Search

Chiral magnets with Dzyaloshinskii-Moriya interactions feature a rich phase diagram with a variety of thermodynamical phases. These include helical and conical spin arrangements and topologically charged objects such as (anti)skyrmions. Crucially, due to hysteresis effects, the thermodynamical phases can co-exist at any given temperature and external magnetic field, typically leading to metastability of, e.g., the material's topological phase. In this work, we use Monte Carlo simulations to study these effects. We compute the relative free energies of co-existing states, enabling us to determine the ground state at all values of the external parameters. We also introduce a method to estimate the activation energy, i.e. the height of the energy barrier that separates the topological phase from the ground state. This is one of the key ingredients for the determination of the skyrmion lifetime, which is relevant for technological applications. Finally, we prescribe predicting the system's evolution through any path in the space of external parameters. This can serve as a guideline to prepare the magnetic material in any desired phase or even trigger a phase transition in an experimental setup., Comment: 12 pages, 6 figures. v2: minor clarifications, updated figures and references

Mechanical straining of skyrmion hosting materials has previously demonstrated increased phase stability through the expansion of the skyrmion equilibrium pocket. Additionally, metastable skyrmions can be generated via rapid field-cooling to form significant skyrmion populations at low temperatures. Using small-angle x-ray scattering and x-ray holographic imaging on a thermally strained 200 nm thick FeGe lamella, we observe temperature-induced strain effects on the structure and metastability of the skyrmion lattice. We find that in this sample orientation (H || [1 1 0]) with no strain, metastable skyrmions produced by field cooling through the equilibrium skyrmion pocket vanish from the sample upon dropping below the well known helical reorientation temperature. However, when strain is applied along [110] axis, and this procedure is repeated, a substantial volume fraction of metastable skyrmions persist upon cooling below this temperature down to 100 K. Additionally, we observe a large number of skyrmions retained after a complete magnetic field polarity reversal, implying that the metastable energy barrier protecting skyrmions from decay is enhanced.

Magnetic skyrmions are vortex-like, swirls of magnetisation whose topological protection and particle-like nature have suggested them to be suitable for a number of novel spintronic devices. One such application is skyrmionic computing, which has the advantage over conventional schemes due to the amalgamation of logic calculations and data storage. Using small-angle neutron scattering from Cu2OSeO3, and applying electric and magnetic fields, we find that the direction of the skyrmion-coexisting conical states can be manipulated by varying the electric field, and explain this using a free energy approach. Our findings unlock the prospect of creating a number of skyrmion devices which may constitute part of a skyrmion computer, as the direction of a skyrmion within a nanosized racetrack can be manipulated into different channels by controllably changing the direction of the localised conical state. We provide time-dependant micromagnetic simulations to demonstrate such a device: a skyrmion double transistor.

Isotropic helimagnets are known to host a diverse range of chiral magnetic states. In 2016, F.N. Rybakov et al. theorized the presence of a surface-pinned stacked spin spiral phase [F.N. Rybakov et al., 2016 New J. Phys. 18 045002], which has yet to be observed experimentally. Here we present experimental evidence for the observation of this state in lamellae of FeGe using resonant x-ray holographic imaging data and micromagnetic simulations. The identification of this state has significant implications for the stability of other coexisting spin textures, and will help complete our understanding of helimagnetic systems.

Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural hierarchies from nano- to macroscale that enable optimization of both strength and toughness (flaw tolerance) simultaneously3-9. These hierarchies typically exhibit structural disorder in the arrangement of pores. The degree of disorder, however, has not been systematically quantified before, and its role in the mechanical performance of cellular biomaterials is generally unknown. Here we have applied Voronoi tessellations to quantify the cell size variation in 2D cross-sections of biological and engineered cellular materials, using a disorder parameter (d) ranging between 0 (highly disordered) to 1.0 (regular hexagonal honeycomb). We demonstrate that various plant, fungi, and animal cellular materials show characteristic ranges of disorder. Using 3D printed analogues and numerical methods, we demonstrate experimentally a range of pseudo-order (d=0.6 to 0.8) that exhibits a > 30% increase in fracture toughness (and equivalent strength) compared to hexagonal honeycombs (d=1.0) of equal density. Our results show this range of disorder is similar to that identified in the biological examples, which suggests convergent evolution. This optimal degree of structural disorder limits catastrophic failure, providing an evolutionary advantage for organism survival. Distributed structural damage limits cracks below a maximum threshold size and also enables tissue repair mechanisms after trauma. Our work shows that tailored disorder should be considered as a new design paradigm for digitally fabricated, lightweight architected materials to improve damage tolerance.

Magnetic skyrmions are topologically protected spin structures that naturally emerge in magnetic materials. While a vast amount of effort has gone into the study of their properties, their counterpart of opposite topological charge, the antiskyrmion, has not received as much attention. We aim to close this gap by deploying Monte Carlo simulations of spin-lattice systems in order to investigate which interactions support antiskyrmions, as well as skyrmions of Bloch and N\'eel type. We find that a suitable combination of ferromagnetic exchange and Dzyaloshinskii-Moriya (DM) interactions is able to stabilize all three types. Considering a three-dimensional spin lattice model, we provide a finite-temperature phase diagram featuring a stable antiskyrmion lattice phase for a large range of temperatures. In addition, we also shed light on the creation and annihilation processes of these antiskyrmion tubes and study the effects of the DM interaction strength on their typical size., Comment: 12 pages, 9 figures

We report small-angle neutron scattering from the conical state in a single crystal of Zn-substituted Cu2OSeO3. Using a 3D vector-field magnet to reorient the conical wavevector, our measurements show that the magnitude of the conical wavevector changes as a function of crystallographic direction. These changes are caused by the anisotropic exchange interaction (AEI), whose magnitude transitions from a maxima to a minima along the <111> and <100> crystallographic directions respectively. We further find that the AEI constant undergoes a change of sign from positive to negative with decreasing temperature. Unlike in the related compound FeGe, where similar behaviour of the AEI induces a reorientation of the helical wavevector, we show that the zero field helical wavevector in (Cu0.98Zn0.02)2OSeO3 remains along the <100> directions at all temperatures due to the competing fourth-order magnetocrystalline anisotropy becoming dominant at lower temperatures.

Skyrmion-containing 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 Bloch skyrmions in FeGe device shapes using Lorentz transmission electron microscopy (LTEM) to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam (FIB) milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions, but that a complex device geometry changes the skyrmion behaviour, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. This could allow methods to be developed to control both the position and number of skyrmions within device structures.

The creation and annihilation of magnetic skyrmions are mediated by three dimensional topological defects known as Bloch points. Investigation of such dynamical processes is important both for understanding the emergence of exotic topological spin textures, and for future engineering of skyrmions in technological applications. However, while the annihilation of skyrmions has been extensively investigated in two dimensions, in three dimensions the phase transitions are considerably more complex. We report field-dependent experimental measurements of metastable skyrmion lifetimes in an archetypal chiral magnet, revealing two distinct regimes. Comparison to supporting three-dimensional geodesic nudged elastic band simulations demonstrates that these correspond to skyrmion annihilation into either the helical or conical states, each exhibiting a different transition mechanism. The results highlight that the lowest energy magnetic configuration of the system plays a crucial role when considering the emergence of topological spin structures via defect-mediated dynamics, and their stability in future devices.

The intermetallic Gd2PdSi3 has recently generated a lot of excitement after reports that it hosts chiral magnetic nano-skyrmions despite its centrosymmetric crystal structure. Using magnetic-field-dependent polarized resonant elastic x-ray scattering (REXS), we find than an unexpected incommensurate charge density wave (CDW) appears below the ordering transition with a wavevector equal to that of the magnetic textures. Furthermore, we show these incommensurate magnetic textures in Gd2PdSi3 are highly anisotropic, with the vast majority of the spin modulation lying within the hexagonal ab-plane. This observation is not compatible with the previously suggested non-coplanar magnetic textures and coplanar alternatives are discussed. Our results thus refute the interpretation of the observed large anomalous Hall and Nernst effects in Gd2PdSi3 as arising from topologically-nontrivial magnetic skyrmions., Comment: We have recently collected new measurements which conflict the main claims of this paper. We will reinterpret our old results together with the new data in due course and will report our findings once the analysis is complete and a better understanding of the complete picture has been achieved

Magnetic skyrmions are nano-sized topological spin textures stabilized by a delicate balance of magnetic energy terms. The chemical substitution of the underlying crystal structure of skyrmion-hosting materials offers a route to manipulate these energy contributions, but also introduces additional effects such as disorder and pinning. While the effects of doping and disorder have been well studied in B20 metallic materials such as Fe$_{1-x}$Co$_x$Si and Mn$_{1-x}$Fe$_x$Si, the consequences of chemical substitution in the magnetoelectric insulator Cu$_2$OSeO$_3$ have not been fully explored. In this work, we utilize a combination of AC magnetometry and small angle neutron scattering to investigate the magnetic phase transition dynamics in pristine and Zn-substituted Cu$_2$OSeO$_3$. The results demonstrate that the first order helical-conical phase transition exhibits two thermally separated behavioural regimes: at high temperatures, the helimagnetic domains transform by large-scale, continuous rotations, while at low temperatures, the two phases coexist. Remarkably, the effects of pinning in the substituted sample are less prevalent at low temperatures, compared to high temperatures, despite the reduction of available thermal activation energy. We attribute this behaviour to the large, temperature-dependent, cubic anisotropy unique to Cu$_2$OSeO$_3$, which becomes strong enough to overcome the pinning energy at low temperatures. Consideration and further exploration of these effects will be crucial when engineering skyrmion materials towards future applications.

We report scanning transmission X-ray microscopy of mixed helical and skyrmion magnetic states in thin FeGe lamellae. This imaging of the out-of-plane magnetism allows clear identification of the different magnetic states, and reveals details about the coexistence of helical and skyrmion states. In particular, our data show that finite length helices are continuously deformable down to the size of individual skyrmions and are hence topologically equivalent to skyrmions. Furthermore, we observe transition states between helical and skyrmion states across the thickness of the lamella that are evidence for frozen Bloch points in the sample after field cooling., Comment: Further analysis by the authors suggests that the evidence we presented for the zipping transition between skyrmions and helices was flawed. This mistaken interpretation resulted from slight misalignment between positive and negative circularly polarized images used to produce the XMCD STXM images

We report small angle X-ray scattering (SAXS) measurements of the skyrmion lattice in two 200~nm thick Cu$_2$OSeO$_3$ lamellae aligned with the applied magnetic field parallel to the out of plane [110] or [100] crystallographic directions. Our measurements show that the equilibrium skyrmion phase in both samples is expanded significantly compared to bulk crystals, existing between approximately 30 and 50~K over a wide region of magnetic field. This skyrmion state is elliptically distorted at low fields for the [110] sample, and symmetric for the [100] sample, possibly due to crystalline anisotropy becoming more important at this sample thickness than it is in bulk samples. Furthermore, we find that a metastable skyrmion state can be observed at low temperature by field cooling through the equilibrium skyrmion pocket in both samples. In contrast to the behavior in bulk samples, the volume fraction of metastable skyrmions does not significantly depend on cooling rate. We show that a possible explanation for this is the change in the lowest temperature of the skyrmion state in this lamellae compared to bulk, without requiring different energetics of the skyrmion state., Comment: 10 pages, 8 figures

Magnetic skyrmions are topologically nontrivial particles with a potential application as information elements in future spintronic device architectures. While they are commonly portrayed as two dimensional objects, in reality magnetic skyrmions are thought to exist as elongated, tube-like objects extending through the thickness of the sample. Study of this skyrmion tube (SkT) state is highly relevant for investigating skyrmion metastability and for implementation in recently proposed magnonic computing. However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the first real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, confirming their extended structure. The formation of these structures at the edge of the sample highlights the importance of confinement and edge effects in the stabilisation of the SkT state, opening the door to further investigations into this unexplored dimension of the skyrmion spin texture.

We report small angle neutron scattering (SANS) measurements of the skyrmion lattice in (Cu$_{0.976}$Zn$_{0.024}$)$_2$OSeO$_3$ under the application of an electric field. These measurements show an expansion of the skyrmion lattice stability region with electric field similar to that seen in pristine Cu$_2$OSeO$_3$. Furthermore, using time-resolved SANS, we observe the slow formation of skyrmions after an electric or magnetic field is applied, which has not been observed in pristine Cu$_2$OSeO$_3$ crystals. The measured formation times are dramatically longer than the corresponding skyrmion destruction times after the external field is removed, and increase exponentially from 100~s at 52.5~K to 10,000~s at 51.5~K. This thermally activated behaviour indicates an energy barrier for skyrmion formation of 1.57(2)~eV, the size of which demonstrates the huge cost for creating these complex chiral objects., Comment: 8 pages, 8 figures

We present the results of x-ray scattering and muon-spin relaxation ($\mu^{+}$SR) measurements on the iron-pnictide compound FeCrAs. Polarized non-resonant magnetic x-ray scattering results reveal the 120$^\circ$ periodicity expected from the suggested three-fold symmetric, non-collinear antiferromagnetic structure. $\mu^+$SR measurements indicate a magnetically ordered phase throughout the bulk of the material below $T_\mathrm{N}$=105(5) K. There are signs of fluctuating magnetism in a narrow range of temperatures above $T_\mathrm{N}$ involving low-energy excitations, while at temperatures well below $T_\mathrm{N}$ behaviour characteristic of freezing of dynamics is observed, likely reflecting the effect of disorder in our polycrystalline sample. Using density functional theory we propose a distinct muon stopping site in this compound and assess the degree of distortion induced by the implanted muon.

Previous observations of metastable magnetic skyrmions have shown that close to the equilibrium pocket the metastable state has a short lifetime, and therefore rapid cooling is required to generate a significant skyrmion population at low temperatures. Here, we report that the lifetime of metastable skyrmions in Cu$_2$OSeO$_3$ is extended by a factor of 50 with the introduction of only 2.5% zinc doping, allowing over 50% of the population to survive when field-cooling at a rate of just 1 K/min. Our systematic study suggests that the lifetime enhancement is due to the removal of spins by the non-magnetic dopant, which entropically limits the number of skyrmion decay pathways. We expect that doping can be exploited to control the lifetime of the metastable SkL state in other chiral magnets, offering a method of engineering skyrmion materials towards application in future devices., Comment: 9 Pages, 7 Figures, submission in progress

We present long-wavelength neutron diffraction data measured on both single crystal and polycrystalline samples of the skyrmion host material Cu$_{2}$OSeO$_{3}$. We observe magnetic satellites around the $(0\bar{1}1)$ diffraction peak not accessible to other techniques, and distinguish helical from conical spin textures in reciprocal space. We confirm successive transitions from helical to conical to field polarised ordered spin textures as the external magnetic field is increased. The formation of a skyrmion lattice with propagation vectors perpendicular to the field direction is observed in a region of the field-temperature phase diagram that is consistent with previous reports. Our measurements show that not only the field-polarised phase but also the helical ground state are made up of ferrimagnetic clusters instead of individual spins. These clusters are distorted Cu tetrahedra, where the spin on one Cu ion is anti-aligned with the spin on the three other Cu ions.

We present an investigation into the structural and magnetic properties of Zn-substituted Cu$_{2}$OSeO$_{3}$, a system in which the skyrmion lattice (SkL) phase in the magnetic field-temperature phase diagram was previously seen to split as a function of increasing Zn concentration. We find that splitting of the SkL is only observed in polycrystalline samples and reflects the occurrence of several coexisting phases with different Zn content, each distinguished by different magnetic behaviour. No such multiphase behaviour is observed in single crystal samples., Comment: 5 pages, 6 figures, includes supplemental material

We present the results of resonant x-ray scattering measurements and electronic structure calculations on the monoarsenide FeAs. We elucidate details of the magnetic structure, showing the ratio of ellipticity of the spin helix is larger than previously thought, at 2.58(3), and reveal both a right-handed chirality and an out of plane component of the magnetic moments in the spin helix. We find that electronic structure calculations and analysis of the spin-orbit interaction are able to qualitatively account for this canting., Comment: 11 pages, 12 Figures

Inverse melting refers to the rare thermodynamic phenomenon in which a solid melts into a liquid upon cooling, a transition that can occur only when the ordered (solid) phase has more entropy than the disordered (liquid) phase, and that has so far only been observed in a handful of systems. Here we report the first experimental observation for the inverse melting of an electronic liquid crystalline order in strontium-doped lanthanum nickelate, a compound isostructural with the superconducting cuprates, with a hole doping concentration of 1/3. Using x-ray scattering, we demonstrate that the isotropic charge modulation is driven to nematic order by fluctuating spins and shows an inverse melting transition. Using a phenomenological Landau theory, we show that this inverse melting transition is due to the interlayer coupling between the charge and spin orders. This discovery points to the importance of the interlayer correlations in the system, and provides a new perspective to study the intricate nature of the electronic liquid crystal phases in strongly correlated electronic systems, including possibly the Cu- and Fe-based high-Tc superconductors., Comment: 7 pages, 7 figures

We present the results of transverse field (TF) muon-spin rotation (muSR) measurements on Cu2OSeO3, which has a skyrmion lattice (SL) phase. We measure the response of the TF muSR signal in that phase along with the surrounding ones, and suggest how the phases might be distinguished using the results of these measurements. Dipole field simulations support the conclusion that the muon is sensitive to the SL via the TF lineshape and, based on this interpretation, our measurements suggest that the SL is quasistatic on a timescale tau > 100 ns., Comment: 8 pages, 8 figures, version 4, corrected typos, increased typeface size on figures

Through powder x-ray diffraction we have investigated the structural behavior of SmVO3, in which orbital and magnetic degrees of freedom are believed to be closely coupled to the crystal lattice. We have found, contrary to previous reports, that SmVO3 exists in a single, monoclinic, phase below 200 K. The associated crystallographic distortion is then stabilized through the magnetostriction that occurs below 134 K. The crystal structure has been refined using synchrotron x-ray powder diffraction data measured throughout the structural phase diagram, showing a substantial Jahn-Teller distortion of the VO6 octahedra in the monoclinic phase, compatible with the expected G-type orbital order. Changes in the vanadium ion crystal field due to the structural and magnetic transitions have then been probed by resonant x-ray diffraction., Comment: Published in Physical Review B

In multiferroic TbMn$_2$O$_5$, the behavior of the terbium ions forms a crucial part of the magneto-electric coupling. The result is a magnetically induced reversal of the electric polarization at 2 T. In this article we present the first direct measurement of the terbium magnetic structure under applied magnetic fields. Contrary to the current interpretation of the magnetic properties of \tmo, we show that upon the electric polarization reversal the terbium sub-lattice adopts a canted antiferromagnetic structure with a large component of magnetic moment parallel to the \textit{a}-axis. Furthermore, we provide evidence for a coupling between the manganese 3d magnetic structure and the terbium $4f$ magnetism, which is of great significance in the elusive magneto-electric mechanisms at play., Comment: 4 pages, 3 figures

Two members of the iso-structural R$_2$CoGa$_8$ inter-metallic series, Er$_2$CoGa$_8$ and Tm$_2$CoGa$_8$, have been studied by powder neutron diffraction. Antiferromagnetic ordering of the rare-earth sublattices was confirmed to occur at 3.0 K and 2.0 K, respectively. Furthermore, determination of the critical exponent showed Er$_2$CoGa$_8$ to adopt a 3D universality class. In spite of a common magnetic easy axis and similar structural characteristics, the antiferromagnetic structures were found to be different for the erbium and thulium based compounds. The corresponding magnetic space groups were determined to be $P_{2a}mmm'$ and $P_Cmmm$. The difference in magnetic structures is discussed based on crystal electric field effects that are known to be prevalent in such materials., Comment: 6 pages, 4 figures, 3 tables

We introduce a 3D porous photonic crystal whose inner surfaces are chemically functionalized in arbitrary spatial patterns with micro-scale resolution. We use this platform to demonstrate pattern-formation., Comment: 2 pages, 1 figure

We report the design and construction of a novel soft x-ray diffractometer installed at Diamond Light Source. The beamline endstation RASOR is constructed for general users and designed primarily for the study of single crystal diffraction and thin film reflectivity. The instrument is comprised of a limited three circle ({\theta}, 2{\theta}, {\chi}) diffractometer with an additional removable rotation ({\phi}) stage. It is equipped with a liquid helium cryostat, and post-scatter polarization analysis. Motorised motions are provided for the precise positioning of the sample onto the diffractometer centre of rotation, and for positioning the centre of rotation onto the x-ray beam. The functions of the instrument have been tested at Diamond Light Source, and initial test measurements are provided, demonstrating the potential of the instrument., Comment: 10 pages, 9 figures

We report the direct measurement of antiferromagnetic spin polarization at the oxygen sites in the multiferroic TbMn2O5, through resonant soft x-ray magnetic scattering. This supports recent theoretical models suggesting that the oxygen spin polarization is key to the magnetoelectric coupling mechanism. The spin polarization is observed through a resonantly enhanced diffraction signal at the oxygen K edge at the commensurate antiferromagnetic wavevector. Using the fdmnes code we have accurately reproduced the experimental data. We have established that the resonance arises through the spin polarization on the oxygen sites hybridized with the square based pyramid Mn3+ ions. Furthermore we have discovered that the position of the Mn3+ ion directly influences the oxygen spin polarization., Comment: 5 pages, 4 figures

The magnetic structures which endow TbMnO$_3$ with its multiferroic properties have been reassessed on the basis of a comprehensive soft x-ray resonant scattering (XRS) study. The selectivity of XRS facilitated separation of the various contributions (Mn $L_2$ edge, Mn 3d moments; Tb M$_4$ edge, Tb 4f moments), while its variation with azimuth provided information on the moment direction of distinct Fourier components. When the data are combined with a detailed group theory analysis, a new picture emerges of the ferroelectric transition at 28 K. Instead of being driven by the transition from a collinear to a non-collinear magnetic structure, as has previously been supposed, it is shown to occur between two non-collinear structures., Comment: Submitted to Physical Review Letters

Magnetite, Fe$_3$O$_4$, displays a highly complex low temperature crystal structure that may be charge and orbitally ordered. Many of the recent experimental claims of such ordering rely on resonant soft x-ray diffraction at the oxygen K and iron L edges. We have re-examined this system and undertaken soft x-ray diffraction experiments on a high-quality single crystal. Contrary to previous claims in the literature, we show that the intensity observed at the Bragg forbidden (001/2)$_c$ reflection can be explained purely in terms of the low-temperature structural displacements around the resonant atoms. This does not necessarily mean that magnetite is not charge or orbitally ordered, but rather that the present sensitivity of resonant soft x-ray experiments does not allow conclusive demonstration of such ordering., Comment: 5 pages, 3 figures

Soft X-ray resonant scattering (XRS) has been used to observe directly, for the first time, the ordering of localized electronic states on both the Mn and Tb sites in multiferroic TbMnO$_3$. Large resonant enhancement of the X-ray scattering cross-section were observed when the incident photon energy was tuned to either the Mn $L$ or Tb $M$ edges which provide information on the Mn 3d and Tb $4f$ electronic states, respectively. The temperature dependence of the XRS signal establishes, in a model independent way, that in the high-temperature phase (28 K $\leq$ T $\leq$ 42 K) the Mn 3d sublattices displays long-range order. The Tb $4f$ sublattices are found to order only on entering the combined ferroelectric/magnetic state below 28 K. Our results are discussed with respect to recent hard XRS experiments (sensitive to spatially extended orbitals) and neutron scattering., Comment: 9 pages, paper has been accepted for publication in Journal of Physics: Condensed Matter as a fast track communication