Figure 6 - uploaded by Shizeng Lin
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(a) The averaged absolute skyrmion charge density, 〈|ρs|〉=14πL2∫dr2|S·(∂xS×∂yS)| with L the system size as a function of annealing rate, where 〈⋯〉 denotes the average of independent annealing process. To obtain a better statistics, the results are obtained by averaging over 20 independent runs with different initial configurations. (b) and (c) correspond to the spin profile and skyrmion topological charge density ρs, respectively, obtained after annealing with annealing rate ΔT=0.00001J1 per Monte Carlo sweep (MCS) at Ha/Hs=1.617. The results are obtained by Monte Carlo annealing in the J1−J2−J3 model on a square lattice. Here, we take Q0=2π/18 and J1−4J2+16J3=0. The saturation field is Hs=0.001856J1.
Source publication
Magnetic skyrmions have attracted considerable attention recently for their
huge potential in spintronic applications. Generally skyrmions are big compared
to the atomic lattice constant, which allows for the Ginzburg-Landau type
description in the continuum limit. Such a description successfully captures
the main experimental observations on skyrm...
Contexts in source publication
Context 1
... a skyrmion is a metastable state in the ferromagnetic state, one natural way to excite skyrmions is by annealing. 064430 In Fig. 6, we present the results obtained by annealing in Monte Carlo simulations of lattice model Eq. (3) in the long-wavelength limit. Initially, the system is equilibrated at high T and is in the paramagnetic state. Then we gradually reduce temperature with a rate T per every Monte Carlo sweep (MCS). In this process, skyrmions and ...
Context 2
... antiskyrmions is nonmonotonic as a function of separation, and since there is a steep energy barrier for the annihilation between skyrmions and antiskyrmions, they are trapped by the local minimum in their interaction potential at low temperatures and they do not annihilate. The density of the skyrmions can be controlled by the annealing rate [ Fig. 6(a)]. At the initial state when T H a , the absolute of skyrmion density does not depend on magnetic field. For a fast annealing, the final state resembles the initial state therefore the skyrmion density almost does not depend on magnetic field. For a slow annealing, the system can reach a lower energy state by reducing the skyrmion ...
Citations
... On the basis of the ground-state phase diagram of the frustrated J 1 -J 2 triangular Heisenberg model obtained by the simulated annealing, it was theoretically suggested that the easy-axis magnetic anisotropy stabilized the SkX state even at T = 0 [10]. While the effect of magnetic anisotropy on the SkX formation was examined further by various authors [14][15][16][17][18][19][20][21], most of them concentrated on the T = 0 properties, with few studies on the temperature (T ) vs. magnetic-field (H) phase diagram (see [15,16,20], however). Even concerning with the T = 0 properties, the proposed magnetic-anisotropy stabilization of the SkX state might deserve further careful examination, since the numerical method employed, e.g., the simulated annealing, might capture the metastable SkX state, while such a metastable, not truly stable SkX state was indeed reported under certain annealing conditions even experimentally [22,23]. ...
... On the basis of the ground-state phase diagram of the frustrated J 1 -J 2 triangular Heisenberg model obtained by the simulated annealing, it was theoretically suggested that the easy-axis magnetic anisotropy stabilized the SkX state even at T = 0 [10]. While the effect of magnetic anisotropy on the SkX formation was examined further by various authors [14][15][16][17][18][19][20][21], most of them concentrated on the T = 0 properties, with few studies on the temperature (T ) vs. magnetic-field (H) phase diagram (see [15,16,20], however). Even concerning with the T = 0 properties, the proposed magnetic-anisotropy stabilization of the SkX state might deserve further careful examination, since the numerical method employed, e.g., the simulated annealing, might capture the metastable SkX state, while such a metastable, not truly stable SkX state was indeed reported under certain annealing conditions even experimentally [22,23]. ...
The nature of the skyrmion-crystal (SkX) formation and various multiple-$q$ phases encompassing the SkX phase are investigated by extensive Monte Carlo simulations on the frustrated $J_1$-$J_3$ triangular-lattice Heisenberg model with the weak easy-axis magnetic anisotropy. Phase diagram in the temperature $T$ vs. magnetic-field $H$ plane are constructed, leading to a rich variety of multiple-$q$ phases. The anisotropy stabilizes the SkX state down to $T=0$ at intermediate fields, while in the lower-field range the SkX state becomes only metastable, and new multiple-$q$ states with a broken $C_3$ symmetry are instead stabilized. Implications to experiments are discussed.
... Our measurements show evidence that composite skyrmion-antiskyrmion systems form in the partially amorphized films, with skyrmions existing in the crystalline phase, and both skyrmions and antiskyrmions in the amorphous phase. Fundamentally, such systems are of interest as testbeds for theoretically predicted phenomena such as spin wave emission by currentinduced skyrmion-antiskyrmion pair annihilation 67 , a skyrmionantiskyrmion liquid 68 , as well as skyrmion-antiskyrmion crystals, interactions, and dynamics [69][70][71] . ...
Skyrmions and antiskyrmions are nanoscale swirling textures of magnetic moments formed by chiral interactions between atomic spins in magnetic noncentrosymmetric materials and multilayer films with broken inversion symmetry. These quasiparticles are of interest for use as information carriers in next-generation, low-energy spintronic applications. To develop skyrmion-based memory and logic, we must understand skyrmion-defect interactions with two main goals—determining how skyrmions navigate intrinsic material defects and determining how to engineer disorder for optimal device operation. Here, we introduce a tunable means of creating a skyrmion-antiskyrmion system by engineering the disorder landscape in FeGe using ion irradiation. Specifically, we irradiate epitaxial B20-phase FeGe films with 2.8 MeV Au ⁴⁺ ions at varying fluences, inducing amorphous regions within the crystalline matrix. Using low-temperature electrical transport and magnetization measurements, we observe a strong topological Hall effect with a double-peak feature that serves as a signature of skyrmions and antiskyrmions. These results are a step towards the development of information storage devices that use skyrmions and antiskyrmions as storage bits, and our system may serve as a testbed for theoretically predicted phenomena in skyrmion-antiskyrmion crystals.
... In materials lacking inversion symmetry, individual skyrmions are stabilized by Dzyaloshinskii-Moriya interaction (DMI) [44][45][46][47][48][49]. Other mechanisms of stabilization of skyrmions include frustrated exchange interactions [50,51], magnetic anisotropy [52,53], disorder [54], and geometrical confinement [55]. ...
We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices in systems of small, medium, and large sizes with the number of skyrmions ranging from $10^{3}$ to over $10^{5}$. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of skyrmion lattices. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the skyrmion lattice. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.
... In centrosymmetric materials the absence of inversion symmetry breaking forbids Dzyaloshinskii-Moriya interaction (DMI). In these materials the skyrmion crystals gets stabilized by competeing exchange interactions coming from geometrical frustration of the short-range two-spin interactions hence termed as 'chiral geometric frustration' [25][26][27][28] or magnetic anisotropies [29]. In non-centrosymmetric crystals, formation of these textures is understood theoretically via interplay between Heisenberg exchange and DMI found in materials lacking inversion symmetry [30][31][32][33][34][35][36]. ...
We report a microscopic mechanism for stabilization of biskyrmions in nature by investigating a minimal classical spin lattice model with nearest neighbour ferromagnetic Heisenberg exchange and static chiral magnetic interaction on the triangular lattice. The model is physically motivated model from the Mott insulators with broken time-reversal symmetry, that is, in the large-$U$ limit of the one band Hubbard model at half-filling on a two-dimensional lattice in the presence of external magnetic field. At order $1/U^{2}$, the external magnetic field can induce a chiral interaction between the three neighbouring spins. We demonstrate that the chiral magnetic interaction results in biskyrmion states above a critical value and its strength affects the size of biskyrmions forming.
... The skyrmion helicity, in a minimal model (in particular in the absence of anisotropies), is known to be a Goldstone mode in frustrated magnets [34][35][36][37] . Therefore, in the absence of energy injection and dissipation, energy conservation enforces the skyrmion size to remain constant while allowing the helicity to rotate at a constant angular frequency. ...
... The interplay of the quadratic and quartic exchange terms captures the details of the competing microscopic exchange interactions. The competing exchange terms give rise to a length scale, which, in the presence of a moderate out-of-plane magnetic field, stabilizes skyrmions 35 . Noncollinear magnetic textures, e.g. ...
Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields.
... 12,13,31,32 Such frustrated-magnet-hosted skyrmions indicate not only a variety in the spin morphology (e.g., coexistence of skyrmions and antiskyrmions) but also exceptional properties, such as enhanced topological Hall effect (THE) and helicity-related complex dynamics. 31,33,34 They can be easily detected and manipulated without a ferromagnetic background. In confined nanostructures, both broken lattice periodicity and asymmetry in magnetic interactions at boundaries should create and stabilize magnetic skyrmions with unique ground states. ...
Magnetic configurations in a hexagonal nanostructure have been simulated using the Monte Carlo method. It has been found that a multiple-skyrmion state is stabilized in the system by a relatively strong interfacial Dzyaloshinskii–Moriya interaction. An aging effect takes place in the thermal evolution of the multiple-skyrmion state. The size and the shape of the skyrmions tend to become uniform with increasing temperature.
... Micromagnetic [69,70] analysis with J 1 and J 2 suggests that the length scale decreases as J 2 is included. Thus, if we include long-range interactions, the energy scale of the J 1based Hamiltonian will change. ...
The lattice Hamiltonian with the presence of a chiral magnetic isotropic Dzyaloshinskii-Moriya interaction (DMI) in a square and hexagonal lattice is numerically solved to give the full phase diagram consisting of skyrmions and merons in different parameter planes. The phase diagram provides the actual regions of analytically unresolved asymmetric skyrmions and merons, and it is found that these regions are substantially larger than those of symmetric skyrmions and merons. With magnetic field, a change from meron or spin spiral to skyrmion is seen. The complete phase diagram for the $C_{nv}$ symmetric system with anisotropic DMI is drawn and it is shown that this DMI helps to change the spin spiral propagation direction. Finally, the well-defined region of a thermodynamically stable antiskyrmion phase in the $C_{nv}$ symmetric system is shown.
... Centrosymmetric materials are a prominent platform for constructing skyrmion quantum processors 3 . In this class of materials, geometrical frustration renders the skyrmion helicity a quantum degree of freedom and leads to a higher density of skyrmions 167 . Here, skyrmions are considerably smaller 5 than those in non-centrosymmetric magnets. ...
Magnetic nano-skyrmions develop quantized helicity excitations, and the quantum tunneling between nano-skyrmions possessing distinct helicities is indicative of the quantum nature of these particles. Experimental methods capable of nondestructively resolving the quantum aspects of topological spin textures, their local dynamical response, and their functionality now promise practical device architectures for quantum operations. With abilities to measure, engineer, and control matter at the atomic level, nano-skyrmions present opportunities to translate ideas into solid-state technologies. Proof-of-concept devices will offer electrical control over the helicity, opening a promising new pathway toward functionalizing collective spin states for the realization of a quantum computer based on skyrmions. This Perspective aims to discuss developments and challenges in this new research avenue in quantum magnetism and quantum information.
... Most often it is the combined effect of the magnetic field and Dzyaloshinskii-Moriya interaction (DMI). [23][24][25] Other mechanisms of skyrmion stabilization include frustrated exchange, 26,27 magnetic anisotropy, [28][29][30] disorder, 31 and geometrical confinement. 32 The stability of a skyrmion to thermal fluctuations capable of kicking it out of a metastable state has been studied by several authors. ...
Contraction and expansion of skyrmions in ferromagnetic films are investigated. In centrosymmetric systems, the dynamics of a collapsing skyrmion is driven by dissipation. The collapse time has a minimum on the damping constant. In systems with broken inversion symmetry, the evolution of skyrmions toward equilibrium size is driven by the Dzyaloshinskii–Moriya interaction. Expressions describing the time dependence of the skyrmion size are derived and their implications for skyrmion-based information processing are discussed.
... In the former case, the underlying spiral structure emerges from the competition between ferromagnetic exchange and the Dzyaloshinskii-Moriya (DM) interaction 39,40 . In contrast, the spiral ordering of centrosymmetric materials arises from frustration, i.e., from the competition between different exchange or dipolar interactions 11,[41][42][43][44] . ...
We consider the problem of extracting a low-energy spin Hamiltonian from a triangular Kondo Lattice Model (KLM). The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange excludes the use of perturbation theory beyond the second order. We then introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions. The resulting spin model reproduces the phase diagram of the original KLM as a function of magnetic field and single-ion anisotropy and reveals the effective four-spin interactions that stabilize the field-induced skyrmion crystal phase. Moreover, this model enables the computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with both models reveals a good agreement for the magnon dispersion even though this information was not included in the training data set.
