Figure - available from: Nature
This content is subject to copyright. Terms and conditions apply.
![Analytical ansatz for the antiferromagnetic skyrmion lattice
a, Schematic for the moment directions in each q component of the triple-q structure at ϕ111 = −π (helical), −3π/2 (collinear) and −9π/8 (distorted helical). b, Comparison between the representative magnetic texture for one sublattice in the (111) plane obtained by the analytical ansatz (left) and Monte Carlo simulations (right) performed at T = 0.5 K and B111 = 5 T. The colour scheme indicates the spin component along the [111] direction, and the arrows show the spin component in the (111) plane.](publication/344360723/figure/fig5/AS:939157190869009@1600923931505/Analytical-ansatz-for-the-antiferromagnetic-skyrmion-lattice-a-Schematic-for-the-moment.jpg)
Analytical ansatz for the antiferromagnetic skyrmion lattice a, Schematic for the moment directions in each q component of the triple-q structure at ϕ111 = −π (helical), −3π/2 (collinear) and −9π/8 (distorted helical). b, Comparison between the representative magnetic texture for one sublattice in the (111) plane obtained by the analytical ansatz (left) and Monte Carlo simulations (right) performed at T = 0.5 K and B111 = 5 T. The colour scheme indicates the spin component along the [111] direction, and the arrows show the spin component in the (111) plane.
Source publication
Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications1–4. Skyrmions have so far been observed in a variety of magnets that exhibit nearly parallel alignment for neighbouring spins, but theoretically skyrmions with anti-parallel neighbouring spins are also possible. Such anti...
Citations
... Identifying novel SSL hosts is crucial for the realization of exotic spin textures like skyrmions [26,27,44] and subdimensional quasiparticles like fractons [45,46], and will also establish new candidate compounds to study the thermal and quantum order-by-disorder (ObD) transitions that are elusive in real materials [1,3,[47][48][49]. According to theoretical studies, SSLs can be classified by their codimension, a quantity that characterizes the dimensional difference between the spiral surface and the host system [10]. ...
A codimension-two spiral spin-liquid is a correlated paramagnetic state with one-dimensional ground state degeneracy hosted within a three-dimensional lattice. Here, via neutron scattering experiments and numerical simulations, we establish the existence of a codimension-two spiral spin-liquid in the effective honeycomb-lattice compound Cs$_3$Fe$_2$Cl$_9$ and demonstrate the selective visibility of the spiral surface through phase tuning. In the long-range ordered regime, competing spiral and spin density wave orders emerge as a function of applied magnetic field, among which a possible order-by-disorder transition is identified.
... This effect leads to a transverse motion due to the Q-dependent Magnus force [2], often resulting in undesired accumulation and annihilation of skyrmions at device edges [27,28]. A promising avenue to avoid the SkHE involves the use of antiferromagnetic (AFM) skyrmions [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. While AFM skyrmions exhibit diminished SkHE [32] and potential for fast spin dynamics [48], their insensitivity to external stimuli, such as the magnetic field, limits the manipulation and detection [49]. ...
Magnetic skyrmions are promising building blocks for future spintronic devices. However, the skyrmion Hall effect (SkHE) remains an obstacle for practical applications based on the in-line transport of skyrmions. Here, we numerically study the static properties and current-driven dynamics of synthetic ferrimagnetic skyrmions. Inspired by graded-index magnonics, we introduce a linear gradient of saturation magnetization (Ms) in the skyrmion-hosting sample, which effectively modulates the skyrmion Hall angle and suppresses the SkHE. Micromagnetic simulations reveal that ferrimagnetic skyrmions could exhibit greater susceptibility to the variation of Ms as compared to their ferromagnetic counterparts. The Thiele analysis is also applied to support the simulation results, which elucidates that the Ms gradient dynamically modifies the intrinsic normalized size of skyrmions, consequently impacting the SkHE. Our results pave the way to the graded-index skyrmionics, which offers novel insights for designing ferrimagnet-based skyrmionic devices.
... This effect leads to a transverse motion due to the Q-dependent Magnus force [2], often resulting in undesired accumulation and annihilation of skyrmions at device edges [27,28]. A promising avenue to avoid the SkHE involves the use of antiferromagnetic (AFM) skyrmions [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. While AFM skyrmions exhibit diminished SkHE [32] and potential for fast spin dynamics [48], their insensitivity to external stimuli, such as the magnetic field, limits the manipulation and detection [49]. ...
Magnetic skyrmions are promising building blocks for future spintronic devices. However, the skyrmion Hall effect (SkHE) remains an obstacle for practical applications based on the in-line transport of skyrmions. Here, we numerically study the static properties and current-driven dynamics of synthetic ferrimagnetic skyrmions. Inspired by graded-index magnonics, we introduce a linear gradient of saturation magnetization ( M s ) in the skyrmion-hosting sample, which effectively modulates the skyrmion Hall angle and suppresses the SkHE. Micromagnetic simulations reveal that ferrimagnetic skyrmions could exhibit greater susceptibility to the variation of M s as compared to their ferromagnetic counterparts. The Thiele analysis is also applied to support the simulation results, which elucidates that the M s gradient dynamically modifies the intrinsic normalized size of skyrmions, consequently impacting the SkHE. Our results pave the way to the graded-index skyrmionics, which offers novel insights for designing ferrimagnet-based skyrmionic devices.
Published by the American Physical Society 2024
... In contrast, antiferromagnetic (AFM) skyrmions offer distinct advantages due to their resistance to the skyrmion Hall effect and insensitivity to external magnetic perturbations [14][15][16][17][18][19]. These intrinsic AFM topological textures have been extensively studied in bulk systems [20,21]. Compared to bulk materials, the inherent thinness of two-dimensional (2D) materials provides enhanced integration capabilities for electronic devices [22][23][24], and thus there is considerable anticipation about AFM skyrmions in 2D magnets. ...
Antiferromagnetic (AFM) skyrmions, which are resistant to both the skyrmion Hall effect and external magnetic perturbations, are expected to be promising candidates for next-generation spintronics devices. Despite being observed in bulk materials and synthetic AFM layered systems, the existence of intrinsic AFM skyrmions within single magnetic layers, which offer potential advantages for spintronic device fabrication, has remained elusive. In this work, taking monolayer CrSi(Te,Se)$_{3}$ as a representative system, we demonstrate the emergence of intrinsic AFM skyrmions in two-dimensional Janus magnets. It is found that under moderate compressive strain, the interplay between considerable Dyzaloshinskii-Moriya interaction and the strain-induced AFM Heisenberg exchange interaction in monolayer CrSi(Te,Se)$_{3}$ would give rise to the emergence of intrinsic AFM skyrmions assembled from AFM spin spirals. Moreover, the application of an external magnetic field could trigger the emergence of AFM merons as well as a canted AFM state. Our findings propose a feasible approach for achieving intrinsic AFM skyrmions in realistic systems, which paves the way for developments in AFM topological spintronics devices.
... However, if we separately plot them for each sublattice in the right panels, we find that each sublattice hosts a skyrmion with the 90-site unit. Similar three-sublattice skyrmions were experimentally found in MnSc 2 S 4 [43,44], which are analyzed theoretically for the J 1 -J 2 -J 3 model [45] and DM model [46]. Interestingly, this skyrmion is a source of the thermal Hall effect based on SU(3) magnons characteristic of a three-sublattice structure [47]. ...
When the material phases exhibit topological quantum numbers, they host defects protected by the nontrivial topology. Magnetic skyrmions are such “quantized” objects, and although many of them are metals, they had been most likely treated in theories as purely classical spin states. Here, we show that the electrons described by the Hubbard model with strong spin-orbit couplings can exhibit various nano- or flake-size skyrmions in their ground state. Importantly, the conducting electrons forming Fermi pockets themselves carry textured magnetic moments in both real and momentum space and on top of that possess Chern numbers in their energy bands. This quantum and conducting skyrmion is related to small skyrmions observed in atomic-layered compounds. We clarify how the effective magnetic interactions and magnetic anisotropies are tied to the spin-orbit coupling, and how they influence the stability of skyrmions beyond the phenomenology.
Published by the American Physical Society 2024
... In the later work, the competition between DMI, dipolar interaction as well as RKKY interaction leads to the formation of these chiral spin textures. Further, skyrmion lattices can be stabilized by various types of other interactions and symmetries, such as multi-spin interactions [27], magnetic frustration [28,29], and bonddependent exchange anisotropy [30][31][32]. However, there are no such reports where skyrmions have been observed just by varying the NM spacer layer thickness between two FM layers having thickness in perfectly PMA regime i.e. far away from the SRT regime. ...
The interlayer exchange coupling (IEC) between two ferromagnetic (FM) layers separated by a non-magnetic (NM) spacer layer gives rise to different types of coupling with the variation of spacer layer thickness. When the NM is metallic, the IEC is attributed to the well-known Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction which shows an oscillatory decaying nature with increasing thickness. Due to this, it is possible to tune the coupling between the two FM to be either ferromagnetic or antiferromagnetic. In this work we have studied a Pt/Co/Ir/Co/Pt system where the Co thickness has been taken in the strong perpendicular magnetic anisotropy regime which is much less than the spin reorientation transition thickness. By tuning the Ir thickness to 2.0 nm, a canted state of magnetization reversal in the system is observed which gives rise to a possibility of nucleating topologically non-trivial spin textures like skyrmions. Further, with the combination of transport and magnetic force microscopy (MFM) measurements, we have confirmed the presence of skyrmions in our system. These findings may be useful for potential applications in emerging spintronic and data storage technologies using skyrmions.
... Brinker et al. [24] proposed a generalized atomistic spin model containing two-spin and four-spin chiral interactions that coupled up to four distinct magnetic sites, and also interpreted the magnetic skyrmions stabilized in an Fe monolayer on Ir(111) [25]. In addition, it has been found that the interplays between SOC and itinerant magnetism, i.e., Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, in polar magnetic conductors [26] and between SOC and dipole-dipole interactions (DDIs) in MnSc 2 S 4 [27,28] both contributed to stabilize magnetic skyrmions. Meanwhile, the significant role of magnetocrystalline anisotropy played on the formation and stability of magnetic skyrmions was increasingly recognized [29]. ...
Magnetic skyrmions emerge when the energy of ferromagnetic exchange interaction promoting parallel alignment of spins enters in competition with energies favoring non-collinear alignment of spins such as Dzyaloshinskii–Moriya interaction (DMI), long-rang dipole–dipole interaction (DDI), or higher-order exchange interactions. We perform an unbiased Monte Carlo simulation to study the DMI-based skyrmion nucleation and stabilization on the surface of magnetic nanotubular monolayer controlled by tuning constants of DDI (g) and next-nearest-neighbor antiferromagnetic exchange interaction (j’) with appropriate balance. Without g and j’, the loosely distributed skyrmions initially nucleate on the surface of nanotube approaching to the magnetic field (h) direction with increasing h in the intermediate range. Then, the skyrmion size, shape, density, distribution and crystal structure, as well as its driven field range, are tailored by g and j’. This work demonstrates the skyrmion nucleation mechanisms in three-dimensional magnetic nanostructures with curvature effect and multiple interactions, serving as a benchmark for a guide to experimentalists for preparation of samples in magnetic skyrmion states.
... Following extensive phenomenology-based predictions 37,39,43,[47][48][49][50] , FM skyrmions coupled antiferromagnetically through a spacer, so-called synthetic AFM skyrmions, were realized in multilayers 40,[51][52][53][54] . Further more complex AFM topological objects were identified in bulk materials [55][56][57] . Ab-initio simulations predicted the emergence of intrinsic AFM skyrmions in Cr films and frustrated multimeronic states in Mn films interfaced with Ir(111) surface 45,58 . ...
Antiferromagnetic (AFM) skyrmions have emerged as a highly promising avenue in the realm of spintronics, particularly for the development of advanced racetrack memory devices. A distinguishing feature of AFM skyrmions is their zero topological charge and hence anticipated zero skyrmion Hall effect (SkHE). Here, we unveil that the latter is surprisingly finite under the influence of spin-transfer torque, depending on the direction of the injected current impinging on intrinsic AFM skyrmions emerging in CrPdFe trilayer on Ir(111) surface. Hinging on first-principles combined with atomistic spin dynamics simulations, we identify origin of the SkHE and uncover that FM skyrmions in the underlying Fe layer act as effective traps for AFM skyrmions, confining them and reducing their velocity. These findings hold significant promise for spintronic applications, the design of multi-purpose skyrmion-tracks, advancing our understanding of AFM-FM skyrmion interactions and hybrid soliton dynamics in heterostructures.
... In recent years, similar magnetic structures have been reported to exist in a wide range of bulk materials. As shown in figures 1(a2)-(d), examples include skyrmion lattice order in GaV 4 S 8 [20], Gd 2 PdSi 3 [21], Gd 3 Ru 4 Al 12 [22], and GdRu 2 Si 2 [12], meron-antimeron lattices in Co 8 Zn 9 Mn 3 [13] and CeAlGe [14], monopoleantimonopole lattices in MnGe [15], or fractionalized antiferromagnetic skyrmion lattice in MnSc 2 S 4 [16]. In addition to these bulk materials, topologically nontrivial magnetic textures have also been reported in thin-film systems in which interfacial Dzyaloshinskii-Moriya interactions are important [10]. ...
... (c) Three-dimensional monopole-antimonopole in cubic MnGe [15]. (d) Fractionalized antiferromagnetic skyrmion lattice in layered MnSc 2 S 4 [16]. Table 1. ...
We advertise rare-earth intermetallics with high-symmetry crystal structures and competing interactions as a possible materials platform hosting spin structures with non-trivial topological properties. Focussing on the series of cubic $R$Cu compounds, where $R$ = Ho, Er, Tm, the bulk properties of these systems display exceptionally rich magnetic phase diagrams hosting an abundance of different phase pockets characteristic of antiferromagnetic order in the presence of delicately balanced interactions. The electrical transport properties exhibit large anomalous contributions suggestive of topologically nontrivial winding in the electronic and magnetic structures. Neutron diffraction identifies spontaneous long-range magnetic order in terms of commensurate and incommensurate variations of $(\pi\pi0)$ antiferromagnetism with the possibility for various multi-$\bm{k}$ configurations. Motivated by general trends in these materials, we discuss the possible existence of topologically nontrivial winding in real and reciprocal space in the class of $R$Cu compounds including antiferromagnetic skyrmion lattices. Putatively bringing together different limits of non-trivial topological winding in the same material, the combination of properties in $R$Cu systems promises access to advanced functionalities.
... Central to nucleating and controlling topological textures are various magneto-crystalline interactions, namely, anisotropy, exchange or spin-orbit torques. AFM systems, thus far, reported to host topological order [10][11][12][13][14] , for example, α-Fe 2 O 3 , CuMnAs and MnSc 2 S 4 , either were bulk crystals 14 or were epitaxially grown on symmetry-matched crystalline substrates through advanced fabrication 10,12,13 . This markedly restricts their utility and flexibility compared with typical FM-based topological-texture-hosting metallic heterostructures, which are polycrystalline and can be simply grown by sputter deposition 1,8 . ...
... Central to nucleating and controlling topological textures are various magneto-crystalline interactions, namely, anisotropy, exchange or spin-orbit torques. AFM systems, thus far, reported to host topological order [10][11][12][13][14] , for example, α-Fe 2 O 3 , CuMnAs and MnSc 2 S 4 , either were bulk crystals 14 or were epitaxially grown on symmetry-matched crystalline substrates through advanced fabrication 10,12,13 . This markedly restricts their utility and flexibility compared with typical FM-based topological-texture-hosting metallic heterostructures, which are polycrystalline and can be simply grown by sputter deposition 1,8 . ...
Antiferromagnets hosting real-space topological textures are promising platforms to model fundamental ultrafast phenomena and explore spintronics. However, they have only been epitaxially fabricated on specific symmetry-matched substrates, thereby preserving their intrinsic magneto-crystalline order. This curtails their integration with dissimilar supports, restricting the scope of fundamental and applied investigations. Here we circumvent this limitation by designing detachable crystalline antiferromagnetic nanomembranes of α-Fe2O3. First, we show—via transmission-based antiferromagnetic vector mapping—that flat nanomembranes host a spin-reorientation transition and rich topological phenomenology. Second, we exploit their extreme flexibility to demonstrate the reconfiguration of antiferromagnetic states across three-dimensional membrane folds resulting from flexure-induced strains. Finally, we combine these developments using a controlled manipulator to realize the strain-driven non-thermal generation of topological textures at room temperature. The integration of such free-standing antiferromagnetic layers with flat/curved nanostructures could enable spin texture designs via magnetoelastic/geometric effects in the quasi-static and dynamical regimes, opening new explorations into curvilinear antiferromagnetism and unconventional computing.
