Magnetic Solitons Research Articles

Emergent elasticity and wavelike to particle-like crossover in a magnetic chiral soliton lattice

Emergent elasticity and wavelike to particle-like crossover in a magnetic chiral soliton lattice

Real-Space Topology-Engineering of Skyrmionic Spin Textures in a van der Waals Ferromagnet Fe3GaTe2.

Realizing magnetic skyrmions in two-dimensional (2D) van der Waals (vdW) ferromagnets offers unparalleled prospects for future spintronic applications. The room-temperature ferromagnet Fe3GaTe2 provides an ideal platform for tailoring these magnetic solitons. Here, skyrmions of distinct topological charges are artificially introduced and engineered by using magnetic force microscopy (MFM). The skyrmion lattice is realized by a specific field-cooling process and can be further erased and painted via delicate manipulation of the tip stray field. The skyrmion lattice with opposite topological charges (S = ±1) can be tailored at the target regions to form topological skyrmion junctions (TSJs) with specific configurations. The delicate interplay of TSJs and spin-polarized device current were finally investigated via the in situ transport measurements, alongside the topological stability of TSJs. Our results demonstrate that Fe3GaTe2 not only serves as a potential building block for skyrmion-based spintronic devices, but also presents prospects for Fe3GaTe2-based heterostructures with the engineered topological spin textures.

Modelling the Elliptical Instability of Magnetic Skyrmions

Two recently developed methods of modelling chiral magnetic soliton elliptical instability are applied in two novel scenarios: the tilted ferromagnetic phase of chiral magnets dominated by easy-plane anisotropy and the general case of the chiral magnet with tilted applied field and arbitrary uniaxial anisotropy. In the former case, the analytical predictions are found to exactly match previous numerical results. In the latter case, the instability of isolated chiral skyrmions has not yet been studied, although interestingly, the predictions correspond to previous numerical investigation into the phase diagram.

Tilted-chiral-state-induced topological Hall effect in chiral magnetic soliton host Cr1/3TaS2

Chromium-intercalated Cr1/3TaS2 is well known for hosting a nontrivial chiral magnetic soliton lattice (CSL) with the reported highest Curie temperature (TC∼151 K) and strongest spin–orbit coupling, which has significant applications in gigahertz and high-speed spintronic devices. Herein, we thoroughly investigate the magneto-electrical transport properties of Cr1/3TaS2 single crystals. For H//ab, our magnetoresistance (MR) measurements reveal distinctive step-like behaviors, which are attributed to the formation and annihilation of chiral magnetic solitons. When under an oblique field, similar but weaker MR behaviors are observed compared to H//ab, indicating the appearance of an inclination-field-induced tilted-CSL. A topological Hall effect is observed under an oblique field, which is suggested to be induced by a nonzero topological charge density resulting from the tilted chiral states. The Cr1/3TaS2 offers an intriguing platform for studying the impact of chiral magnetic structures on magneto-electrical properties, which holds promise for both future spintronic device applications and fundamental investigation.

Three-dimensional magnetization reconstruction from electron optical phase images with physical constraints

The ability to characterize three-dimensional (3D) magnetization distributions in nanoscale magnetic materials and devices is essential to fully understand their static and dynamic magnetic properties. Phase contrast techniques in the transmission electron microscope (TEM), such as electron holography and electron ptychography, can be used to record two-dimensional (2D) projections of the in-plane magnetic induction of 3D nanoscale objects. Although the 3D magnetic induction can in principle be reconstructed from one or more tilt series of such 2D projections, conventional tomographic reconstruction algorithms do not recover the 3D magnetization within a sample directly. Here, we use simulations to describe the basis of an improved model-based algorithm for the tomographic reconstruction of a 3D magnetization distribution from one or more tilt series of electron optical phase images recorded in the TEM. The algorithm allows a wide range of physical constraints, including a priori information about the sample geometry and magnetic parameters, to be specified. It also makes use of minimization of the micromagnetic energy in the loss function. We demonstrate the reconstruction of the 3D magnetization of a localized magnetic soliton — a hopfion ring — and discuss the influence of noise, choice of magnetic constants, maximum tilt angle and number of tilt axes on the result. The algorithm can in principle be adapted for other magnetic contrast imaging techniques in the TEM, as well as for other magnetic characterization techniques, such as those based on X-rays or neutrons.

Topological Spin Textures: Basic Physics and Devices.

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, we summarize current research on promising topological spin structures in addition to skyrmions. Beyond two-dimensional structures, exploration also extends to one-dimensional magnetic solitons and three-dimensional spin textures. In addition, we introduce a diverse array of emerging magnetic materials, including antiferromagnets and two-dimensional van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, we offer a comprehensive overview of experimental and theoretical advances in the research of topological magnetism. Finally, we summarize both conventional and unconventional applications based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics. This article is protected by copyright. All rights reserved.

Kagomerization of transition metal monolayers induced by two-dimensional hexagonal boron nitride

The kagome lattice is an exciting solid state physics platform for the emergence of nontrivial quantum states driven by electronic correlations: topological effects, unconventional superconductivity, charge and spin density waves, and unusual magnetic states such as quantum spin liquids. While kagome lattices have been realized in complex multi-atomic bulk compounds, here we demonstrate from first-principles a process that we dub kagomerization, in which we fabricate a two-dimensional kagome lattice in monolayers of transition metals utilizing an hexagonal boron nitride (h-BN) overlayer. Surprisingly, h-BN induces a large rearrangement of the transition metal atoms supported on a fcc(111) heavy-metal surface. This reconstruction is found to be rather generic for this type of heterostructures and has a profound impact on the underlying magnetic properties, ultimately stabilizing various topological magnetic solitons such as skyrmions and bimerons. Our findings call for a reconsideration of h-BN as merely a passive capping layer, showing its potential for not only reconstructing the atomic structure of the underlying material, e.g. through the kagomerization of magnetic films, but also enabling electronic and magnetic phases that are highly sought for the next generation of device technologies.

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.

Spacetime magnetic hopfions from internal excitations and braiding of skyrmions

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.

Antiferromagnetic droplet soliton driven by spin current

We demonstrate that a spin current flowing through a nanocontact into a uniaxial antiferromagnet with first- and second-order anisotropy can excite a self-localized dynamic magnetic soliton, known as a spin-wave droplet in ferromagnets. The droplet nucleates at a certain threshold current with the frequency of the Néel vector precession laying below the antiferromagnetic resonance. The frequency exhibits nonlinear behavior with the increase in the applied current. At the high value of the applied torque, the soliton mode transforms, and the oscillator emits spin waves propagating in the antiferromagnetic layer.

Manipulating topological charge of nested skyrmion bags by microwave magnetic fields

Nested skyrmion bags, as magnetic solitons with arbitrary integer topological charges (Q), hold potential for applications in data encoding. A crucial issue is the local manipulation of skyrmions within nested skyrmion bags to control the total Q. In this study, we explore different possible ground states and resonant excitation spectra of nested skyrmion bags through micromagnetic simulations. More importantly, we demonstrate that the manipulation of the Q of nested skyrmion bags can be achieved by using microwave magnetic fields, i.e., the inner, middle, and outer skyrmions within the nested skyrmion bags are selectively excited by using the diverse out-of-plane excitation modes. By calculating the energy of skyrmions, we further analyze the relationship between the annihilation of skyrmions at different positions and the out-of-plane microwave magnetic fields. Our findings present a promising approach for manipulating the Q of nested skyrmion bags, potentially advancing their application in storage and logic devices.

Magnetic soliton and breather interactions for the higher-order Heisenberg ferromagnetic equation via the iterative N-fold Darboux transformation

This paper focuses on a higher-order Heisenberg ferromagnetic equation, which may describe the motion of the magnetic vector of isotropic ferromagnetism. The iterative N-fold Darboux transformation is first constructed to generate the dark and anti-dark magnetic solitons on the non-zero constant backgrounds, bright and dark breathers on the trigonometric function and non-zero constant backgrounds as well as breathers on the trigonometric function and vanishing backgrounds. We discover that the soliton structures of three different components can generate rotation with different constant seed solutions. Meanwhile, the trajectory curve and the direction of the magnetic vector are also discussed from the perspective of magnetism, we find that for constant seed solutions, the motion of the magnetic vector is limited to the hemisphere, while for trigonometric seed solutions, the motion of the magnetic vector can be distributed throughout the whole sphere. These novel phenomena may be helpful to understand the dynamics of the magnetic vector in the magnetic materials.

Magnetic droplet soliton pairs

We demonstrate magnetic droplet soliton pairs in all-perpendicular spin-torque nano-oscillators (STNOs), where one droplet resides in the STNO free layer (FL) and the other in the reference layer (RL). Typically, theoretical, numerical, and experimental droplet studies have focused on the FL, with any additional dynamics in the RL entirely ignored. Here we show that there is not only significant magnetodynamics in the RL, but the RL itself can host a droplet driven by, and coexisting with, the FL droplet. Both single droplets and pairs are observed experimentally as stepwise changes and sharp peaks in the dc and differential resistance, respectively. While the single FL droplet is highly stable, the coexistence state exhibits high-power broadband microwave noise. Furthermore, micromagnetic simulations reveal that the pair dynamics display periodic, quasi-periodic, and chaotic signatures controlled by applied field and current. The strongly interacting and closely spaced droplet pair offers a unique platform for fundamental studies of highly non-linear soliton pair dynamics.

Electric-field control of magnetic anisotropies: Applications to Kitaev spin liquids and topological spin textures

Magnetic anisotropies often originate from the spin-orbit coupling and determine magnetic ordering patterns. We develop a microscopic theory for dc electric-field controls of magnetic anisotropies in magnetic Mott insulators and discuss its applications to Kitaev materials and topological spin textures. Throughout this paper, we take a microscopic approach based on Hubbard-type lattice models, tight-binding models with onsite interactions. We derive a low-energy spin Hamiltonian from a fourth-order perturbation expansion of the Hubbard-type model. We show in the presence of a strong intra-atomic spin-orbit coupling that dc electric fields add non-Kitaev interactions such as a Dzyaloshinskii-Moriya interaction and an off-diagonal Γ′ interaction to the Kitaev-Heisenberg model and can induce a topological quantum phase transition between Majorana Chern insulating phases. We also investigate the interatomic Rashba spin-orbit coupling and its effects on topological spin textures. dc electric fields turn out to create and annihilate magnetic skyrmions, hedgehogs, and chiral solitons. We propose several methods of creating topological spin textures with external electromagnetic fields. Our theory clarifies that the strong but feasible electric field can control Kitaev spin liquids and topological spin textures. Published by the American Physical Society 2024

Unveiling stable one-dimensional magnetic solitons in magnetic bilayers

Unveiling stable one-dimensional magnetic solitons in magnetic bilayers

Manipulation of 2D and 3D Magnetic Solitons Under the Influence of DMI Gradients

Manipulation of 2D and 3D Magnetic Solitons Under the Influence of DMI Gradients

Hopfion rings in a cubic chiral magnet

Magnetic skyrmions and hopfions are topological solitons1—well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions2,3 are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions4–9 are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging10 and has only been reported in a synthetic material11. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion–hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets.

Effect of the Oersted field on the dynamics of magnetic drop solitons formed at a nanocontact

The magnon drop soliton is a non-topological structure formed at a nanocontact, and it is referred to as a dynamic soliton since it is stabilized by uniform precession of the magnetization. Because of magnetization precession there is a time dependent interaction between the magnetization and the magnetic field produced by the nanocontact current (referred to as the Oersted field). At a particular instant of precession the Oersted field forces the soliton off-center, but owing to precession this force will average to zero over one precession period. However, when the soliton orbits the nanocontact center at a period equal to the precession period, this force will become constant forcing the soliton off-center. This lowers the Oersted energy with an increase in the soliton orbital kinetic energy. A balance is attained with the soliton undergoing circular orbital motion about the nanocontact, and the orbit radius is determined by minimization of these energies. Previous low frequency approximations are used semi-analytically obtain these energies as well as the orbit radius.

Anisotropic microwave response in Cr1∕3TaS2 hosting chiral magnetic soliton

Chromium-intercalated hexagonal Cr1∕3TaS2 possesses exotic properties, such as high-temperature magnetic soliton, crossover of critical behavior, and nontrivial magnetism. In this study, we employ the electron spin resonance (ESR) technique to modulate and study the chiral magnetic soliton lattice (CSL) in Cr1∕3TaS2 using microwave at X-band. The experimental results show that Cr1∕3TaS2 has a particularly strong microwave response when H⊥c but very weak feedback when H//c, revealing an anisotropic microwave response. When H⊥c, the resonance peak at lower fields results from the surface barrier induced by the competition between Dzyaloshinsky–Moriya interaction, Zeeman energy, and exchange energy. The dominant resonance is caused by the ferromagnetic mode with the twisted region as the boundary condition, which transforms into a paramagnetic resonance above the phase transition temperature (TC). Furthermore, an unusual temperature dependence of ESR spectra is revealed. The crystalline electric field (CEF) excitation owing to large strong spin–orbit coupling results in the widening of the ESR linewidth above TC. Furthermore, an abrupt shift in the resonance field Hr2 and ESR linewidth ΔHPP2 is observed around TC, which is attributed to a sudden change in spin-exchange interactions and magnetic anisotropy around TC, as Cr1∕3TaS2 was previously observed for spin interaction transition from strong anisotropic 3D-Ising type to isotropic 3D-Heisenberg magnetic interaction below TC. This work demonstrates that the ESR can detect the CSL state and investigate materials with nontrivial magnetism.

Voltage-controlled magnetic solitons motion in an anisotropic ferromagnetic nanowire

The precise manipulation of magnetic solitons remains a challenge and is considered a crucial process in magnetic storage. In this paper, we investigate the control of velocity and spatial manipulation of magnetic solitons using the voltage-controlled magnetic anisotropy effect. A long-wave model, known as the generalized derivative nonlinear Schrödinger (GDNLS) equation, is developed to describe the dynamics of magnetic solitons in an anisotropic ferromagnetic nanowire. By constructing the Lax pair for the GDNLS equation, we obtain the exact solutions including magnetic dark solitons, anti-dark solitons, and periodic solutions. Moreover, we propose two approaches to manipulate magnetic solitons: direct voltage application and inhomogeneous insulation layer design. Numerically results show the direct modulation of soliton velocity by a constant voltage, while time-varying voltage induces periodic oscillations. Investigation of Gaussian-type defects reveals soliton being trapped beyond a critical defect depth. These results provide a theoretical basis for future applications in magnetic soliton-based memory devices.