Motivated by a recent magnetization reversal experiment on a TbFeCo thin film, we study a topological excitation in the anisotropic nonlinear sigma model together with the Zeeman and magnetic dipole-dipole interactions. Dipole-dipole interactions turn a ferromagnet into a frustrated spin system, which allows a nontrivial spin texture such as a giant skyrmion. We derive an analytic formula for the skyrmion radius. The radius is controllable by the external magnetic field. It is intriguing that a skyrmion may have already been observed as a magnetic domain. A salient feature is that a single skyrmion can be created or destroyed experimentally. An analysis is made also on skyrmions in chiral magnets.
Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Recently $β$-Mn structure-type Co-Zn-Mn alloys were identified as a new class of chiral magnet to host such skyrmion crystal phases, while $β$-Mn itself is known as hosting an elemental geometrically frustrated spin liquid. Here we report the intermediate composition system Co$_7$Zn$_7$Mn$_6$ to be a unique host of two disconnected, thermal-equilibrium topological skyrmion phases; one is a conventional s…
Topologically stable structures include vortices in a wide variety of matter, such as skyrmions in ferro- and antiferromagnets, and hedgehog point defects in liquid crystals and ferromagnets. These are characterized by integer-valued topological quantum numbers. In this context, closed surfaces are a prominent subject of study as they form a link between fundamental mathematical theorems and real physical systems. Here we perform an analysis on the topology and stability of equilibrium magnetization states for a thin spherical shell with easy-axis anisotropy in normal directions. Skyrmion solu…
Topological spin textures in an itinerant ferromagnet, SrRuO$_3$ is studied combining Hall transport measurements and numerical simulations. We observe characteristic signatures of the Topological Hall Effect associated with skyrmions. A relatively large thickness of our films and absence of heavy metal layers make the interfacial Dzyaloshinskii-Moriya interaction an unlikely source of these topological spin textures. Additionally, the transport anomalies exhibit an unprecedented robustness to magnetic field tilting and temperature. Our numerical simulations suggest that this unconventional be…
We report small-angle neutron scattering studies of the lacunar spinel GaV$_4$S$_8$, which reveal the long-wavelength magnetic states to be cycloidally modulated. This provides direct support for the formation of Néel-type skyrmions recently claimed to exist in this compound. In striking contrast with all other bulk skyrmion host materials, upon cooling the modulated magnetic states transform into a ferromagnetic state. These results indicate all of the modulated states in GaV$_4$S$_8$, including the skyrmion state, gain their stability from thermal fluctuations, while at lower temperature the…
Magnetic skyrmions are promising spin textures for building next-generation magnetic memories and spintronic devices. Nevertheless, one of the major challenges in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures in different geometries. Here we numerically study the skyrmion-skyrmion interaction potential that arises due to the dynamics of itinerant electrons coupled to the magnetic texture in a ferromagnetic background with racetrack geometry. We consider different topological textures (ferromagnetic (FM) and antiferromagnetic (AFM)), namely: skyr…
Magnetic skyrmions, topological spin textures observed in chiral magnets, have attracted huge interest due to their applications in the field of spintronics. In this work we study the stability of circular isolated skyrmions in ferromagnetic chiral magnets under the influence of different perturbations and external fields. To this end we develop a general systematic procedure based in a harmonic expansion series of the skyrmion boundary which allows the identifycation of the breakdown of the skyrmion circular shape on each instability channel independently. We apply our approach to a few repre…
Magnetic structures and their stability of the multiple helical spin density waves (MHSDW) and related magnetic skyrmions in itinerant electron system have been investigated on the basis of both the phenomenological and microscopic theories. It is shown by using the Ginzburg-Landau (GL) theory and the Application Visualization System (AVS) that the magnetic skyrmion structures emerge as a MHSDW and can be stabilized in itinerant electron system on the fcc lattice even if there is no Dzyaloshinskii-Moriya interaction. Moreover, by using the generalized Hartree-Fock theory for the Hubbard model,…
We theoretically propose a new stabilization mechanism of a skyrmion crystal (SkX) in a bilayer triangular lattice system consisting of the ferromagnetic and the antiferromagnetic layers. By performing variational calculations and Monte Carlo simulations in a complementary way, we find that a magnetic frustration between the ferromagnetic and antiferromagnetic layers is a source of a finite-Q spiral state and the SkX in the strong interlayer coupling regime. We also show that the degree of frustration is related to the interlayer exchange interaction. The stronger interlayer coupling tends to …
Magnetic skyrmions in 2D chiral magnets are in general stabilized by a combination of Dzyaloshinskii-Moriya interaction and external magnetic field. Here, we show that skyrmions can also be stabilized in twisted moiré superlattices in the absence of an external magnetic field. Our setup consists of a 2D ferromagnetic layer twisted on top of an antiferromagnetic substrate. The coupling between the ferromagnetic layer and the substrate generates an effective alternating exchange field. We find a large region of skyrmion crystal phase when the length scales of the moiré periodicity and skyrmions …
A giant Skyrmion collapses to a singular point by emitting spin waves in a thin ferromagnetic film, when external magnetic field is increased beyond the critical one. The remnant is a single-spin flipped (SSF) point. The SSF point has a quantum diffusion dynamics governed by the Heisenberg model. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two SSF points after two Skyrmion bursts. Quantum walks for $S=1/2$ and 1 are exact solvable. The system presents a new type of quantum walk for $S>1/2$, where a SSF poi…
When two magnetic skyrmions - whirl-like, topologically protected quasiparticles - form a bound pair, a biskyrmion state with a topological charge of $N_\mathrm{Sk}=\pm 2$ is constituted. Recently, especially the case of two partially overlapping skyrmions has brought about great research interest. Since for its formation the individual skyrmions need to posses opposite in-plane magnetizations, such a biskyrmion cannot be stabilized by the Dzyaloshinskii-Moriya-interaction (DMI), which is the interaction that typically stabilizes skyrmions in non-centrosymmetric materials and at interfaces. He…
We theoretically investigate the origin of the square-type skyrmion crystal in centrosymmetric itinerant magnets, motivated from the recent experimental finding in GdRu$_2$Si$_2$ [N. D. Khanh $\mathit{et}$ $\mathit{al.}$, Nat. Nanotech. $\mathbf{15}$, 444 (2020)]. By simulated annealing for an effective spin model derived from the Kondo lattice model on a square lattice, we find that a square skyrmion crystal composed of a superposition of two spin helices is stabilized in a magnetic field by synergy between the positive biquadratic, bond-dependent anisotropic, and easy-axis anisotropic intera…
Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications. Until now, skyrmions have been observed in a variety of magnets that exhibit nearly parallel alignment for the neighbouring spins, but theoretically, skyrmions with anti-parallel neighbouring spins are also possible. The latter, antiferromagnetic skyrmions, may allow more flexible control compared to the conventional ferromagnetic skyrmions. Here, by combining neutron scattering and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattic…
A spin texture called skyrmion has been recently observed in certain chiral magnets without inversion symmetry. The observed skyrmions are extended objects with typical linear sizes of 10 nm to 100 nm that contain $10^3$ to $10^5$ spins and can be deformed in response to external perturbations. Weak deformations are characterized by the internal modes which are localized around the skyrmion center. Knowledge of internal modes is crucial to assess the stability and rigidity of these topological textures. Here we compute the internal modes of a skyrmion in the ferromagnetic background state by n…
We theoretically report an instability toward a skyrmion crystal in centrosymmetric magnets under hexagonal and trigonal single-ion anisotropy. The results are obtained for a minimal spin model with a crystal-dependent single-ion anisotropy on a triangular lattice by performing simulated annealing. By constructing magnetic phase diagrams in the presence of six different types of single-ion anisotropy while changing the amplitudes of external magnetic field and single-ion anisotropy in a systematic way, we find that the hexagonal and trigonal single-ion anisotropy becomes a source of the skyrmi…
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…
The stability of the four known stationary points of the cubic helimagnet energy functional: the ferromagnetic state, the conical helix, the conical helicoid, and the skyrmion lattice, is studied by solving the corresponding spectral problem. The only stable points are the ferromagnetic state at high magnetic field and the conical helix at low field, and there is no metastable state. Thermal fluctuations around the stationary point, included to quadratic order in the saddle point expansion, destabilize the conical helix in a region where the ferromagnetic state is unstable. Thus, a new interme…
The helicity-orbital coupling is an intriguing feature of magnetic skyrmions in frustrated magnets. Here, we explore the skyrmion dynamics in a frustrated magnet based on the $J_{1}$-$J_{2}$-$J_{3}$ classical Heisenberg model explicitly by including the dipole-dipole interaction. The skyrmion energy acquires a helicity dependence due to the dipole-dipole interaction, resulting in the current-induced translational motion with a fixed helicity. The lowest energy states are the degenerate Bloch-type states, which can be used for building the binary memory. By increasing the driving current, the h…
Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle point textures and energy barriers of large skyrmions. The sign of the spin stiffne…
The electrical resistivity of several relatively clean metallic ferromagnets, as well as the helimagnet MnSi, is commonly observed to exhibit non-Fermi-liquid behavior at low temperatures. This behavior, which is found in both ordered and disordered phases, and both near and away from the magnetic transition, remains a major unsolved problem. We derive and discuss three novel mechanisms underlying such behavior that are based on electron scattering mediated by the exchange of (1) ferromagnons or (2) skyrmionic fluctuations, both in conjunction with weak disorder, or (3) helimagnons in clean sy…
Achieving control over magnon spin currents in insulating magnets - where dissipation due to Joule heating is highly suppressed - is an active area of research that could lead to energy-efficient spintronics applications. However, magnon spin currents supported by conventional systems with uniform magnetic order have proven hard to control. An alternative approach that relies on topologically protected magnonic edge states of spatially periodic magnetic textures has recently emerged. A prime example of such textures is the ferromagnetic skyrmion crystal which hosts chiral edge states providing…
Recent experiments have reported on controlled nucleation of individual skyrmions in chiral magnets. Here we show that in magnetic ultra-thin films with interfacial Dzyaloshinskii-Moriya interaction, single skyrmions of different radii can be nucleated by creating a local distortion in the magnetic field. In our study, we have considered zero temperature quantum nucleation of a single skyrmion from a ferromagnetic phase. The physical scenario we model is one where a uniform field stabilizes the ferromagnet, and an opposing local magnetic field over a circular spot, generated by the tip of a lo…
We present a microscopic electronic description of how antiskyrmions can be stabilized in a Dresselhaus spin-orbit coupled magnetic metal. Furthermore, we show that the antiskyrmions can be tuned into Bloch skyrmions via a change in sign of hopping integral. The results are based on the state of the art hybrid Monte Carlo simulations. Origin of such topological textures is understood via an effective spin-only model. Our results uncover a novel connection between two very distinct topological spin textures of immense current interest, and present a microscopic explanation of skyrmion formation…
We theoretically study spin and charge excitations of skyrmion crystals stabilized by conduction-electron-mediated magnetic interactions via spin-charge coupling in a centrosymmetric Kondo-lattice model by large-scale spin-dynamics simulations combined with the kernel polynomial method. We reveal clear segregation of spin and charge excitation channels and nonreciprocal nature of the spin excitations governed by the Fermi-surface geometry, which are unique to the skyrmion crystals in centrosymmetric itinerant hosts and can be a source of novel physical phenomena.
Skyrmions are nanometric spin whirls that can be stabilized in magnets lacking inversion symmetry. The properties of isolated skyrmions embedded in a ferromagnetic background have been intensively studied. We show that single skyrmions and clusters of skyrmions can also form in the helical phase and investigate theoretically their energetics and dynamics. The helical background provides natural one-dimensional channels along which a skyrmion can move rapidly. In contrast to skyrmions in ferromagnets, the skymion-skyrmion interaction has a strong attractive component and thus skyrmions tend to …
We present a comprehensive theory of the magnetic phases in twisted bilayer Cr-trihalides through a combination of first-principles calculations and atomistic simulations. We show that the stacking-dependent interlayer exchange leads to an effective moiré field that is mostly ferromagnetic with antiferromagnetic patches. A wide range of noncollinear magnetic phases can be stabilized as a function of the twist angle and Dzyaloshinskii-Moriya interaction as a result of the competing interlayer antiferromagnetic coupling and the energy cost for forming domain walls. In particular, we demonstrate …
We study the evolution of the magnetic phase diagram of Mn$_{1-x}$Fe$_{x}$Ge alloys with concentration $x$ ($0 \leq x \leq 0.3$) by small-angle neutron scattering. We unambiguously observe the absence of a skyrmion lattice (or A-phase) in bulk MnGe and its onset under a small Mn/Fe substitution. The A-phase is there endowed with an exceptional skyrmion density, and is stabilized within a very large temperature region and a field range which scales with the Fe concentration. Our findings highlight the possibility to fine-tune properties of skyrmion lattices by means of chemical doping.
We report simulation results of skyrmions on fluctuating 2D lattices, where the vertices ${\bf r}_i (\in {\bf R}^3)$ are treated as a dynamical variable and, hence, there is no crystalline structure. On the fluctuating surfaces, an external magnetic field perpendicular to the surface, Dzyaloshinskii-Moriya and ferromagnetic interactions are assumed in addition to the Helfrich-Polyakov Hamiltonian for membranes. The surface (or frame) tension $τ$ is calculated under both isotropic and uniaxial strain conditions, and this calculation clarifies a non-trivial dependence of $τ$ on the skyrmion, str…
We construct the general free energy governing long-wavelength magnetism in two-dimensional oxide heterostructures, which applies irrespective of the microscopic mechanism for magnetism. This leads, in the relevant regime of weak but non-negligible spin-orbit coupling, to a rich phase diagram containing in-plane ferromagnetic, spiral, cone, and skyrmion lattice phases, as well as a nematic state stabilized by thermal fluctuations. The general conclusions are vetted by a microscopic derivation for a simple model with Rashba spin-orbit coupling.
We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in the ferromagnetic layer. A continuum low energy field theory is utilized to study such systems. We develop a phase diagram as a function of the strength of inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining perturbative and strong coupling analyses with numerical simulations using Landau-Lifshitz-Gilbert equations. Various moiré-periodic commensurate phases are found, and the commensurate-incommensurate transition is dis…
The Dzyaloshinkii-Moriya (DM) interaction that originates from relativistic spin-orbit coupling in noncentrosymmetric magnets is a source of topological spin textures. We theoretically investigate the possibility of a skyrmion crystal by focusing on the role of the out-of-plane DM interaction that is different from the polar- and chiral-type DM interaction. By performing the simulated annealing for a spin model on a triangular lattice belonging to the $D_{3h}$ point group, we construct low-temperature magnetic phase diagrams in an applied magnetic field. As a result, we find the instability to…
Based on analytical estimation and lattice simulation, a proposal is made that magnetic skyrmions can be generated through the pinning effect in 2D chiral magnetic materials, in absence of an external magnetic field or magnetic anisotropy. In our simulation, stable magnetic skyrmions can be generated in the pinning areas. The properties of the skyrmions are studied for various values of ferromagnetic exchange strength and the Dzyaloshinskii-Moriya interaction strength.
The emergence of a magnetic skyrmion crystal in a nonsymmorphic lattice system with the screw symmetry is numerically investigated. By performing the simulated annealing for a layered spin model with the isotropic exchange interaction and the antisymmetric Dzyaloshinskii-Moriya interaction, and then constructing a low-temperature phase diagram, we reveal that the skyrmion crystal is stabilized in both zero and nonzero fields even without the threefold rotational symmetry in the two-dimensional plane. We show that a competition between the ferromagnetic interlayer exchange interaction and the l…
We study the dynamics of skyrmions in chiral magnets in the presence of a spin polarized current. The motion of skyrmions in the ferromagnetic background excites spin waves and contributes to additional damping. At a large current, the spin wave spectrum becomes gapless and skyrmions are created dynamically from the ferromagnetic state. At an even higher current, these skyrmions are strongly deformed due to the damping and become unstable at a threshold current, leading to a chiral liquid. We show how skyrmions can be created by increasing the current in the magnetic spiral state. We then cons…
We show that a vortex current is created around a skyrmion spin texture under magnetic field due to a radial spin motive force in a two-dimensional metal with localized magnetic moments even in the absence of any superconductivity correlations. The effect is expected both for ferromagnetic and for antiferromagnetic systems. The Skyrmion-induced vortex mechanism provides a picture for large Nernst signals observed in the pseudogap phase of the high-$T_c$ cuprates.
Understanding the spin-wave excitations of chiral magnetic order, such as the skyrmion crystal (SkX), is of fundamental interest to confirm such exotic magnetic order. The SkX is realized by competing Dzyaloshinskii-Moriya and ferromagnetic-exchange interactions with a magnetic field or anisotropy. Here we compute the dynamical spin structure factor, using Monte Carlo and spin dynamics simulations, extracting the spin-wave spectrum in the SkX, in the vicinity of the paramagnet to SkX transition. Inside the SkX, we find six spin-wave modes, which are supplemented by another mode originating fro…
Magnetic skyrmions are swirling spin textures with topologically protected noncoplanarity. Recently, skyrmions with the topological number of unity have been extensively studied in both experiment and theory. We here show that a skyrmion crystal with an unusually high topological number of two is stabilized in itinerant magnets at zero magnetic field. The results are obtained for a minimal Kondo lattice model on a triangular lattice by an unrestricted large-scale numerical simulation and variational calculations. We find that the topological number can be switched by a magnetic field as $2\lef…
Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose--Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall become…
Skyrmion and meron phases induced by spin-phonon coupling
Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET（拉普拉塔国立大学-国家科学技术研究委员会 液体与生物系统物理研究所（IFLYSIB））；Universidad Nacional de La Plata（拉普拉塔国立大学）
We report experimental evidence of formation of antiferromagnetic clusters in composites made of a cuprate superconductor La1.85Sr0.15CuO4 (LCu) and a ferromagnet La0.6Sr0.4CoO3 (LCo). From linear and non-linear ac-susceptibility measurement on this composite material it is found that the exchange field of LCo suppress the dynamic antiferromagnetic spin fluctuation of LCu and convert it into the short range ordered superparamagnetic type antiferromagnetic (AFM) clusters at the cost of superconducting volume fraction. These shrank superconducting volume fraction shows quantum size effect (QSE) …
We derive the quantization of magnetic helicity in the solid-state and demonstrate tunable macroscopic quantum tunneling, coherence, and oscillation for a skyrmion spin texture stabilized in frustrated magnets. We also discuss the parameter space for the experimental realization of quantum effects. Typically, for a skyrmion of 5 nm radius, quantum tunneling between two macroscopic states with distinct helicities occurs with an inverse escape rate within seconds below 100 mK, and an energy splitting in the MHz regime. Feasibility of quantum tunneling of an ensemble of magnetic spins inspires ne…
Several challenges in designing an operational Skyrmion racetrack memory are well-known. Among those challenges, a few contradictions can be identified if researchers were to rely only on metallic materials. Hence, expanding the exploration on Skyrmion Physics into oxide materials is essential to bridge the contradicting gap. In this topical review, we first briefly revise the theories and criteria involved in stabilizing and manipulating Skymions, followed by studying the behaviors of dipolar-stabilized magnetic bubbles. Next, we explore the properties of multiferroic Skyrmions with magnetoel…
Topological spin structures, such as magnetic skyrmions, hold great promises for data storage applications, thanks to their inherent stability. In most cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while spontaneous skyrmion lattices have been reported in centrosymmetric itinerant magnets with long-range interactions. Here, a spontaneous anti-biskyrmion lattice with unique topology and chirality is predicted in the monolayer of a semiconducting and centrosymmetric metal halide, NiI$_2$. Our fi…
Intricate spin textures in helimagnets, identified as stable topological Skyrmions, were observed experimentally, where Skyrme lattice was supposed to exhibit symmetric structures in the ground state. We show the possibility of asymmetric Skyrmions in a helimagnetic model, for individual Skyrmion as well as for the hexagonal Skyrme crystal with higher charge, as perturbative deformation and stabilization of exact ferromagnetic solitons. Such nonsymmetric configurations for the Skyrme lattice, predicted here theoretically, need to be verified in precision experiments.
We demonstrate a fast numerical method of theoretical studies of skyrmion lattice or spiral order in magnetic materials with Dzyaloshinsky-Moriya interaction. The method is based on the Fourier expansion of the magnetization combined with a minimization of the free energy functional of the magnetic material in Fourier space, yielding the optimal configuration of the system for any given set of parameters. We employ a Lagrange multiplier technique in order to satisfy micromagnetic constraints. We apply this method to a system that exhibits, depending on the parameter choice, ferromagnetic, skyr…
