Symposium F.NM04—Material Systems for Manipulating and Controlling Magnetic Skyrmions

We report a magnetic resonance study of the chiral multilayer Ir/Fe/Co/Pt hosting Néel skyrmions at room temperature. Employing in-plane ac fields, experiments reveal two distinct resonances of the skyrmion phase with frequencies between 6-12 GHz. Complementary micromagnetic simulations indicate that both resonances exhibit a counterclockwise rotation of the net magnetic dipole moment. Whereas the magnon probability distribution for the lower-frequency resonance is well localized to the skyrmion core, it extends over the inter-skyrmion area for the resonance with higher frequency. The properties of both modes depend sensitively on the interlayer distance due to the dipolar coupling between ferromagnetic layers. Our work reveals the tunability of the resonance response of skyrmions in magnetic architectures over a broadband frequency range, a promising avenue towards tailored microwave applications based on room temperature topological spintronics.

Magnetic skyrmions are topologically-nontrivial spin textures with particle-like properties [1]. Their size, topological stability, and mobility suggest their use in future generations of spintronic devices, the prototype of which is the skyrmion racetrack [2]. To realise a racetrack requires three basic operations: the nucleation (writing), propagation (manipulation), and detection (reading) of a skyrmion, all by electrical means. Here we show that all three are experimental feasible at room temperature in Pt/Co/Ir or Pt/CoB/Ir multilayers in which the different heavy metals above and below the magnetic layer break inversion symmetry and induce chirality by means of the Dzyaloshinskii-Moriya interaction, defining the structure of Néel skyrmion spin textures [3]. We show deterministic nucleation on nanosecond timescales using an electrical point contact on top of the multilayer [4] , current-driven propagation along a wire in which the skyrmions are channelled by defects in the multilayer [5], and their detection by means of the Hall effect that reveals an unexpectedly large contribution to the Hall signal that correlates with the topological winding number [6].

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Magnetic skyrmions are swirling topological spin textures in either non-centrosymmetric magnetic bulk compounds or thin films resulted from broken inversion symmetry. Their presence is the result of the balance among the Dzyaloshinskii–Moriya interaction, the Heisenberg exchange interaction, magnetic anisotropy, and the Zeeman energy and was first demonstrated in cryogenic temperatures. Skyrmions behave as particles, which can be created, annihilated, and manipulated and can be as small as a few nanometers by careful design of material structures. The study of skyrmions is of great interest as they may be a strong candidate for high density and energy-efficient information storage and processing. In this talk, we will briefly review the requirements for the presence and the establishment of the phase diagram of skyrmions in various thin films. Particularly we will discuss the room-temperature skyrmion phase diagram as affected by DMI, anisotropy, and the Zeeman energy. Because of the interest in applications in logics and memories, there is an increased interest in using electric means, current or voltage, to create and manipulate skyrmions in ferromagnetic and antiferromagnetic thin-film materials platforms. For room-temperature skyrmions, nonuniform current in geometric restrictions was used to create and move skyrmions. We will describe the use of magneto-transport and the Kerr effect to study and image skyrmions, followed by the discussion on the use of neutron scattering, X-ray magnetic dichroism, and others to study the interface magnetism of heterostructures and to understand their creation and annihilation by torques of different origins. The materials platforms to be discussed include ferromagnetic and antiferromagnetic (AFM) materials. The use of metallic CoFeB/MgO/heavy metal (Ta, W, etc.) was used to demonstrate and image skyrmions. Other examples include topological insulator/AFM (MnTe) heterostructures, which will be described to show the use of the induced exchange bias via interface proximity effect for controlling the topological charge number via field cooling. Structures consisting of antiferromagnetic (AFM) and ferri-magnetic materials (FRM) offer the speed advantage to THz for information propagation in the form of spin and skyrmion current. In this area, we will discuss the exchange coupling of the two sub-lattices of FRM and AFM as revealed from x-ray dichroism and neutron scattering. In particular, the use of insulator heterostructures will be discussed, which have the advantage of having no electrical charge current. The voltage control of perpendicular anisotropy will be discussed to show the creation and annihilation of skyrmions and their dynamics without the use of an applied magnetic field. Lastly, we will discuss the recent progress of 2D materials for skyrmionics and in general for spintronics as 2D materials make possible a wider choice of materials available to experiments. In addition, the 2-D van der Waals gap may offer different interaction characteristics for their presence as well as creation and manipulations under current and voltage drives. The study of skyrmions and anti-skyrmions in analogy with the creation and annihilation of particles and antiparticle may provide a condensed matter platform for studying the particle counterparts.

Supported by ARO, NSF, and DOE.

Topologically protected chiral spin textures, such as magnetic skyrmions, that exhibit quasi-particle like behavior have been envisioned to enable low-power information technologies, and consequently have engaged considerable the interest of the scientific community in recent years [1]. To this end, inversion asymmetric multilayers consisting of ferromagnetic and heavy metal layers have been explored and have been shown to host chiral domain walls and stabilize magnetic skyrmions due to interfacial Dzyaloshinskii-Moriya interactions. The controlled generation and manipulation of these spin structures is key to harnessing their potential in applications. We have shown that diverging electric charge currents can locally generate skyrmions. The diverging currents can be created by making use of geometric constrictions [2,3], and from nonmagnetic conducting point contacts [4]. Due to spin orbit torques at the interfaces, the spin textures can also be manipulated by charge currents. Magnetic skyrmions have been shown to exhibit a transverse motion relative to the current direction, i.e., the skyrmion Hall effect [5]. This effect arises due to the non-trivial topological charge of the skyrmions and is the analogue of the ordinary Hall effect for electrical charges in the presence of a magnetic field. The skyrmion Hall effect should vanish for antiferromagnetic skyrmions because of the cancelation of opposite topological charges and likewise for ferrimagnets at the compensation temperature. To explore this idea, have investigated the current driven motion in artificially ferrimagnetic multilayers consisting of Co and Gd. We have studied the temperature dependence of the motion from room temperature down to temperatures below the compensation point of around 100 K and find a dependency of the skyrmion Hall angle and domain wall speed on the applied temperature.
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Most magnetic materials show collinear magnetic ordering due to the large exchange interaction between neighbouring magnetic moments. If provided the Dzyaloshinskii-Moriya interaction (DMI) is strong enough to overcome the exchange interaction, magnetic spins tend to align in a non-collinear manner with fixed homochirality. In any structures where the broken inversion symmetry leads to sufficiently large DMI, non-trivial small cylindrical swirling spin structures, called magnetic skyrmions can be energetically stable. Magnetic skyrmions are topologically protected spin textures that have nanoscale dimensions and can be manipulated by an electric current. These properties make the structures potential information carriers in data storage, processing and transmission devices.
The room temperature stabilization of magnetic skyrmions and their current pulse-induced displacement on nano-tracks has been reported in magnetic heterostructures. While such current controlled skyrmion motion is applicable to an actual device scheme, the deterministic writng and deleting of a single isolated magnetic skyrmion is required for fully functional skyrmionic devices.
In order to utilize skyrmion for any electrical electronic devices, we have studied current driven dynamics of skyrmions and inhibition of the skyrmion Hall effect which is detrimental to application. [1~3] We have shown that the current-induced creation, motion, detection and deletion of skyrmions at room temperature can be used to store information as well as to mimic the potentiation and depression behaviours of biological synapses. In particular, the accumulation and dissipation of magnetic skyrmions in ferrimagnetic multilayers can be controlled with electrical pulses to represent the variations in the synaptic weights. [4]
In this talk, I will briefly introduce current induced dynamics of skyrmions and discuss about future application of skyrmions in terms of non-volatile memory and synapse devices for neuromorphic computing.

Magnetic skyrmions are topological spin textures with potential applications in next-generation memory and logic. Controlling the inversion symmetry breaking interfacial Dzyaloshinskii-Moriya Interaction (DMI) is the key to stabilizing skyrmions in magnetic multilayers. We investigate the DMI of compensated ferrimagnetic GdCo alloy using Density Functional Theory (DFT), and explain the impact of Tungsten (W) alloying in a Pt/GdCo/Pt_1-xW_x structure. We find that a small amount of W (~10%) is sufficient to give rise to a non-zero DMI by breaking the inversion symmetry of Pt/GdCo/Pt. We also find that the DMI increases as a function of W composition (x), but saturates at higher W composition, in agreement with experiment. We show that the vanishing of spin-orbit coupling (SOC) energy to the adjacent metal layers of the top interface and the simultaneous constancy of the bottom interface is responsible for such saturating behavior of the DMI. Additionally, we investigate Pt/GdCo/X, where X = Ta, W, Ir to demonstrate the effect of capping layer heavy metals on the DMI. Our results predict that W in the capping layer favors a higher value of the DMI than Ta and Ir. Our results open up exciting combinatorial possibilities for controlling the DMI in ferrimagnets to nucleate and manipulate ultrasmall high-speed skyrmions.

Broken magnetic symmetry is a key aspect in condensed matter physics and in particular in magnetism. It results in the appearance of chiral effects, e.g. topological Hall effect [1] and non-collinear magnetic textures including chiral domain walls and skyrmions [2,3]. These chiral structures are in the heart of novel concepts for magnonics [4], antiferromagnetic spintronics [5], spin-orbitronics [6] and oxitronics [7].
The main origin of the chiral symmetry breaking and thus for the magnetochiral effects in magnetic materials is associated to an antisymmetric exchange interaction, the intrinsic Dzaloshinskii-Moriya interaction (DMI). At present, tailoring of DMI is done rather conventionally by optimizing materials, either doping a bulk single crystal or adjusting interface properties of thin films and multilayers. A viable alternative to the conventional material screening approach can be the exploration of the interplay between geometry and topology. This interplay is of fundamental interest throughout many disciplines in condensed matter physics, including thin layers of superconductors [8] and superfluids [9], nematic liquid crystals [10], cell membranes [11], semiconductors [12]. In the emergent field of curvilinear magnetism chiral effects are associated to the geometrically broken inversion symmetries [13]. Those appear in curvilinear architectures of even conventional materials. There are numerous exciting theoretical predictions of exchange and magnetostatically-driven curvature effects, which do not rely on any specific modification of the intrinsic magnetic properties, but allow to create non-collinear magnetic textures in a controlled manner by tailoring local curvatures and shapes [14,15]. Until now the predicted chiral effects due to curvatures remained a neat theoretical abstraction.
Here, we demonstrate the very first experimental confirmation of the existence of the curvature-induced chiral interaction with exchange origin in a conventional soft ferromagnetic material [16]. It is experimentally explored the theoretical predictions, that the magnetisation reversal of flat parabolic stripes shows a two step process. At the first switching event, a domain wall pinned by the curvature induced exchange-driven DMI is expelled leading to a magnetisation state homogeneous along the parabola’s long axis. Measuring the depinning field enables to quantify the effective exchange-driven DMI interaction constant. The magnitude of the effect can be tuned by the parabola’s curvature. It is found that the strength of the exchange-induced DMI interaction for the experimentally realised geometries is remarkably strong, namely ≈ 0.4 mJ/m² , compared the surface induced DMI. The presented study legitimates the predictive power of full-scale micromagnetic simulations to design the properties of ferromagnets through their geometry, thus stabilising chiral textures.

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Magnetic skyrmions are compact spin textures that show remarkably unique, particle-like properties. They are widely regarded as promising candidates for emergent magnetic devices as they are small in size and easily maneuverable. The Dzyaloshinskii-Moriya interaction (DMI) is often critical to the generation and manipulation of skyrmions. However, there has been a fundamental lack of understanding of the microscopic origin of DMI or the mechanisms by which DMI stabilizes skyrmions in magnetic bilayers. Little has been known of the material parameters that determine the value of DMI. This knowledge is critical for rational design of skyrmion-hosting materials and further development of skyrmion technology. Here we investigate DMI in a series of magnetic bilayers using first principles methods. We present a new theoretical model that explains the microscopic origin of DMI in magnetic bilayers. We demonstrate that the value of DMI depends on two material parameters, interfacial hybridization and orbital contributions of the heavy metal. Using these parameters, we explain experimentally observed DMI trends. We also report four new materials systems predicted to have giant DMI and can be expected to outperform the best materials known so far, and new designs for magnetic multilayers. Our results provide a new understanding of DMI, discover highly promising materials and suggest pathways for the controlled generation of skyrmions.

Microscopic spin textures and their dynamics are key to understand and control the properties, behavior and functionalities of novel magnetic materials. Of particular interest are topological systems, as they hold the promise to improve speed, size and energy efficiency of future spin driven technologies. Advanced characterization tools that provide magnetic sensitivity to spin textures at high spatial resolution, ultimately at buried interfaces and in all three dimensions [1], and at high temporal resolution to capture the spin dynamics across scales, are therefore of large scientific interest.
Magnetic soft X-ray spectro-microscopies [2] provide unique characterization opportunities to study the statics and dynamics of spin textures in magnetic materials combining X-ray magnetic circular dichroism (X-MCD) as element specific, quantifiable magnetic contrast mechanism with spatial and temporal resolutions down to fundamental magnetic length, time, and energy scales.
Current developments of x-ray sources aim to increase dramatically the coherence of x-rays opening the path to new approaches and characterization tools, such as ptychography [3] or x-ray photo-correlation spectroscopy (XPCS) [4] that allow unprecedented studies of nanoscale heterogeneity, complexity, and fluctuations.
I will review recent results studying the static properties and dynamic behavior of magnetic skyrmion [5,6] textures with potential application to novel magnetic logic and storage devices, as well as first results from target skyrmions that are seen as precursors for hopfions [7]. An unexpected and drastic change of the correlation times in nanoscale spin fluctuations near phase boundaries, i.e., in the skyrmion phase, and near the boundary with the stripe phase of a multilayered Fe/Gd system [4] was observed in an XPCS study at LCLS with a novel 2-pulse scheme.

Acknowledgement
This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division Contract No. DE-AC02-05-CH1123 in the Non-Equilibrium Magnetic Materials Program (MSMAG).

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Chiral skyrmions [1] are particle-like topological solitons with complex non-coplanar spin structures stabilized in noncentrosymmetric magnetic materials by specific Dzyaloshinskii-Moriya interaction (DMI). Being surrounded by the homogeneously magnetized state, skyrmions represent ensembles of weakly repulsive axisymmetric particles [2] oriented along the field. With the onset of the conical phase, skyrmions become non-axisymmetric and due to the attractive interaction tend to produce multi-skyrmion bound states - clusters [3]. Both types of skyrmions were observed experimentally in PdFe/Ir(111) bilayers with induced DMI [2] and in thin (≈70 nm) single-crystal samples of Cu₂OSeO₃ [3]. Moreover, the attracting skyrmions were predicted to underlie precursor phenomena (e.g., A-phase in B20 magnets) and to have prospects of being used in spintronics as an effective alternative to the common axisymmetric skyrmions [4]. Prototypes of spintronic devices based on the crossover of skyrmion-skyrmion interaction and low spin currents required to set skyrmions into motion were suggested in Ref. [4]. Note that the cross-section of isolated skyrmions within the conical phase has the typical structure of bimerons introduced in Ref. [5] and shown to develop an anisotropic character of skyrmion-skyrmion interaction in lacunar spinels GaV₄Se₈ with the C_3v symmetry and easy-plane uniaxial anisotropy.
Skyrmions may also become oblique with respect to the field. In particular, in Cu₂OSeO₃ due to the competing exchange and cubic anisotropies [6], the conical phase tilts away from the field direction and thus underlies the deviation of skyrmions. As a result, attracting oblique skyrmions may potentially form extended networks in which their axes are not parallel to each other as in previously reported skyrmion clusters. Skyrmion networks with mutually orthogonal isolated skyrmions [7] were directly visualized in thin layers of chiral liquid crystals. We used chiral nematics as a model system for probing the skyrmion behavior due to the similarity of phenomenological models for both condensed-matter systems, chiral magnets and liquid crystals.
Thus, in the present abstract by experimental and theoretical means, I will introduce different classes of oblique non-axisymmetric skyrmions and elucidate the principles of their meshing into a large diversity of extended three-dimensional skyrmionic networks in chiral magnets and liquid crystals.
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In this talk, various three-dimensional (3D) topological spin textures in magnets without inversion symmetry will be introduced. The first part of the talk features the recent observation of target skyrmions in chiral magnet nanodisks through theory-experiment collaborations. Two types of zero-field target skyrmions are confirmed, and Bloch points are identified during topological transition between different types of target skyrmions. The spectrum of collective spin wave modes in target skyrmions also reveal the 3D nature of spin excitations.

Second part of the talk introduces a very recent work on hopfions in chiral magnetic nanodisk. This is one of the first experimentally feasible prediction on magnetic hopfions. The hopfion in this setup is confirmed by analyzing the linking between any two equal-spin loops and calculating the Hopf invariant. Another topological configuration, the pairing between monopole and anti-monopole, is also identified in the same system. Transition from this state to hopfion, being identical to sphere-torus topological deformation, can be achieved by an external magnetic field. Dynamics of hopfions will also be discussed.

This work is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. de-sc0020221.

Magnetic non-collinear spin textures that have chiral structures are of great current interest. The same type of Dzyaloshinskii-Moriya (DMI) vector exchange interactions that stabilize chiral Néel domain walls in magnetic multilayers ^1-3 results in the formation of topological spin textures in bulk compounds. We recently discovered magnetic antiskyrmions in a tetragonal inverse Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn using Lorentz transmission electron microscopy (LTEM)⁴. Unlike skyrmions in B20 compounds, that have been extensively studied, the size of the anti-skyrmion can be tuned by varying the thickness of the host material allowing for sizes varying from nanometer to microns in the same material⁵. This is due to long range magneto-dipole interactions that are important in this compound that has a complex DMI interaction with a symmetry that follows the D_2d symmetry of its crystalline structure. The same symmetry ensures that anti-skyrmions are robust to temperature and magnetic field⁶. The magnetic dipole-dipole interactions also allow for the formation of metastable “elliptical skyrmions” in this same material⁷. These have Bloch-like boundaries that we can directly observe using LTEM. Finally, we discuss our recent discovery of novel Néel like skyrmions in a metallic compound that exist almost to room temperature and that are also tunable in size⁸. Chiral spin textures in ferro-, ferri- and anti-ferrimagnetic materials and thin film heterostructures are of fundamental interest with potential for spintronic applications especially Racetrack Memory.
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Structures and dynamics of spin textures in magnets are the subject of extensive studies, which is a crucial issue also for applications. The structures and their motion in the bulk are rather well understood, but the influence of the boundaries is less studied. In this talk I would focus on the effects of boundaries such as surfaces and edges as revealed by theoretical analysis. It includes (i) the skyrmion string in a thin film with associated topological defects, and (ii) the helix with boundaries.
In the former case with an out-of-plane magnetic field, a step edge on the thin film substantially affects the motion of a skyrmion string, leading to its splitting and annihilation. These processes are understood by introducing two types of topological indices, i.e., the bulk monopole number and the surface skyrmion number. For an in-plane magnetic field, on the other hand, several kinds of topological defects are found to appear, which is consistent with the experimental observations.
Recently, the helix structure was proposed to show inductance under an ac current. Therefore, the nonlinear dynamics of the helix are an important issue, which we have investigated both by numerical simulations and analytical calculations. It turns out that the role of the boundary is crucial to determine the direction of the wavevector of the helix: There is a 90° difference between periodic boundary condition and open boundary condition, revealing the vital role of the boundary.

The lamellar morphology of chiral spin textures is analogous to liquid crystals and biological systems. Analogous to cholesteric liquid crystals, chiral magnets possess a periodic layered structure and form a wide variety different types of non-trivial topological defects. Using magnetic force microscopy (MFM) on the near-room temperature helimagnet FeGe we resolve 1D and 2D topological defects, including disclinations and dislocations with nonzero topological winding number, as well as three fundamental types of helimagnetic domain walls. Interestingly, in addition to their non-trivial structure, all topological defects in FeGe exhibit an unusual magnetic response in MFM, which is not observed in regions with perfect lamellar-like order. This magnetic signature is reminiscent of the so-called “lines of flare” in cholesteric liquid crystals, suggesting local variations in magnetic susceptibility. We investigate the origin of the magnetic signature of the topological defects and discuss the possibilities to utilize the local MFM response as read-out signal in spintronics devices.

In the quest for post-CMOS technologies, ferromagnetic domain walls and topological skyrmions have shown great promise as elements in spintronic racetrack devices. Recently, attention has been shifted to antiferromagnetic (AFM) analogues, as they are anticipated to demonstrate relativistic dynamics, fast motion without transverse deflection and size scaling. Despite this, experimental implementations in natural antiferromagnetic systems at room temperature are yet to emerge. Here, we demonstrate a family of topological antiferromagnetic spin-textures in α-Fe₂O₃ – an earth-abundant oxide insulator – capped with a Pt over-layer. By varying temperature and doping, we stabilize exotic AFM merons-antimerons (half-skyrmions), and AFM bimerons, which can be erased by magnetic fields and re-generated by temperature cycling. Controlled by current-based spin-torques from the heavy-metal over-layer, these AFM textures could emerge as prime candidates for low-energy antiferromagnetic spintronics.

Magnetic skyrmion, i.e., a topologically stable swirling spin configuration, has recently attracted attention as a particle-like object potentially suitable for the design of high-density information bits. Previous observations of skyrmions have mostly focused on noncentrosymmetric systems, where Dzyaloshinskii-Moriya interaction plays an important role[1,2]. On the other hand, recent theoretical studies suggest that skyrmions can be stabilized even in centrosymmetric systems by considering different microscopic mechanisms. For example, geometrical frustration of short-range exchange interactions on triangular lattice is predicted to stabilize a hexagonal lattice of skyrmions[3]. Another potential mechanism is the RKKY and four-spin interactions mediated by itinerant electrons, which is expected to favor a skyrmion lattice state for highly-symmetric (such as hexagonal or tetragonal) crystal lattice systems[4].
In this talk, I overview the recent experimental discovery of skyrmions in centrosymmetric systems[5-7]. In particular, we focus on the case of centrosymmetric tetragonal magnet GdRu₂Si₂, where the square lattice of skyrmions with extremely small diameter (1.9nm, i.e. the smallest value ever reported for single-component bulk materials) has been observed[7]. Our results demonstrate that skyrmions can be stabilized even without geometrically frustrated lattice nor inversion symmetry breaking, and suggest that rare-earth intermetallics with highly-symmetric crystal lattice may ubiquitously host nanometric skyrmions of exotic origins.

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In our information-everywhere society IT is a major player for energy consumption. Novel spintronic devices can play a role in the quest for GreenIT if they are stable and can transport and manipulate spin with low power. Devices have been proposed, where switching by energy-efficient approaches, such as spin-polarized currents is used [1],
Firstly, to obtain ultimate stability of states, topological spin structures that emerge due to the Dzyaloshinskii-Moriya interaction (DMI) at structurally asymmetric interfaces, such as chiral domain walls and skyrmions with enhanced topological protection can be used [2-5]. We have investigated in detail their dynamics and find that it is governed by the topology of their spin structures [2]. By designing the materials, we can even obtain a skyrmion lattice phase as the ground state [3].
Secondly, for ultimately efficient spin manipulation, we use spin-orbit torques, that can transfer more than 1hbar per electron by transferring not only spin but also orbital angular momentum. We combine ultimately stable skyrmions with spin orbit torques into a skyrmion racetrack device [3-5], where the real time imaging of the trajectories allows us to quantify the novel skyrmion Hall effect [5,6].
Beyond conventional memory, we furthermore use spin-orbit torque induced skyrmion dynamics for non-conventional stochastic computing applications, where we have developed a skyrmion reshuffler device [6]. Here we use thermal skyrmion motion to implement a key component for stochastic computing [6]. Such thermal skyrmion diffusion can also be controlled by symmetry breaking [7] and this is useful for token – based Brownian computing.
Finally the thermal dynamics of skyrmion quasi-particles lends itself to exploiting this system for the study of phases and phase transitions in 2D. We have studied the transition of skyrmion arrangements from the liquid phase across the hexatic phase unique to 2D systems into the solid phase [8]. These transitions occur in a wide range of skyrmions systems [8,9], thus showing that skyrmions have evolved from an object of study themselves and are now being understood controlled sufficiently well for use as model systems to study exciting statistical physics in 2D.

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Skyrmions are novel topologically stable spin vortices that show promise for next-generation magnetic storage due to their nanoscale domains to enable high information storage density and their low threshold for current-driven motion to enable ultralow energy consumption. One-dimensional (1D) nanowires are ideal hosts for skyrmions since they not only serve as a natural platform for magnetic racetrack memory devices but also can stabilize skyrmions. We have developed synthetic methods for nanowires (and nanoplates) of non-centrosymmetic cubic B20 monosilicides (MnSi, FeSi, CoSi) and monogermanides (FeGe) and their alloys (such as Fe_xCo_1-xSi and Fe_1-xCo_xGe), many of which display exotic helimagnetic and skyrmion magnetic phases with domain sizes from 10 to 230 nm. Collaborating with several groups, we have used Lorentz TEM, off-axis electron holography (EH), magnetotransport measurements to confirm that magnetic skyrmion phases are stable over a larger magnetic field-temperature range in these nanostructures compared to bulk crystals and thin films. Magnetoresistance (MR) measurements revealed the critical magnetic fields for the transitions between different magnetic spin structures at different temperatures. Topological Hall effect (THE) measurements of MnSi nanowires and Fe_1-xCo_xGe (x<0.1) nanoplates further confirmed the extended skyrmion stability, for example, in FeGe nanowires and Fe_1-xCo_xGe (x<0.1) nanoplates with skyrmions stabile up to about 280 K. We have further demonstrated the current-driven motion of skyrmions in this extended skyrmion phase region in MnSi nanowires. Correlating real space magnetic imaging with the magnetotransport measurements reveals previously unexplored transformation of skyrmion strings and other magnetic ordering due to nanoscale confinements. These results open up the exploration of nanowires as an attractive platform for investigating skyrmion physics in 1D systems and exploiting skyrmions in magnetic storage concepts.

Skyrmions are particle-like topological spin textures stabilized by the Dzyaloshinskii-Moriya interaction, which have recently stimulated great interests in spintronics community. The dynamics of which have been frequently studied via using magnetic fields and current-induced spin torques. On the other hand, a comprehensive understanding of thermal effects, including random thermal fluctuation and directional thermal currents, on the dynamics of skyrmions are not fully established yet.

In this talk, I will first discuss our recent experimental observation of the thermal fluctuation-induced random walk of a single isolated Néel-type magnetic skyrmion in an interfacially asymmetric Ta/CoFeB/TaO_x multilayer. In particular, an intriguing topology dependent Brownian gyromotion behavior of skyrmions has been identified. The onset of Brownian gyromotion of a single skyrmion induced by the thermal effects, including a nonlinear temperature-dependent diffusion coefficient and topology-dependent gyromotion are further formulated based on the stochastic Thiele equation.

Subsequently, I will discuss the thermal generation, manipulation and detection of nanoscale skyrmions, which were made in microstructured devices made of different multilayers – [Ta/CoFeB/MgO]₁₅, [Pt/CoFeB/MgO/Ta]₁₅ and [Pt/Co/Ta]₁₅ integrated with on-chip heaters, by using a full-field soft X-ray microscopy. In particular, the thermal generation of densely packed skyrmions at the device edge, together with the unidirectional diffusion of skyrmions from the hot region towards the cold region were experimentally observed. These thermally generated skyrmions can be further electrically detected by measuring the accompanied anomalous Nernst voltages. These results could open another exciting avenue for enabling skyrmionics, and promote interdisciplinary studies among spin caloritronics, magnonics and skyrmionics.
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Skyrmions represent a class of chiral magnetic textures with unique properties relevant for spintronic and spin-orbitronic applications [1]. Geometrical curvature can be used as an efficient mean to tailor chiral and anisotropic responses of thin ferromagnetic shells [2-4]. This was recently confirmed by quantifying the strength of the Dzyaloshinskii-Moriya interaction (DMI) in curved nanostripes [5]. Furthermore, there are numerous predictions of the stabilization of curvature-driven of small-radius skyrmions in spherical shells [6] and an appearance of skyrmion lattices as the ground state in intrinsically chiral curvilinear thin films [7].

Here, we demonstrate a new pathway of stabilizing Neel skyrmion and skyrmionium states relying on the gradient of curvature using a magnetic thin film hosting a circular nanoindentation [8]. These skyrmion states can be formed in a material even without an intrinsic DMI. We propose a physical picture of this effect, which is related to the pinning of a chiral magnetic domain wall at the bend of a nanoindentation. Geometry of the film is described by two principal curvatures k1(r), describing film geometry in radial direction, and k2(r) inversely proportional to the distance from origin. In this respect, the spatial inhomogeneity of the curvature-induced DMI governing by k1(r) is responsible for the stabilization of the skyrmion state. The lateral dimensions of the stabilized chiral magnetic textures are varied in a broad range by engineering the size of the nanoindentation. We describe the stability condition of skyrmion states. Furthermore, on the fundamental side, we put forth a general analytical framework allowing us to map a complex problem of the description of a magnetic texture at a surface of revolution to a standard planar problem with modified constants of DMI and magnetic anisotropy. In this respect, our model predicts a new mechanism of pinning of magnetic domain walls in planar ferromagnetic films with intrinsic DMI on inhomogeneities of the DMI.


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Magnetic skyrmions are topological spin textures that have shown promise due to their potential applications in high density and energy efficient memory nanodevices. Chiral helimagnets with the non-centrosymmetric cubic B20 crystal structure host Bloch-type skyrmions due to the antisymmetric spin exchange interaction known as the Dzyaloshinskii-Moriya interaction (DMI). Although magnetic skyrmions are depicted as two-dimensional spin texture in bulk crystals, in reality, they possess a three-dimensional structure of skyrmions that looks like elongated strings extending throughout the thickness of the sample. In geometrically confined nanostructures, such as FeGe nanowires or nanoplates, these skyrmion strings (SkS) are stabilized over large range of temperature and magnetic field. We have developed “bottom-up” chemical vapor deposition (CVD) synthetic techniques to synthesize single-crystal FeGe nanowires and Fe_1-xCo_xGe (x<0.1) nanoplates. We have observed increased sensitivity of magnetotransport measurements towards magnetic phase transitions in FeGe nanostructures when the applied magnetic field is parallel to the current, which could be mapped to the transformations of conical and helimagnetic spin textures to/from SkS. We further implemented Lorentz TEM imaging technique on nanostructures with applied magnetic field perpendicular to the observation direction to visualize the topological transformations of SkS to helical/conical spin states in real space. These Lorentz TEM imaging in correlation with the magnetotransport measurements reveal previously unexplored transformation of skyrmion strings due to nanoscale confinements.

The formation of magnetic skyrmions is intrinsically controlled by the coupling between magnetic interactions and the underlying crystal structure, meaning that skyrmion phase stability is particularly sensitive to chemical variations, structural transitions and mechanical deformation. The GaM₄X₈ (M=V/Mo, X=S/Se) lacunar spinels are a versatile class of model materials for studying these couplings as they exhibit a variety of skyrmionic phase diagrams across several structures and chemistries. First, we use electronic-structure calculations and generalized cluster expansions to derive a universal magnetic phase diagram for materials in this space, and argue that reported variations in skyrmion stability are quantitatively explained by structurally- and chemically-induced changes to magnetocrystalline anisotropy[1]. In particular, skyrmion stability across all temperatures below T_c reported in some of these materials is a direct consequence of minimal uniaxial anisotropy. Second, we combine experimental and first-principles computational analysis to demonstrate that subtle variations in the structural evolution of GaMo₄Se₈ lead to dramatic changes in magnetic behavior, switching from skyrmion host to ferromagnet[2] and corresponding to a giant effective magnetostructural coupling. Our results reveal specific materials design strategies for engineering robust skyrmion-host materials, and controlling skyrmion behavior through mechanical means.

[1] Kitchaev, D. A., Schueller, E. C., and Van der Ven, A. Physical Review B, 101(5), 054409. (2020).
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Magnetic skyrmions are swirling topological spin textures in either non-centrosymmetric magnetic bulk compounds or thin films resulted from broken inversion symmetry. Their presence is the result of the balance among the Dzyaloshinskii–Moriya interaction, the Heisenberg exchange interaction, magnetic anisotropy, and the Zeeman energy and was first demonstrated in cryogenic temperatures. Skyrmions behave as particles, which can be created, annihilated, and manipulated and can be as small as a few nanometers by careful design of material structures. The study of skyrmions is of great interest as they may be a strong candidate for high density and energy-efficient information storage and processing. In this talk, we will briefly review the requirements for the presence and the establishment of the phase diagram of skyrmions in various thin films. Particularly we will discuss the room-temperature skyrmion phase diagram as affected by DMI, anisotropy, and the Zeeman energy. Because of the interest in applications in logics and memories, there is an increased interest in using electric means, current or voltage, to create and manipulate skyrmions in ferromagnetic and antiferromagnetic thin-film materials platforms. For room-temperature skyrmions, nonuniform current in geometric restrictions was used to create and move skyrmions. We will describe the use of magneto-transport and the Kerr effect to study and image skyrmions, followed by the discussion on the use of neutron scattering, X-ray magnetic dichroism, and others to study the interface magnetism of heterostructures and to understand their creation and annihilation by torques of different origins. The materials platforms to be discussed include ferromagnetic and antiferromagnetic (AFM) materials. The use of metallic CoFeB/MgO/heavy metal (Ta, W, etc.) was used to demonstrate and image skyrmions. Other examples include topological insulator/AFM (MnTe) heterostructures, which will be described to show the use of the induced exchange bias via interface proximity effect for controlling the topological charge number via field cooling. Structures consisting of antiferromagnetic (AFM) and ferri-magnetic materials (FRM) offer the speed advantage to THz for information propagation in the form of spin and skyrmion current. In this area, we will discuss the exchange coupling of the two sub-lattices of FRM and AFM as revealed from x-ray dichroism and neutron scattering. In particular, the use of insulator heterostructures will be discussed, which have the advantage of having no electrical charge current. The voltage control of perpendicular anisotropy will be discussed to show the creation and annihilation of skyrmions and their dynamics without the use of an applied magnetic field. Lastly, we will discuss the recent progress of 2D materials for skyrmionics and in general for spintronics as 2D materials make possible a wider choice of materials available to experiments. In addition, the 2-D van der Waals gap may offer different interaction characteristics for their presence as well as creation and manipulations under current and voltage drives. The study of skyrmions and anti-skyrmions in analogy with the creation and annihilation of particles and antiparticle may provide a condensed matter platform for studying the particle counterparts.

Supported by ARO, NSF, and DOE.

We report a magnetic resonance study of the chiral multilayer Ir/Fe/Co/Pt hosting Néel skyrmions at room temperature. Employing in-plane ac fields, experiments reveal two distinct resonances of the skyrmion phase with frequencies between 6-12 GHz. Complementary micromagnetic simulations indicate that both resonances exhibit a counterclockwise rotation of the net magnetic dipole moment. Whereas the magnon probability distribution for the lower-frequency resonance is well localized to the skyrmion core, it extends over the inter-skyrmion area for the resonance with higher frequency. The properties of both modes depend sensitively on the interlayer distance due to the dipolar coupling between ferromagnetic layers. Our work reveals the tunability of the resonance response of skyrmions in magnetic architectures over a broadband frequency range, a promising avenue towards tailored microwave applications based on room temperature topological spintronics.

Structures and dynamics of spin textures in magnets are the subject of extensive studies, which is a crucial issue also for applications. The structures and their motion in the bulk are rather well understood, but the influence of the boundaries is less studied. In this talk I would focus on the effects of boundaries such as surfaces and edges as revealed by theoretical analysis. It includes (i) the skyrmion string in a thin film with associated topological defects, and (ii) the helix with boundaries.
In the former case with an out-of-plane magnetic field, a step edge on the thin film substantially affects the motion of a skyrmion string, leading to its splitting and annihilation. These processes are understood by introducing two types of topological indices, i.e., the bulk monopole number and the surface skyrmion number. For an in-plane magnetic field, on the other hand, several kinds of topological defects are found to appear, which is consistent with the experimental observations.
Recently, the helix structure was proposed to show inductance under an ac current. Therefore, the nonlinear dynamics of the helix are an important issue, which we have investigated both by numerical simulations and analytical calculations. It turns out that the role of the boundary is crucial to determine the direction of the wavevector of the helix: There is a 90° difference between periodic boundary condition and open boundary condition, revealing the vital role of the boundary.

Magnetic non-collinear spin textures that have chiral structures are of great current interest. The same type of Dzyaloshinskii-Moriya (DMI) vector exchange interactions that stabilize chiral Néel domain walls in magnetic multilayers ^1-3 results in the formation of topological spin textures in bulk compounds. We recently discovered magnetic antiskyrmions in a tetragonal inverse Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn using Lorentz transmission electron microscopy (LTEM)⁴. Unlike skyrmions in B20 compounds, that have been extensively studied, the size of the anti-skyrmion can be tuned by varying the thickness of the host material allowing for sizes varying from nanometer to microns in the same material⁵. This is due to long range magneto-dipole interactions that are important in this compound that has a complex DMI interaction with a symmetry that follows the D_2d symmetry of its crystalline structure. The same symmetry ensures that anti-skyrmions are robust to temperature and magnetic field⁶. The magnetic dipole-dipole interactions also allow for the formation of metastable “elliptical skyrmions” in this same material⁷. These have Bloch-like boundaries that we can directly observe using LTEM. Finally, we discuss our recent discovery of novel Néel like skyrmions in a metallic compound that exist almost to room temperature and that are also tunable in size⁸. Chiral spin textures in ferro-, ferri- and anti-ferrimagnetic materials and thin film heterostructures are of fundamental interest with potential for spintronic applications especially Racetrack Memory.
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Magnetic skyrmions are topologically-nontrivial spin textures with particle-like properties [1]. Their size, topological stability, and mobility suggest their use in future generations of spintronic devices, the prototype of which is the skyrmion racetrack [2]. To realise a racetrack requires three basic operations: the nucleation (writing), propagation (manipulation), and detection (reading) of a skyrmion, all by electrical means. Here we show that all three are experimental feasible at room temperature in Pt/Co/Ir or Pt/CoB/Ir multilayers in which the different heavy metals above and below the magnetic layer break inversion symmetry and induce chirality by means of the Dzyaloshinskii-Moriya interaction, defining the structure of Néel skyrmion spin textures [3]. We show deterministic nucleation on nanosecond timescales using an electrical point contact on top of the multilayer [4] , current-driven propagation along a wire in which the skyrmions are channelled by defects in the multilayer [5], and their detection by means of the Hall effect that reveals an unexpectedly large contribution to the Hall signal that correlates with the topological winding number [6].

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In this talk, various three-dimensional (3D) topological spin textures in magnets without inversion symmetry will be introduced. The first part of the talk features the recent observation of target skyrmions in chiral magnet nanodisks through theory-experiment collaborations. Two types of zero-field target skyrmions are confirmed, and Bloch points are identified during topological transition between different types of target skyrmions. The spectrum of collective spin wave modes in target skyrmions also reveal the 3D nature of spin excitations.

Second part of the talk introduces a very recent work on hopfions in chiral magnetic nanodisk. This is one of the first experimentally feasible prediction on magnetic hopfions. The hopfion in this setup is confirmed by analyzing the linking between any two equal-spin loops and calculating the Hopf invariant. Another topological configuration, the pairing between monopole and anti-monopole, is also identified in the same system. Transition from this state to hopfion, being identical to sphere-torus topological deformation, can be achieved by an external magnetic field. Dynamics of hopfions will also be discussed.

This work is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. de-sc0020221.

In our information-everywhere society IT is a major player for energy consumption. Novel spintronic devices can play a role in the quest for GreenIT if they are stable and can transport and manipulate spin with low power. Devices have been proposed, where switching by energy-efficient approaches, such as spin-polarized currents is used [1],
Firstly, to obtain ultimate stability of states, topological spin structures that emerge due to the Dzyaloshinskii-Moriya interaction (DMI) at structurally asymmetric interfaces, such as chiral domain walls and skyrmions with enhanced topological protection can be used [2-5]. We have investigated in detail their dynamics and find that it is governed by the topology of their spin structures [2]. By designing the materials, we can even obtain a skyrmion lattice phase as the ground state [3].
Secondly, for ultimately efficient spin manipulation, we use spin-orbit torques, that can transfer more than 1hbar per electron by transferring not only spin but also orbital angular momentum. We combine ultimately stable skyrmions with spin orbit torques into a skyrmion racetrack device [3-5], where the real time imaging of the trajectories allows us to quantify the novel skyrmion Hall effect [5,6].
Beyond conventional memory, we furthermore use spin-orbit torque induced skyrmion dynamics for non-conventional stochastic computing applications, where we have developed a skyrmion reshuffler device [6]. Here we use thermal skyrmion motion to implement a key component for stochastic computing [6]. Such thermal skyrmion diffusion can also be controlled by symmetry breaking [7] and this is useful for token – based Brownian computing.
Finally the thermal dynamics of skyrmion quasi-particles lends itself to exploiting this system for the study of phases and phase transitions in 2D. We have studied the transition of skyrmion arrangements from the liquid phase across the hexatic phase unique to 2D systems into the solid phase [8]. These transitions occur in a wide range of skyrmions systems [8,9], thus showing that skyrmions have evolved from an object of study themselves and are now being understood controlled sufficiently well for use as model systems to study exciting statistical physics in 2D.

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