetric Dzyaloshinskii-Moriya interactions (DMI) and surface magnetic anisotropy, whose relative strengths may be tuned to achieve stable nanometer sized magnetic objects with fixed chirality. While in most of the cases this is obtained by engineering complex mu…
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…
Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear optics and spintronics to biology and pharmaceuticals. However, chirality is usually an invariable inherent property of a given material that cannot be easily changed at will. Here, we demonstrate that ferroelectric nanodots support skyrmions the chirality of which can be controlled and switched. We devise protocols for realizing control and efficient manipulations of the different types of skyrmions. O…
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 …
Unveiling Three-Dimensional Skyrmion Transitions Through Vortices and Monopoles
Oak Ridge National Laboratory（橡树岭国家实验室）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics & Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；School of Physics, The University of New South Wales（新南威尔士大学物理学院）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Department of Chemistry, University of Waterloo（滑铁卢大学化学系）；Department of Physics, University at Buffalo, State University of New York（纽约州立大学布法罗分校物理系）；Laboratory for Neutron Scattering and Imaging, PSI Center for Neutron and Muon Sciences（瑞士保罗谢勒研究所中子与缪子科学中心中子散射与成像实验室）
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 overa…
Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature Néel-type skyrmions in magnetic multilayer films are an important step towards their use in ultra-low power devices. We have investigated the magnetization reversal in a [Pt/Co/Ta]11 multilayer sample under a tilted magnetic field using the in-situ Lorentz tunneling electron microscopy. On decreasing the magnetic field individual skyrmions appear that subsequently evolve into snake-like structures growing in the direction opposite to the in-p…
The controllable phase transition and nanopatterning of topological states in a ferroelectric system under external stimuli are critical for realizing the potential applications in nanoelectronic devices such as logic, memory, race-track, etc. Herein, using the phase-field simulations, we demonstrate the mechanical manipulation of polar skyrmions in ferroelectric superlattices by applying external local compressive stress through an atomic force microscopy (AFM) tip. Different switching pathways are observed: under small to moderate force (<1 uN), the skyrmions coalesce to form a long stripe; …
We discover that the multiple degrees of freedom associated with magnetic skyrmions: size, position, and chirality, can all be used to control the Josephson effect and 0-pi transitions occurring in superconductor/magnetic skyrmion/superconductor junctions. In the presence of two skyrmions, the Josephson effect depends strongly on their relative chirality and leads to the possibility of a chirality-transistor effect for the supercurrent where the critical current is changed by several orders of magnitude simply by reversing the chirality of a magnetic skyrmion. Moreover, we demonstrate that the…
We investigate the field-induced crossover between two types of isolated skyrmions that exist within the conical phase of cubic helimagnets and orient themselves either along or perpendicular to the field. Such a crossover takes place for the same value of the field, at which the closely packed skyrmion lattice was predicted to stabilize in the A-phase region. The clusters and a skyrmion lattice comprised by the skyrmions perpendicular to the field, however, are unfavorable and lose their stability as compared with the skyrmions parallel to the field. We also followed transformation of perpend…
Magnetic skyrmions have been the focus of intense research with promising applications in memory, logic and interconnect technology. Several schemes have been recently proposed and demonstrated to nucleate skyrmions. However, they either result in an uncontrolled skyrmion bubble production or are mostly targeted towards integration with racetrack memory device. In this work, we propose a novel scheme for a controlled single skyrmion nucleation in a confined nanowire geometry with sub-100 nm width using a generalized approach of "localized spin current injection" technique in material systems e…
In the quest for miniaturizing magnetic devices, the effects of boundaries and surfaces become increasingly important. Here we show how the recently predicted boundary-induced Dzyaloshinskii-Moriya interaction (DMI) affects the magnetization of ferromagnetic films with a $C_{\infty v}$ symmetry and a perpendicular magnetic anisotropy. For an otherwise uniformly magnetized film, we find a surface twist when the magnetization in the bulk is canted by an in-plane external field. This twist at the surfaces caused by the boundary-induced DMI differs from the common canting caused by internal DMI ob…
External magnetic field, temperature, and spin-polarized current are usually employed to create and control nanoscale vortex-like spin configurations such as magnetic skyrmions. Although these methods have proven successful, they are not energy-efficient due to high power consumption and dissipation. Coupling between magnetic properties and mechanical deformation, the magnetoelastic (MEL) effect, offers a novel approach to energy-efficient control of magnetism at the nanoscale. It is of great interest in the context of ever-decreasing length scales of electronic and spintronic devices. Therefo…
Time dependence of the size and chirality of a ferromagnetic skyrmion in a Heisenberg model with the magnetic field on a square lattice has been studied analytically and numerically. The lattice and the magnetic field generate strong time dependence of the skyrmion chirality. Due to nonlinearity, the lattice alone also generates strong intrinsic damping that leads to the skyrmion collapse via the emission of spin waves. In the absence of the magnetic field the collapse is slow for a large skyrmion but it becomes exponentially fast in the presence of the Landau-Lifshitz damping when the field i…
We demonstrate the controlled generation and annihilation of (anti)skyrmions with tunable chirality in magnetic heterostructures by means of micromagnetic simulations. By making use of magnetic (anti)vortices in patterned ferromagnetic layer, we stabilize full lattices of (anti)skyrmions in an underlying skyrmionic thin film in a reproducible manner. The stability of the (anti)skyrmion depends on the polarization of the (anti)vortex, whereas their chirality is given by those of the (anti)vortices. Furthermore, we demonstrate that the core coupling between the (anti)vortices and (anti)skyrmions…
The breathing mode of a skyrmion, corresponding to coupled oscillations of its size and chirality angle is studied numerically for a conservative classical-spin system on a $500\times500$ lattice. The dependence of the oscillation frequency on the magnetic field is computed. It is linear at small fields, reaches maximum on increasing the field, then sharply tends to zero as the field approaches the threshold above which the skyrmion loses stability and collapses. Physically transparent analytical model is developed that explains the results qualitatively and provides the field dependence of th…
Topological spin textures such as skyrmions hold high potential for use as magnetically active elements in diverse near-future applications. While skyrmions in metallic multilayers attract great attention in this context, unleashing the myriad potential of skyrmions for various applications requires the discovery and customization of alternative host system paradigms. Here we developed and applied a chemical method to synthesize octahedral particles of the chiral insulating skyrmion host Cu2OSeO3 with both narrow size distribution, and tailored dimensions approaching the nanoscale. Combining m…
When electrons are driven through unconventional magnetic structures, such as skyrmions, they experience emergent electromagnetic fields that originate several Hall effects. Independently, ground state emergent magnetic fields can also lead to orbital magnetism, even without the spin-orbit interaction. The close parallel between the geometric theories of the Hall effects and of the orbital magnetization raises the question: does a skyrmion display topological orbital magnetism? Here we first address the smallest systems with nonvanishing emergent magnetic field, trimers, characterizing the orb…
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 spin…
In this paper we investigate a magnetic racetrack consisting of a junction of three materials with different properties. Indeed, this magnetic system is composed by two distinct regions (racetracks) connected by a thin interface: the first region (termed sector $1$) has isotropic in-plane magnetic chirality and supports skyrmion ($S$) excitations while the second (sector $3$) has anisotropic chirality and consequently supports antiskyrmions ($A$). The interface, which would be a third region (sector $2$, connecting sectors $1$ and $3$) located in the central part of the racetrack, is an easy-a…
We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge wave traveling along the boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We find that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the thin-film, but also by the Poisson ratio of the crystal. We discover three qualitatively different regions distinguished by the chirality …
Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for experimental investigation of topological solitons and understanding of their nonsingular field configurations. Here we introduce a paradigm of facile skyrmionic networks with mutually-orthogonal orientations of constituent isolated skyrmions. Such networks are envisioned as a novel concept of spintronic devices and are presumably responsible for precursor …
Magnetic skyrmions are textures behaving as quasiparticles which are topologically different from other states. Their discovery in systems with broken inversion symmetry sparked the search for materials containing such magnetic phase at room temperature. Their topological properties combined with the chirality-related spin-orbit torques make them interesting objects to control the magnetization at nanoscale. Here we show that a pair of coupled skyrmions with the same topological charge and opposite chiralities can be stabilized in a symmetric magnetic bilayer system by combining Dzyaloshinskii…
