UK Skyrmion Project

Skyrmions are excitations of matter which hold promise for technological deployment as highly efficient memory elements. We wish to increase our understanding of these mysterious particles and engineer them towards application.

Skyrmions

The skyrmion is a topological defect much like the magnetic domain wall and the superconducting vortex. If skyrmions can be made energetically stable they should occur within many systems exhibiting broken symmetry and show a characteristic set of excitations.

The UK Skyrmion Project (UKSP)

In July 2016 the EPSRC funded a five year Programme Grant - Skyrmionics: From Magnetic Excitations to Functioning Low-Energy Devices (EP/N032128/1). The project involving 5 UK universities as well as a number of national and international partners, set out to understand the physics of skyrmions and develop skyrmionic materials towards the point of deployment in device applications. The project was extended due to the COVID 19 pandemic and formally ended in January 2023. The following pages outline the work carried out under the three Research Challenges set by the project team, introduce the team members, and list the publications that resulted from this work. If you have any questions about this project, please do not hesitate to contact the Research Challenge team leaders.

Meet the Team

In order to better understand the science behind skyrmions we have built a multidisciplinary team with a variety of expertise, based at the Universities of Cambridge, Durham, Oxford, Southampton and Warwick.

The project also involved a number of national and international partners based at other academic institutions and central facilities, as well as industrial organisations.

A full list of team members can be found on the Project Team page.

Publications

Details of the papers published as a result of work carried out by the UK Skyrmion Project team in Research Challenges 1, 2 and 3, including a link to each paper in the journal can be found on the Publications section of these web pages.

Some of the early papers are the result of pilot studies carried out my members of the UKSP team before the project was funded by the EPSRCLink opens in a new window.

Research Challenge 1 - Skyrmion materials

Skyrmion materials - Team leader Professor Geetha Balakrishnan

Research Challenge 1 concerns the synthesis and characterization of skyrmionic materials. Polycrystalline and single-crystals of skyrmion materials are produced using a range of techniques.

In the study of skyrmion lattices, one class of materials has occupied a prominent place in the literature: crystals that adopt the P213 space group (or B20 phase). The first systems identified were a group of transition metal compounds, all of which lack space-inversion symmetry and host the Dzyaloshinskii-Moriya (DM) interaction. Examples of this class are FeGe/Si, Fe_1-xCo_xSi and MnSi. An interesting example of the B20 type materials that is not metallic is the magneto-electric Cu₂OSeO₃, also exhibiting helimagnetic order. It has a much more complex unit cell, with the Cu building blocks of which offer opportunities to tune the structure-property relationship observed in the variety of B20 structures.

In our programme of materials preparation we have grown examples of B20 materials. In addition to the B20's, there are other related structures such as the β-Mn types that may host exotic magnetic objects and allow the study of skyrmion lattices and related phenomena. The search for new materials that exhibit skyrmion lattices has been a significant part of our materials research in the programme. We have investigated compounds that exhibit chiral/helical magnetic ordering or alternatively, a ferromagnetic phase that can be switched to a helimagnetic phase.

Polycrystalline materials synthesis and single-crystal growth

Much of the synthesis of polycrystalline samples and single-crystals of skyrmion hosting materials is carried out in the Physics Department at the University of Warwick, whose Superconductivity and Magnetism Group has excellent facilities for research into skyrmionic materials. Warwick is well-known for the growth of high-quality single-crystals of oxides, intermetallics and related materials, with over 50 national and international partners engaged with this work. It is equipped with three optical mirror furnaces (including one with Xe arc lamps which uniquely allows us to reach temperatures of up to 2800 °C), a tetra-arc furnace, as well as facilities for crystal growth by the Bridgman method, the flux method, and chemical vapour transport.

Polycrystalline materials

Polycrystalline samples of new and interesting materials are prepared using a suite of box and annealing furnaces.

Flux technique

Suitable flux materials for the materials under study are chosen from an analysis of the phase diagrams.

Optical mirror furnaces

We employ either the Floating Zone (FZ) or Solvent Floating Zone (TSFZ) techniques to grow single crystals. The different optical furnaces provide a range of preparation conditions allowing us to vary, for example, the temperature definition in the molten zone and the growth rates. A wide variety of systems, which have both congruent and incongruent melting points can be prepared using these methods. Different growth atmospheres and pressures can be used. Materials that have been prepared include oxides as well as intermetallic materials.

A 2-mirror optical furnace used for single crystal growth at Warwick.

Bridgman and vapour transport methods

For some materials, the Bridgman or vapour transport growth techniques are more suitable. In the Bridgman method the material is contained in a crucible, e.g. a sealed quartz ampoule or a boron nitride crucible, and cooled from the molten state through a temperature gradient.

For crystals that cannot be obtained from molten material, the chemical vapour transport (CVT) technique can be used. This is the most popular technique to obtain several skyrmion materials.

Here, the precursor material is mixed with a transporting agent (such as iodine or chlorine) and placed in an evacuated sealed quartz tube. A furnace with a hot zone at temperature T₂ heats a precursor, that is then transported to a colder zone T₁ where it is deposited as crystals. These growths typically last for several weeks for each growth, and the growth periods and conditions have to be optimized for each material.

CVT grown single crystals of Cu₂OSeO₃

Single crystals of several pure and doped systems hosting skyrmions have been prepared using CVT.

Single crystals of Cu₂OSeO₃ were grown from pre-reacted polycrystalline powder using chemical vapour transport with TeCl₄ as a transporting agent. The skyrmion lattices was studied using x-rays

(a) Schematic diagram of the experimental setup.

(b) Small-angle x-ray scattering pattern of the helical state of Cu₂OSeO₃.

(c) Energy scan of x-ray transmission (blue) and magnetic scattering (red) for a 200-nm-thick Cu₂OSeO₃ lamella at 20 K and zero magnetic field, aligned with the incoming beam ∥ [110]. Representative transmitted intensity was determined by summing inside the blue circle on (b), and the scattered intensity was taken by summing the red circles and subtracting the green circles as background [18 - 2020].

Characterization of skyrmion materials

The materials that have been prepared are characterized in the laboratories of the Skyrmion Project partners. Structural studies include x-ray diffraction and electron microscopy. Samples are also analyzed using thermogravimetric and differential thermal analysis. A real-time x-ray Laue back reflection system at Warwick allows fast, direct examination of the quality of the as-grown single crystals and the alignment and cutting of samples.

Electron diffraction

A. E. Hall, J. C. Loudon, P. A. Midgley, A. C. Twitchett-Harrison, S. J. R. Holt, D. A. Mayoh, J. P. Tidey, Y. Han, M. R. Lees, G. Balakrishnan, Comparative study of the structural and magnetic properties of Mn1/3NbS2 and Cr1/3NbS2, Physical Review Materials 6, 024407 (2022).

Comparative study of the structural and magnetic properties of single crystals of Mn_1/3NbS₂ and Cr_1/3NbS₂ (a) Unit cell of Mn_1/3NbS₂ or Cr_1/3NbS₂ viewed down the [001] direction. (b) Simulated electron diffraction patterns along the [001] direction for both the noncentrosymmetric P6₃22 structure and the centrosymmetric P6₃/mmc structure, which differ from each other in the relative intensities of key spots (200) and (030), assuming kinematic scattering. An electron micrograph (c) of a crystal of Mn_1/3NbS₂ and an electron diffraction pattern from the same area are shown and match well with the simulation for the P6₃22 space group, with the especially faint (200) spot marked with an arrow. (d) The unit cell viewed along [100] direction. (e) A simulation of the corresponding electron diffraction pattern. (f) Bright-field images and electron diffraction patterns from Cr_1/3NbS₂ and (g) Mn_1/3NbS₂. While the Cr_1/3NbS₂ pattern matches well with the simulation, Mn_1/3NbS₂ displays extra reflections indicating a superlattice with a period of 3c in the c direction and 7d₀₁₀ in the b^∗ direction [8 - 2022].

AC susceptibility

T. J. Hicken, S. J. R. Holt, K. J. A. Franke, Z. Hawkhead, A. Štefančič, M. N. Wilson, M. Gomilšek, B. M. Huddart, S. J. Clark, M. R. Lees, F. L. Pratt, S. J. Blundell, G. Balakrishnan, T. Lancaster, Magnetism and Néel skyrmion dynamics in GaV4S8-y Sey Physical Review Research 2, 032001 (2020).

In-depth experimental studies are carried out at all the Skyrmion Project host institutions using a range of probes including AC and DC magnetic measurements, specific heat studies, transport measurements (resistivity, Hall effect, thermopower), as a function of temperature, magnetic field, and pressure. We have facilities for magnetometry, transport, and thermodynamic measurements from 50 mK to 800 K in magnetic fields up to 17 T. Transport (30 kbar) and magnetization (10 kbar) studies can also be carried out as a function of pressure.

The figure shows the real component of AC susceptibility in constant field B_ext for GaV₄S_8-ySe_y where (a) y = 0 (b) y = 0.1, (c) y = 8, and (d) y = 7.9. Dashed black lines indicate fields where μSR measurements were performed with white highlighting proposed skyrmion lattice regions. [11 - 2020].

Skyrmion materials for Research Challenges 2 and 3

The materials we have prepared are used for further studies by members of the Skyrmion Project under Research Challenge 2 and Research Challenge 3. At Cambridge University advanced microcopy techniques are used to investigate materials right down the level of an individual skyrmion. Samples are used for experiments at central facilities, both here in the UK at ISIS and Diamond, as well at international facilities such as PSI, ILL, ESRF and SOLEIL.

M. Crisanti, N. Reynolds, I. Živković, A. Magrez, H. M. Rønnow, R. Cubitt, J. S. White, In situ control of the helical and skyrmion phases in Cu2OSeO3 using high-pressure helium gas up to 5 kbar, Physical Review B 101, 214435 (2020).

Small-angle neutron scattering

Pressure stability of the skyrmion lattice in Cu₂OSeO₃ in the μ₀H parallel k_i geometry. Small angle neutron scattering (SANS) patterns of the skyrmion lattice at T = 56 K, μ₀H = 25 mT, and (a) ambient pressure or (b) P = 5 kbar. (c) and (d) show SANS patterns obtained at ambient pressure and P = 5 kbar, respectively, each with fixed T = 58.5 K, μ₀H = 21 mT [9 - 2020].

Crystals for other projects

Single crystals have also been shared with collaborators both here in the UK and overseas for studies complementary to those of the UK Skyrmion Project team.

Research Challenge 2 - Skyrmion science

Skyrmion science - Team leader Professor Tom Lancaster

Research Challenge 2 concerns Skyrmion Science: the basic physics of skyrmionic states of matter. Before skyrmions can be exploited in devices it is necessary to understand their properties, potentialities and their status within the general framework of fundamental physics.

The skyrmion is a topological defect much like the magnetic domain wall and the superconducting vortex. If skyrmions can be made energetically stable they should occur within many systems showing broken symmetry and show a characteristic set of excitations.

How do skyrmion phases occur and what determines the form of the skyrmionic texture?

Stereographic projection (denoted P) squashes the hedgehog into D = 2, where it becomes a skyrmion. The left-hand version is a Néel skyrmion; the right-hand version, where the spins have been combed over (denoted R), is a Bloch skyrmion [9 - 2019Link opens in a new window and references therein].

Skyrmions

At one time, magnetic skyrmions were thought only to be realised in B20 magnetic systems.

Recently it has become clear that a far richer variety of skyrmion textures may occur in a diverse range of systems. These textures include not only the Bloch-like skyrmion occurring in B20 chiral magnets but also the Neel-type skyrmion.

Bulk materials and phase diagrams

In bulk materials, the skyrmion lattice (SL) phase generally occurs within a narrow region of the applied magnetic field-temperature phase diagram. The reason for this, the nature of the phase transition, the possibility of precursor phases and the critical behavior on entering the skyrmion phase have all required detailed study.

M. T. Birch, D. Cortés-Ortuño, N. D. Khanh, S. Seki, A. Štefančič, G. Balakrishnan, Y. Tokura, P. D. Hatton, Topological defect-mediated skyrmion annihilation in three dimensions, Communications Physics 4, 175 (2021).

The magnetic phase diagram of the (Cu_1−xZn_x)₂OSeO₃ sample, as determined by measurements of the electric polarisation P along the [001] crystallographic axis, when the magnetic field is applied along the [110] axis. The phase diagram was determined by field cooling (FC) at 20 mT, as indicated by the green arrow. The uniform magnetisation (UM, white), conical (C, blue), helical (H, red) and equilibrium skyrmion lattice (SkL, yellow) phases are labelled. The metastable SkL phase is divided into two regions, where it overlays the equilibrium conical (yellow hatched) and helical (yellow dotted) phases [1 - 2021Link opens in a new window].

How does dimensionality affect the skyrmion?

When bulk, crystalline samples are thinned the skyrmion phase becomes more stable, extending over a greater range of temperatures and applied magnetic fields. However, the observation of skyrmions in thin magnetic films has proved highly controversial, with no widely accepted observation of skyrmions in such films. The latter is of extreme importance since the manipulation of skyrmions in devices will most likely rely on magnetic thin-film technology. We have investigated the confinement of the SL along with the phase diagrams and spin textures realized in near-single layer samples and thin films.

R. Fujita, P. Bassirian, Z. Li, Y. Guo, M. A. Mawass, F. Kronast, G. van der Laan, T. Hesjedal, Layer-Dependent Magnetic Domains in Atomically Thin Fe5GeTe2, ACS Nano 16, 10545 (2022).

Layer-dependent magnetic domain structures in on Fe₅GeTe₂. The images obtained for (a,b) 4 layer and 3 layer, and (c) 2 layer flakes show a strong dependence on thickness (T = 50 K). The distribution of up (red) and down (blue) domains for each thickness are indicated in (a) and (c). [6 - 2022Link opens in a new window].

How does the skyrmion evolve on different scales?

The skyrmion phase promotes a range of emergent physics. Using our suite of technique we have probed the excitations of the skyrmion phase on a number of length-, time- and energy-scales. There is also evidence that the extent of the SL phase is dependent on sample cooling rates, with quench-cooling stabilizing a larger skyrmion phase. Investigations of non-equilibrium effects have allowed us to stabilize these objects under a variety of conditions.

How robust is the skyrmion and the SL?

Little is known about the effects of disorder on the skyrmion phase. We have investigated the stability of skyrmion lattice and other related structures in bulk and thin film samples. We have examined the effects of confinement and dimensionality. We have also studied how introducing disorder, for example, by chemical doping alter the structure and stability of the skymion lattice.

S. Zhang, D. M. Burn, N. Jaouen, J.-Y. Chauleau, A. A. Haghighirad, Y. Liu, W. Wang, G. van der Laan, T. Hesjedal, Robust Perpendicular Skyrmions and Their Surface Confinement, Nano Letters 20, 1428 (2020).

REXS measurements on surface and bulk skyrmions in Cu₂OSeO₃. (a) Temperature-field phase diagram mapped by REXS. The dots represent measured data points. The skyrmion bulk state region, defined by the characteristic REXS pattern as shown in Figure 1(f), is marked in red. The bulk phase boundary is consistent with the ac susceptibility measurements for both field-cooled and zero-field-cooled protocols. The skyrmion surface state (SSS) region is marked in yellow. (b) Magnetic phase diagram showing the ac susceptibility plot (real component χ′) obtained using the same protocol as for the REXS plot in (a), i.e., field cooling from above T_C. (c, d) Reciprocal space maps of the surface state measured under surface-sensitive (931.2 eV) and bulk-sensitive (926.2 eV) conditions, respectively. (e) Illustration of the skyrmion surface state [20 - 2020Link opens in a new window].

Experimental techniques

We have investigated phase transitions and skyrmion textures in a variety of materials using a broad range of experimental techniques and theoretical modelling.

Our starting point was to exploit the similarity between the skyrmion lattice (SL) and another topological defect state: the vortex lattice (VL) in type-II superconductors. This approach has allowed us to identify a powerful set of probes and tools for use in the project.

Neutron diffraction

Neutron diffraction techniques have an advantage in examining large-scale magnetic structures such as SLs in that they produce data corresponding to the morphology of the field distribution in the bulk of a sample rather than a surface view provided by many methods.

M. Crisanti, M. T. Birch, M. N. Wilson, S. H. Moody, A. Štefančič, B. M. Huddart, S. Cabeza, G. Balakrishnan, P. D. Hatton, R. Cubitt, Position-dependent stability and lifetime of the skyrmion state in nickel-substituted Cu2OSeO3 Physical Review B 102, 224407 (2020).

a) SANS H-T phase diagram of the Ni-substituted Cu₂OSeO₃, derived by summing the scattered neutron intensity in the region of the detector between the two white circles indicated in (b). The dashed lines identify the boundaries between the various magnetic phases in the sample. The solid white vertical line indicates the value of T_C measured with ac susceptibility. (b) Typical skyrmion lattice scattering pattern recorded using SANS in Ni-substituted Cu₂OSeO₃ at 22 mT and 57 K [8 - 2020Link opens in a new window].

Transmission Electron Microscopy

Transmission Electron Microscopy Magnetic imaging techniques (known collectively as Lorentz microscopy) are based on the fact that the Lorentz force from internal magnetic fields deflects electrons as they pass through a material, altering the phase of the electron wavefunction. We have used the technique to measure the magnetic profile of individual skyrmions and track magnetic phase transitions. Electron microscopy is the only imaging technique which gives information on the internal magnetic structure of the SL rather than just the stray field, and allows imaging at video rate.

J. C. Loudon, A. O. Leonov, A. N. Bogdanov, M. C. Hatnean, G. Balakrishnan, Direct observation of attractive skyrmions and skyrmion clusters in the cubic helimagnet Cu2OSeO3, Physical Review B 97, 134403 (2018).

LTEM images showing two skyrmion clusters (outlined in red) embedded in the cone phase of Cu₂OSeO₃ at 11 K in an out-of-plane applied magnetic field of μ₀H = 116 mT. (b)–(d) show changes in the shape of the left-hand cluster with (c) taken 0.5 s and (d) taken 34.4 s after (b) [5 - 2018Link opens in a new window].

X-ray diffraction

Using x-ray diffraction we have studied magnetic superlattice reflections such as magnetic spin density waves and antiferromagnetic and incommensurate reflections. We have used polarized soft x-ray diffraction, where we measure the polarization of the scattered x-rays to provide element-specific information on magnetic anisotropy.

Advanced imaging techniques including high-resolution ptychographic imaging have been used to examine skyrmions in bulk and thin film samples.

W. Li, I. Bykova, S. Zhang, G. Yu, R. Tomasello, M. Carpentieri, Y. Liu, Y. Guang, J. Gräfe, M. Weigand, D. M. Burn, G. van der Laan, T. Hesjedal, Z. Yan, J. Feng, C. Wan, J. Wei, X. Wang, X. Zhang, H. Xu, C. Guo, H. Wei, G. Finocchio, X. Han, G. Schütz, Anatomy of Skyrmionic Textures in Magnetic Multilayers, Advanced Materials 31, 1807683 (2019).

Ptychographic imaging is used to map the 2D spin texture of skyrmions in a Ta/[CoFeB/MgO/Ta]16 multilayer. The sample is raster-scanned while the focused X-ray beam remains fixed. The focusing of the beam is achieved by a Fresnel zone plate (FZP), where an order sorting aperture (OSA) blocks the nondiffracted zero-order light. A diffraction image is recorded in the far-field by a CCD camera (at distance L) for every scanning position. Applying an iterative phase retrieval algorithm allows for the reconstruction of the phase and amplitude images [10 - 2019Link opens in a new window].

Muon-spin spectroscopy

Muon-spin rotation provides a means of accurately measuring the internal magnetic field distribution in a material through the implantation of spin-polarized muons. The technique has been used to provide key measurements of skyrmion dynamics, and we have shown that the technique allows an insight into the physics of the SL.

K. J. A. Franke, B. M. Huddart, T. J. Hicken, F. Xiao, S. J. Blundell, F. L. Pratt, M. Crisanti, J. A. T. Barker, S. J. Clark, A. Stefancic, M. C. Hatnean, G. Balakrishnan, and T. Lancaster, Magnetic phases of skyrmion-hosting GaV4S8-ySey (y = 0, 2, 4, 8) probed with muon spectroscopy, Physical Review B 98, 054428 (2018).

Typical muon spectroscopy time-domain spectra measured for GaV₄S₈ (left) and GaV₄Se₈ (right) in zero-field in the ferromagnetic (FM), cycloidal (C), and paramagnetic (PM) phases. Lines are fits described in the text and the curves have been offset vertically for clarity [3 - 2018Link opens in a new window].

Theoretical methods and modelling

We have employed state-of-the-art multiscale theoretical and computational methods applicable in broad ranges of time, length and energy scales, and big data analysis tools, to understand the fundamental aspects of skyrmion physics. This theoretical work will guide and allow us to understand our experimental results.

We have used first principles calculations, such as DFT, to identify the physics at play, and has been followed by modelling and calculations of static properties and excitations such as magnons and phonons. Other techniques employed in this Challenge include: (i) lattice spin models and Monte-Carlo simulations to establish phase diagrams; (ii) Langevin spin dynamics simulations to probe skyrmion lifetimes and dynamics; (iii) micromagnetic simulations to model confinement effects and interactions with defects; (iv) micromagnetic, Monte-Carlo and large-scale spin dynamics simulations to model skyrmion interactions, long time-scale dynamics of the spin textures. Spin models were also used to compute the static and dynamic structure factors to directly support scattering experiments.

M. T. Birch, D. Cortés-Ortuño, L. A. Turnbull, M. N. Wilson, F. Groß, N. Träger, A. Laurenson, N. Bukin, S. H. Moody, M. Weigand, G. Schütz, H. Popescu, R. Fan, P. Steadman, J. A. T. Verezhak, G. Balakrishnan, J. C. Loudon, A. C. Twitchett-Harrison, O. Hovorka, H. Fangohr, F. Y. Ogrin, J. Gräfe, P. D. Hatton, Real-space imaging of confined magnetic skyrmion tubes, Nature Communications 11, 1726 (2020).

Three dimensional visualisation of three magnetic skyrmion tubes from micromagnetic simulations illustrating their extended spin structure. The inset highlights the location of the magnetic Bloch point at the end of each skyrmion tube [1 - 2020Link opens in a new window].

Research Challenge 3 - Thin films, modelling and devices

Thin Films, modelling and devices - Team leader Professor Thorsten Hesjedal

Research Challenge 3 involves investigations of thin films, modelling and devices. How do we transfer the desired properties materials to application-enabling thin films? Our interdisciplinary strategy involves film synthesis, patterning, architecture and micromagnetic simulation.

How do we transfer the desired properties of bulk crystals to application-enabling thin films?

Our thin film growth provides insights into the materials challenges currently holding back this field. Currently skyrmions can only be observed in bulk single crystals, and bulk samples that have been thinned down for electron microscopy. Successful attempts to grow high-quality, phase-pure thin films have not resulted in the unambiguous observation of skyrmions. As is known from B20 thin film systems, strain is a critical, presumably detrimental, parameter for the formation of a skyrmion phase. However, strain is also the key to enhance the magnetic transition temperature.

A. I. Figueroa, S. L. Zhang, A. A. Baker, R. Chalasani, A. Kohn, S. C. Speller, D. Gianolio, C. Pfleiderer, G. van der Laan, T. Hesjedal, Strain in epitaxial MnSi films on Si(111) in the thick film limit studied by polarization-dependent extended x-ray absorption fine structure, Physical Review B 94, 174107 (2016).

Our study of the strain state of epitaxial MnSi films on Si(111) substrates in the thick film limit (100–500 Å) as a function of film thickness using polarization-dependent extended x-ray absorption fine structure (EXAFS) [2 - 2016].

A. C. Twitchett-Harrison, J. C. Loudon, R. A. Pepper, M. T. Birch, H. Fangohr, P. A. Midgley, G. Balakrishnan, P. D. Hatton, Confinement of Skyrmions in Nanoscale FeGe Device-like Structures, ACS Applied Electronic Materials (2022).

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure [14 - 2022]. .

How can we efficiently and reliably generate skyrmions?

A skyrmion-based data storage device must contain an efficient and reliable writing module, based on well-controlled and localised skyrmion creation. This can be achieved using either the localised application of a spin-polarised current or an external magnetic field. We will determine the optimal design of a skyrmion generator and determine the circumstances under which the skyrmions are created. We will determine how the essential writing parameters (speed, reliability, energy efficiency) depend on different designs and parameters of skyrmion generators. We will avoid the use of mechanical parts that are still present in conventional hard disk drives, and which are the main limiting factor in terms of robustness, speed and cost.

How do we develop skyrmion transport devices?

We have worked to understand how an array of skyrmions can be moved along a nanostructure that forms the core of a shift-register-like system. The crucial parameter is the optimal current density required to drive a train of skyrmions. Since a single information bit is encoded by the skyrmion's presence/absence, we must study whether this skyrmion chain can be moved uniformly, without changing their relative distances.

How do we develop skyrmion detectors?

After exciting and transporting skyrmions, a means of detection needs to be developed. Magnetic spin-valve and tunnel structures have been studied, as well other schemes, before a recommendation will be given for the fabrication of the structures.

A straightforward approach is to use the topological Hall effect (THE). Generally, however, the expected THE voltage is rather small, making it necessary to enhance the signal.

R. Brearton, L. A. Turnbull, J. A. T. Verezhak, G. Balakrishnan, P. D. Hatton, G. van der Laan, T. Hesjedal, Deriving the skyrmion Hall angle from skyrmion lattice dynamics, Nature Communications 12, 2723 (2021).

We have developed reciprocal space techniques to determine the skyrmion Hall angle in the skyrmion lattice state of FeGe [2 - 2021].

Materials synthesis

Materials synthesis has been carried out via molecular beam epitaxy (MBE) and UHV magnetron sputtering. Hitherto we have successfully grown the B20 materials MnSi, FeGe, and MnGe in thin film form.

Thin film growth

For this project, we have four thin film growth systems at our disposal, covering the materials classes from intermetallics, to oxides, chalcogenides, and silicides. Two state-of-the-art MBE systems are located on the Rutherford-Appleton Laboratory site in Harwell, dedicated for oxides and chalcogenides. A third MBE, for intermetallics and silicides, as well as a UHV magnetron sputterer, are located in the Clarendon Laboratory at Oxford, and have been successfully used for the growth of B20 thin films.

We have grown skyrmion hosting materials in the form of thin films and of nanostructures using molecular beam epitaxy (MBE), UHV sputtering, and chemical vapor deposition; their structural, magnetic, and electrical characterization; as well as exploratory device studies.

Experimental methodology

Thin films

Thin films are patterned into nanodevices in Oxford's nanofabrication cleanrooms. Photolithography e-beam lithography, and focused ion beam are employed for fabricating a variety of structures that are then optimised for their respective purpose: in-plane contact structures, Hall bars for magnetotransport studies, spin valves, and magnetic tunnel junction-like structures for skyrmion excitation and detection.

K. Ran, Y. Liu, Y. Guang, D. M. Burn, G. van der Laan, T. Hesjedal, H. Du, G. Yu, S. Zhang, Creation of a Chiral Bobber Lattice in Helimagnet-Multilayer Heterostructures, Physical Review Letters 126, 017204 (2021).

We have created a chiral bobber structure via heterostructure engineering. (a) Illustration of the heterostructure by contacting two different skyrmion species with comparable lateral dimensions. (b) Simulation results of the skyrmion tube structure at field between B_A1 and B_A2. (c) z component of the dipolar field distribution from a skyrmion in the multilayer. (d) Calculated chiral bobber structure formed in Cu₂OSeO₃ at a field between the first and second upper critical fields B_A2 and B_A3, respectively [16 - 2021].

LTEM and X-rays

We have investigated the magnetic states in these films by magnetometry, neutron diffraction, ferromagnetic resonance and muon-spin spectroscopy. We have also used many advanced techniques such as LTEM, resonant elastic X-ray scattering including CD-REXS, small angle neutron scattering, and X-ray holography to image the skyrmion lattice and other magnetic textures, in both 2D and 3D.

S. Zhang, G. van der Laan, J. Müller, L. Heinen, M. Garst, A. Bauer, H. Berger, C. Pfleiderer, T. Hesjedal, Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet, Proceedings of the National Academy of Sciences 115, 6386 (2018).

We have studied the full 3D spin order in the skyrmion lattice of Cu₂OSeO₃ by means polarized REXS as a depth-dependent probe. Here we illustrate the skyrmion order ranging from Néel- to Bloch-twisting with increasing depth below a surface. (A1–A4) Hedgehog spin configuration on the surface of a sphere for skyrmions with winding number N = 1 varying between pure Néel-twisting (A1) and pure Bloch-twisting (A4). (B1–B4) Real-space planar spin configuration varying between pure Néel-twisting (B1) and pure Bloch-twisting (B4). A stereographic projection connects the planar patterns shown in B1–B4 with the hedgehog configurations shown in A1–A4, respectively. (C1–C4) Calculated dichroic REXS diffraction pattern associated with a hexagonal lattice composed of the spin configurations shown in B1–B4. The orientation of the extinction line marked by a white arrow corresponds to the helicity angle χ denoted on the right-hand side of the panels. Consequently, the chirality of the skyrmions can be straightforwardly determined. (C1) χ = 180^○ and (C4) χ = 90^○ correspond to pure Néel- and pure Bloch-twisting, respectively. (D) Schematic illustration of the change from Néel- to Bloch-twisting with increasing depth below the surface. The colour coding reflects the z direction of the magnetization [9 - 2018].

Simulations and modelling

Micromagnetic simulations have been used in order to determine the optimal implementation method for the development of novel high-density, low-power skyrmion-based data storage and processing devices. The use of skyrmions in thin film devices requires them to be stable in zero external magnetic field. We have worked to refine the finite-difference and finite-element simulation tools to cover thin films and finite dimensions, at T = 0 K and at finite temperatures. Design of the skyrmion-based data storage device requires the multidisciplinary approach including micromagnetic modeling, numerical analysis, complexity, software development, and more. The simulation tools have already been fully developed at the University of Southampton. We have made use of the University's High Performance Computing Facilities, which has allowed us to perform simulations by varying different parameters over a very wide range.