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Skyrmions have been proposed as new information carriers in racetrack memory devices. To realise such devices, a small size; high speed of propagation; and minimal skyrmion Hall angle are required. Synthetic antiferromagnets (SAFs) present the ideal materials system to realise these aims. In this work, we use micromagnetic simulations to propose a new method for manipulating them using exclusively global magnetic fields. An out-of-plane microwave field induces oscillations in the skyrmions radius which in turn emits spin waves. When a static in-plane field is added, this breaks the symmetry of the skyrmions and causes asymmetric spin wave emission. This in turn drives motion of the skyrmions, with the fastest velocities observed at the frequency of the intrinsic out-of-phase breathing mode of the pair of skyrmions. This behaviour is investigated over a range of experimentally realistic antiferromagnetic interlayer exchange coupling strengths, and the results compared to previous works studying similar motion driven with an oscillating electric field. Through this the true effect of varying the exchange coupling strength is determined, and greater insight is gained into the mechanism of skyrmion motion. These results will help to inform the design of future novel computing architectures based on the dynamics of skyrmions in synthetic antiferromagnets.

An antiferromagnet emits spin currents when time-reversal symmetry is broken. This is typically achieved by applying an external magnetic field below and above the spin-flop transition or by optical pumping. In this work we apply optical pump-THz emission spectroscopy to study picosecond spin pumping from metallic FeRh as a function of temperature. Intriguingly we find that in the low-temperature antiferromagnetic phase the laser pulse induces a large and coherent spin pumping, while not crossing into the ferromagnetic phase. With temperature and magnetic field dependent measurements combined with atomistic spin dynamics simulations we show that the antiferromagnetic spin-lattice is destabilised by the combined action of optical pumping and picosecond spin-biasing by the conduction electron population, which results in spin accumulation. We propose that the amplitude of the effect is inherent to the nature of FeRh, particularly the Rh atoms and their high spin susceptibility. We believe that the principles shown here could be used to produce more effective spin current emitters. Our results also corroborate the work of others showing that the magnetic phase transition begins on a very fast picosecond timescale, but this timescale is often hidden by measurements which are confounded by the slower domain dynamics.

In synthetic antiferromagnets (SAFs) the combination of antiferromagnetic order and synthesis using conventional sputtering techniques is combined to produce systems that are advantageous for spintronics applications. Here we present the preparation and study of SAF multilayers possessing both perpendicular magnetic anisotropy and the Dzyaloshinskii-Moriya interaction. The multilayers have an antiferromagnetically (AF) aligned ground state but can be forced into a full ferromagnetic (FM) alignment by applying an out-of-plane field $\sim 100$~mT. We study the spin textures in these multilayers in their ground state as well as around the transition point between the AF and FM states, at fields $\sim 40$~mT, by imaging the spin textures using complementary methods: photo-emission electron, magnetic force, and Lorentz transmission electron microscopies. The transformation into a FM state by field proceeds by a nucleation and growth process, where first skyrmionic nuclei form, which broaden into regions containing a FM-aligned labyrinth pattern that eventually occupies the whole film. This process remarkably occurs without any significant change in the net magnetic moment of the multilayer. The mix of AF- and FM-aligned regions on the micron scale in the middle of this transition is reminiscent of a first-order phase transition that exhibits phase coexistence. These results are important for guiding the design of spintronic devices using chiral magnetic textures made from SAFs.

Synthetic antiferromagnets have great potential as skyrmion carriers in which new properties are expected for these spin textures, owing to changed magnetostatics and the absence of net topological charge. Here we numerically simulate the static and dynamic behaviour of skyrmions in these systems and clearly highlight the benefits compared to ferromagnetic single layers. In particular, our results show a reduction of the skyrmion radius, an increase of their velocity under current, and a vanishing of their topological deflection. We also provide a robust and straightforward analytical model that captures the physics of such skyrmions. Finally, by extending the model to the case of an unbalanced SAF, we show some conditions for the system that optimise the properties of the skyrmion for potential spintronic devices.

N\'eel magnetic domain walls that are stabilized by achiral energy terms instead of the usual Dzyaloshinskii-Moriya interaction will be bistable, with the two possible chiral forms being degenerate. Here we focus on the theoretical study of the spin-orbit torque driven dynamics of such bistable N\'eel domain walls. We find that, for a given domain wall, two propagation directions along a nanowire are possible, depending on its initial state. These dynamics also exhibit complex dependence on the spin-orbit torque magnitude, leading to important transient regimes. Finally, a few ways are proposed for controlled or random reversal of the domain wall propagation direction. A robust analytical model which handles all the observed behaviors of such domain walls is developed and validated by comparing with numerical simulations. The obtained new dynamics open the way for new uses of domain walls in information storage and processing devices.

Skyrmions are small topologically protected magnetic structures that hold promise for applications from data storage to neuromorphic computing and they have been shown to possess internal microwave frequency excitations. Skyrmions in a synthetic antiferromagnet have been predicted to be smaller and faster than their ferromagnetic equivalents, and also shown to possess more internal modes. In this work we consider the breathing modes of skyrmions in a four repetition synthetic antiferromagnetic multilayer by means of micromagnetic simulations and examine the further splitting of the modes into different arrangements of out-of-phase and in-phase modes. This results in a lowering of frequencies which is promising for skyrmion sensing applications in a synthetic antiferromagnet., Comment: 6 pages, 4 figures

We use spin polarized low energy electron microscopy to investigate domain pattern transfer in a multiferroic heterostructure consisting of a $(111)$-oriented BaTiO$_{\mathrm{3}}$ substrate and an epitaxial Ni film. After in-situ thin film deposition and annealing through the ferroelectric phase transition, interfacial strain transfer from ferroelastic domains in the substrate and inverse magnetostriction in the magnetic thin film introduce a uniaxial in-plane magnetic anisotropy that rotates by $60^{\circ}$ between alternating stripe regions. We show that two types of magnetic domain wall can be initialized in principle. Combining experimental results with micromagnetic simulations we show that a competition between the exchange and magnetostatic energies in these domain walls have a strong influence on the magnetic domain configuration.

We report on domain pattern transfer from a ferroelectric BaTiO$_{\mathrm{3}}$ substrate with a $(111)$-orientation of the surface to an epitaxial Co film grown on a Pd buffer layer. Spatially modulated interfacial strain transfer from ferroelectric/ferroelastic domains and inverse magnetostriction in the ferromagnetic film induce stripe regions with a modulation of the in-plane uniaxial magnetic anisotropy direction. Using spin-polarized low energy electron microscopy, we observe the formation of two distinct anisotropy configurations between stripe regions. Moreover, through application of a magnetic field parallel or perpendicular to these stripes, head-to-head or head-to-tail magnetization configurations are initialized. This results in four distinct magnetic domain wall types associated with different energies and widths, which in turn affects whether domain pattern transfer can be achieved.

Here we review various themes of current research within mesoscopic magnetic systems., Comment: APL Special Topic Guest Editorial

Here we study the effect of an additional interfacial spin-transfer torque, as well as the well established spin-orbit torque and bulk spin-transfer torque, on skyrmion collections - group of skyrmions dense enough that they are not isolated from on another - in ultrathin heavy metal / ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show the experimental results are in good agreement with modelling when including the interfacial spin-transfer torque, and cannot be reproduced by using the spin-orbit torque alone. We also show that for skyrmion collections the velocity is approximately independent of diameter, in marked contrast to the motion of isolated skyrmions, as the group of skyrmions move together at an average group velocity. Moreover, the calculated skyrmion velocities are comparable to those obtained in experiments when the interfacial spin-transfer torque in included, whilst modelling using the spin-orbit torque alone shows large discrepancies with the experimental data. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which is of similar strength to the spin-orbit torque, and both significantly larger than the bulk spin-transfer torque. Due to the good agreement with experiments, we conclude that the interfacial spin-transfer torque should be included in numerical modelling for correct reproduction of experimental results., Comment: 25pages, 5 figures

It has been shown previously that the presence of a Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films stabilizes N\'eel type domain walls. We demonstrate, using micromagnetic simulations and analytical modeling, that the presence of a uniaxial in-plane magnetic anisotropy can also lead to the formation of N\'eel walls in the absence of a Dzyaloshinskii-Moriya interaction. It is possible to abruptly switch between Bloch and N\'eel walls via a small modulation of both the in-plane, but also the perpendicular magnetic anisotropy. This opens up a route towards electric field control of the domain wall type with small applied voltages through electric field controlled anisotropies.

The Dzyaloshinskii-Moriya interaction (DMI), being one of the origins of chiral magnetism, is currently attracting considerable attention in the research community focusing on applied magnetism and spintronics. For future applications, an accurate measurement of its strength is indispensable. Here we present a review of the state-of-the-art of measuring the coefficient of the Dzyaloshinskii-Moriya interaction, the DMI constant $D$, focusing on systems where the interaction arises from the interface between two materials (i.e. interfacial DMI). We give an overview of the experimental techniques as well as their theoretical background and models for the quantification of the DMI constant. The measurement techniques are divided into three categories: a) domain wall-based measurements, b) spin wave-based measurements and c) spin-orbit torque-based measurements. We analyze the advantages and disadvantages of each method and compare $D$ values at different interfaces. The review aims to obtain a better understanding of the applicability of the different techniques to various stacks and of the origin of apparent disagreements among literature values., Comment: 60 pages, 29 figures; Version 3

Spin crossover (SCO) molecules are promising bi-stable magnetic switches with applications in molecular spintronics. However, little is known about the switching effects of a single SCO molecule when it is confined between two metal electrodes. Here we examine the switching properties of a [Fe(III)(EtOSalPet )(NCS)] SCO molecule that is specifically tailored for surface deposition and binding to only one gold electrode in a nanogap device. Temperature dependent conductivity measurements on SCO molecule containing electromigrated gold break junctions show voltage independent telegraphic-like switching between two resistance states at temperature below 200 K. The transition temperature is very different from the transition temperature of 83 K that occurs in a bulk film of the same material. This indicates that the bulk, co-operative SCO phenomenon is no longer preserved for a single molecule and that the surface interaction drastically increases the temperature of the SCO phenomenon. Another key finding of this work is that some devices show switching between multiple resistance levels. We propose that in this case, two SCO molecules are present within the nanogap with both participating in the electronic transport and switching., Comment: 13 pages, 4 figures, supplementary information (5 pages, 5 figures)

The phase coexistence present through a first-order phase transition means there will be finite regions between the two phases where the structure of the system will vary from one phase to the other, known as a phase boundary wall. This region is said to play an important but unknown role in the dynamics of the first-order phase transitions. Here, by using both x-ray photon correlation spectroscopy and magnetometry techniques to measure the temporal isothermal development at various points through the thermally activated first-order metamagnetic phase transition present in the near-equiatomic FeRh alloy, we are able to isolate the dynamic behavior of the domain walls in this system. These investigations reveal that relaxation behavior of the domain walls changes when phase coexistence is introduced into the system and that the domain wall dynamics is different to the macroscale behavior. We attribute this to the effect of the exchange coupling between regions of either magnetic phase changing the dynamic properties of domain walls relative to bulk regions of either phase. We also believe this behavior comes from the influence of the phase boundary wall on other magnetic objects in the system., Comment: Main Paper: 13 pages, 8 figures. Supplementary information: 13 pages, 8 figures

To advance the use of thermally-activated magnetic materials in device applications it is necessary to examine their behaviour on the localised scale in operando conditions. Equi-atomic FeRh undergoes a magnetostructural transition from an antiferromagnetic (AF) to a ferromagnetic (FM) phase above room temperature (~ 75 to 105 {\deg}C) and hence is considered a very desirable material for the next generation of novel nanomagnetic or spintronic devices. For this to be realised, we must fully understand the intricate details of AF to FM transition and associated FM domain growth on the scale of their operation. Here we combine in-situ heating with a comprehensive suite of advanced transmission electron microscopy techniques to investigate directly the magnetostructural transition in nano-scale FeRh thin films. Differential phase contrast imaging visualizes the stages of FM domain growth in both cross-sectional and planar FeRh thin films as a function of temperature. Small surface FM signals are also detected due to interfacial strain with the MgO substrate and Fe deficiency after HF etching of the substrate, providing a directional bias for FM domain growth. Our work provides high resolution imaging and quantitative measurements throughout the transition, which were previously inaccessible, and offers new fundamental insight into their potential use in magnetic devices.

Rotating all islands in square artificial spin ice (ASI) uniformly about their centres gives rise to the recently reported pinwheel ASI. At angles around 45$^\mathrm{o}$, the antiferromagnetic ordering changes to ferromagnetic and the magnetic configurations of the system exhibit near-degeneracy, making it particularly sensitive to small perturbations. We investigate through micromagnetic modelling the influence of dipolar fields produced by physically extended islands in field-driven magnetisation processes in pinwheel arrays, and compare the results to hysteresis experiments performed in-situ using Lorentz transmission electron microscopy. We find that magnetisation end-states induce a Heisenberg pseudo-exchange interaction that governs both the inter-island coupling and the resultant array reversal process. Symmetry reduction gives rise to anisotropies and array-corner mediated avalanche reversals through a cascade of nearest-neighbour (NN) islands. The symmetries of the anisotropy axes are related to those of the geometrical array but are misaligned to the array axes as a result of the correlated interactions between neighbouring islands. The NN dipolar coupling is reduced by decreasing the island size and, using this property, we track the transition from the strongly coupled regime towards the pure point dipole one and observe modification of the ferromagnetic array reversal process. Our results shed light on important aspects of the interactions in pinwheel ASI, and demonstrate a mechanism by which their properties may be tuned for use in a range of fundamental research and spintronic applications., Comment: 14 pages, 13 figures; post revision

Magnetic skyrmions are topologically non-trivial nanoscale objects. Their topology, which originates in their chiral domain wall winding, governs their unique response to a motion-inducing force. When subjected to an electrical current, the chiral winding of the spin texture leads to a deflection of the skyrmion trajectory, characterized by an angle with respect to the applied force direction. This skyrmion Hall angle was believed to be skyrmion diameter-dependent. In contrast, our experimental study finds that within the plastic flow regime the skyrmion Hall angle is diameter-independent. At an average velocity of 6 $\pm$ 1 m/s the average skyrmion Hall angle was measured to be 9{\deg} $\pm$ 2{\deg}. In fact, in the plastic flow regime, the skyrmion dynamics is dominated by the local energy landscape such as materials defects and the local magnetic configuration.

The B2-ordered alloy FeRh shows a metamagnetic phase transition, transforming from antiferromagnetic (AF) to ferromagnetic (FM) order at a temperature $T_\mathrm{t} \sim 380 $~K in bulk. As well as temperature, the phase transition can be triggered by many means such as strain, chemical doping, or magnetic or electric fields. Its first-order nature means that phase coexistence is possible. Here we show that a phase boundary in a 300~nm diameter nanopillar, controlled by a doping gradient during film growth, is moved by an electrical current in the direction of electron flow. We attribute this to spin injection from one magnetically ordered phase region into the other driving the phase transition in a region just next to the phase boundary. The associated change in resistance of the nanopillar shows memristive properties, suggesting potential applications as memory cells or artificial synapses in neuromorphic computing schemes.

Magnetic skyrmions are topological solitons that exhibit an increased stability against annihilation, and can be displaced with low current densities, making them a promising candidate as an information carrier. In order to demonstrate a viable skyrmion-based memory device, it is necessary to reliably and reproducibly nucleate, displace, detect, and delete the magnetic skyrmions. While the skyrmion displacement and detection have both been investigated in detail, much less attention has been dedicated to the study of the sub-ns dynamics of the skyrmion nucleation process. Only limited studies on the statics and above-ns dynamics have been performed, leaving still many open questions on the dynamics of the nucleation process. Furthermore, the vast majority of the presently existing studies focus on the nucleation from random natural pinning sites, or from patterned constrictions in the magnetic material itself, which limit the functionality of the skyrmion-based device. Those limitations can be overcome by the fabrication of a dedicated injector device on top of the magnetic material. In this study, we investigate the nucleation of magnetic skyrmions from a dedicated nano-engineered injector, demonstrating the reliable magnetic skyrmion nucleation at the remnant state. The sub-ns dynamics of the skyrmion nucleation process were also investigated, allowing us to shine light on the physical processes driving the nucleation.

We report on the time-resolved investigation of current- and field-induced domain wall motion in perpendicularly magnetized microwires exhibiting asymmetric exchange interaction by means of scanning transmission x-ray microscopy using a time step of 200 ps. Dynamical domain wall velocities on the order of 50-100 m s$^{-1}$ were observed. The improvement in the temporal resolution allowed us to observe the absence of incubation times for the motion of the domain wall, together with indications for a negligible inertia. Furthermore, we observed that, for short current and magnetic field pulses, the magnetic domain walls do not exhibit a tilting during its motion, providing a mechanism for the fast, tilt-free, motion of magnetic domain walls.

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is important for chiral domain walls (DWs) and for stabilizing magnetic skyrmions. We study the effects of introducing increasing thicknesses of Ir, from zero to 2 nm, into a Pt/Co/Ta multilayer between the Co and Ta. We observe a marked increase in magnetic moment, due to the suppression of the dead layer at the interface with Ta, but the perpendicular anisotropy is hardly affected. All samples show a universal scaling of the field-driven domain wall velocity across the creep and depinning regimes. Asymmetric bubble expansion shows that DWs in all of the samples have the left-handed N\'{e}el form. The value of in-plane field at which the creep velocity shows a minimum drops markedly on the introduction of Ir, as does the frequency shift of the Stokes and anti-Stokes peaks in Brillouin light scattering measurements. Despite this qualitative similarity, there are quantitative differences in the DMI strength given by the two measurements, with BLS often returning higher values. Many features in bubble expansion velocity curves do not fit simple models commonly used to date, namely a lack of symmetry about the velocity minimum and no difference in velocities at high in-plane field. These features are explained by the use of a model in which the depinning field is allowed to vary with in-plane field in a way determined from micromagnetic simulations. This theory shows that velocity minimum underestimates the DMI field, consistent with BLS returning higher values. Our results suggest that the DMI at an Ir/Co interface has the same sign as the DMI at a Pt/Co interface.

Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects., Comment: 10 pages, 5 figures

Chiral domain walls in ultrathin perpendicularly magnetised layers have a N\'{e}el structure stabilised by a Dzyaloshinskii-Moriya interaction (DMI) that is generated at the interface between the ferromagnet and a heavy metal. Different heavy metals are required above and below a ferromagnetic film in order to generate the structural inversion asymmetry needed to ensure that the DMI arising at the two interfaces does not cancel. Here we report on the magnetic properties of epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers grown by sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0 to 1 a structural inversion asymmetry is generated. We characterise the epilayer structure with x-ray diffraction and cross-sectional transmission electron microscopy, revealing (111) stacking. The saturation magnetization falls as the proximity magnetisation in Pt is reduced, whilst the perpendicular magnetic anisotropy $K_\mathrm{u}$ rises. The micromagnetic DMI strength $D$ was determined using the bubble expansion technique and also rises from a negligible value when $x=0$ to $\sim 1$ mJ/m$^2$ for $x = 1$. The depinning field at which field-driven domain wall motion crosses from the creep to the depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater spatial fluctuations of the domain wall energy with increasing Au concentration. Meanwhile, the increase in DMI causes the Walker field to rise from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x = 1$ sample is the steady flow regime accessible. The full dependence of domain wall velocity on driving field bears little resemblance to the prediction of a simple one-dimensional model, but can be described very well using micromagnetic simulations with a realistic model of disorder. These reveal a rise in Gilbert damping as $x$ increases.

For over ten years, arrays of interacting single-domain nanomagnets, referred to as artificial spin ices, have been engineered with the aim to study frustration in model spin systems. Here, we use Fresnel imaging to study the reversal process in 'pinwheel' artificial spin ice, a modified square ASI structure obtained by rotating each island by some angle about its midpoint. Our results demonstrate that a simple 45{\deg} rotation changes the magnetic ordering from antiferromagnetic to ferromagnetic, creating a superferromagnet which exhibits mesoscopic domain growth mediated by domain wall nucleation and coherent domain propagation. We observe several domain-wall configurations, most of which are direct analogues to those seen in continuous ferromagnetic films. However, novel charged walls also appear due to the geometric constraints of the system. Changing the orientation of the external magnetic field allows control of the nature of the spin reversal with the emergence of either 1-D or 2-D avalanches. This unique property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.

Antiferromagnetic materials present us with rich and exciting physics, which we can exploit to open new avenues in spintronic device applications. We explore perpendicularly magnetized exchange biased systems of Pt/Co/IrMn and Pt/Co/FeMn, where the crossover from paramagnetic to antiferromagnetic behavior in the IrMn and FeMn layers is accessed by varying the thickness. We demonstrate, through magneto-optical imaging, that the magnetic domain morphology of the ferromagnetic Co layer is influenced by the N${\'e}$el order of the antiferromagnet (AFM) layers. We relate these variations to the anisotropy energy of the AFM layer and the ferromagnet-antiferromagnet (FM-AFM) inter-layer exchange coupling. We also quantify the interfacial Dzyaloshinskii-Moriya interaction (DMI) in these systems by Brillouin light scattering spectroscopy. The DMI remains unchanged, within experimental uncertainty, for different phases of the AFM layers, which allows us to conclude that the DMI is largely insensitive to both AFM spin order and exchange bias. Understanding such fundamental mechanisms is crucial for the development of future devices employing chiral spin textures, such as N${\'e}$el domain walls and skyrmions, in FM-AFM heterostructures.

Epitaxial films of the B20-structure alloy Fe$_{1-y}$Co$_y$Ge were grown by molecular beam epitaxy on Si (111) substrates. The magnetization varied smoothly from the bulk-like values of one Bohr magneton per Fe atom for FeGe to zero for non-magnetic CoGe. The chiral lattice structure leads to a Dzyaloshinskii-Moriya interaction (DMI), and the films' helical magnetic ground state was confirmed using polarized neutron reflectometry measurements. The pitch of the spin helix, measured by this method, varies with Co content $y$ and diverges at $y \sim 0.45$. This indicates a zero-crossing of the DMI, which we reproduced in calculations using first principle methods. We also measured the longitudinal and Hall resistivity of our films as a function of magnetic field, temperature, and Co content $y$. The Hall resistivity is expected to contain contributions from the ordinary, anomalous, and topological Hall effects. Both the anomalous and topological Hall resistivities show peaks around $y \sim 0.5$. Our first principles calculations show a peak in the topological Hall constant at this value of $y$, related to the strong spin-polarisation predicted for intermediate values of $y$. Half-metallicity is predicted for $y = 0.6$, consistent with the experimentally observed linear magnetoresistance at this composition. Whilst it is possible to reconcile theory with experiment for the various Hall effects for FeGe, the large topological Hall resistivities for $y \sim 0.5$ are much larger then expected when the very small emergent fields associated with the divergence in the DMI are taken into account.

Artificial spin ices (ASI) are arrays of single domain nano-magnetic islands, arranged in geometries that give rise to frustrated magnetostatic interactions. It is possible to reach their ground state via thermal annealing. We have made square ASI using different FePd alloys to vary the magnetization via co-sputtering. From a polarized state the samples were incrementally heated and we measured the vertex population as a function of temperature using magnetic force microscopy. For the higher magnetization FePd sample, we report an onset of dynamics at $T = 493$ K, with a rapid collapse into $>90\%$ ground state vertices. In contrast, the low magnetization sample started to fluctuate at lower temperatures, $T = 393$ K and over a wider temperature range but only reached a maximum of $25\%$ of ground state vertices. These results indicate that the interaction strength, dynamic temperature range and pathways can be finely tuned using a simple co-sputtering process. In addition we have compared our experimental values of the blocking temperature to those predicted using the simple N\'{e}el-Brown two-state model and find a large discrepancy which we attribute to activation volumes much smaller than the island volume., Comment: 10 pages, 6 figures

Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements, provides a fascinating opportunity to observe the physics of out of equilibrium systems. Initial studies concentrated on the static, frozen state, whilst more recent studies have accessed the out-of-equilibrium dynamic, fluctuating state. This opens up exciting possibilities such as the observation of systems exploring their energy landscape through monopole quasiparticle creation, potentially leading to ASI magnetricity, and to directly observe unconventional phase transitions. In this work we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. We have investigated the effect of the interaction strength on the magnetization dynamics at different temperatures in the range where the nanomagnets are thermally active and have observed that they follow an Arrhenius-type N\'eel-Brown behaviour. An unexpected negative correlation of the average blocking temperature with the interaction strength is also observed, which is supported by Monte Carlo simulations. The magnetization relaxation measurements show faster relaxation for more strongly coupled nanoelements with similar dimensions. The analysis of the stretching exponents obtained from the measurements suggest 1-D chain-like magnetization dynamics. This indicates that the nature of the interactions between nanoelements lowers the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to quantify the effective interaction energy of a square ASI system, and compare it to the interaction energy calculated from a simple dipole model and also to the magnetostatic energy computed with micromagnetic simulations.

Magnetic skyrmions are knot-like quasiparticles. They are candidates for non-volatile data storage in which information is moved between fixed read and write terminals. Read-out operation of skyrmion-based spintronic devices will rely upon electrical detection of a single magnetic skyrmion within a nanostructure. Here, we present Pt/Co/Ir nanodiscs which support skyrmions at room temperature. We measured the Hall resistivity whilst simultaneously imaging the spin texture using magnetic scanning transmission x-ray microscopy (STXM). The Hall resistivity is correlated to both the presence and size of the skyrmion. The size-dependent part matches the expected anomalous Hall signal when averaging the magnetisation over the entire disc. We observed a resistivity contribution which only depends on the number and sign of skyrmion-like objects present in the disc. Each skyrmion gives rise to 22$\pm$2 n{\Omega} cm irrespective of its size. This contribution needs to be considered in all-electrical detection schemes applied to skyrmion-based devices., Comment: 13 pages, 3 figures

We have created and studied artificial magnetic quasicrystals based on Penrose tiling patterns of interacting nanomagnets that lack the translational symmetry of spatially periodic artificial spin ices. Vertex-level degeneracy and frustration induced by the network topology of the Penrose pattern leads to a low energy configuration that we propose as a ground state. Topologically induced emergent frustration means that this ground state cannot be constructed from vertices in their ground states. It has two parts, a quasi-one-dimensional rigid "skeleton" that spans the entire pattern and is capable of long-range order, and "flippable" clusters of macrospins within it. These lead to macroscopic degeneracy for the array as a whole. Magnetic force microscopy imaging of Penrose tiling arrays revealed superdomains that are larger for more strongly coupled arrays. The superdomain size is larger after AC-demagnetisation and especially after annealing the array above its blocking temperature.

Collective spin ensembles known as skyrmion bubbles can exist in ultrathin magnetic film heterostructures and promise miniscule diameters and low-power all-electrical manipulation. The nucleation, identification and manipulation of skyrmions is of great interest, in part, because of their non-trivial topology. Here we ascertain the topology of 100 nm isolated hedgehog skyrmion bubbles and probe their response to external fields at room temperature in [ Pt \ Co (0.8 nm) \ Ir ] films. We find that structural disorder can stabilize skyrmion bubble states which exhibit creep-like domain wall motion. This makes the extraction of DMI from observations difficult and could explain the larger than predicted bubble sizes observed in interfacial DMI films. Intriguingly, we report on a critical size for hedgehog skyrmions, above which the bubbles lose circular symmetry and take up an irregular shape. Combining Lorentz TEM and fully three dimensional multi-layered simulations, we demonstrate the unique behavior of these topologically non-trivial spin textures., Comment: 12 pages, 5 figures

Under the correct conditions, Dzyaloshinskii-Moriya interactions (DMI) can lead to topologically protected spin textures such as skyrmions. The application of DMI for spin-based computation and memory technologies is promising and requires a detailed consideration of the role intrinsic energies have on stabilizing the diverse textures observed thus far. Here we experimentally investigate the effect of dipolar energy from interlayer coupling on the remanent spin textures found at room temperature for interfacial DMI multilayers of [ Pt \ Co \ Ir ]$_{\times N}$. The total dipolar energy is modified by increasing the number of layer repetitions N which result in different phases of chiral magnetic textures. We use the phase transitions to estimate the DMI energy present in the ultrathin films to be D = 2.1 $\pm$ 0.1 mJ m$^{-2}$. Unlike traditional perpendicular magnetic anisotropy films, these multilayer films with finite DMI exhibit isolated hedgehog skyrmion bubbles as well as sub 100 nm labyrinth domains with cycloidal homochiral N\'eel walls which are dependent on DMI as well as the total dipolar energy., Comment: 10 pages, 5 figures

We study the effect of sputter-deposition conditions, namely substrate temperature and chamber base pressure, upon the interface quality of epitaxial Pt/Co/Pt thin films with perpendicular magnetic anisotropy. Here we define interface quality to be the inverse of the sum in quadrature of roughness and intermixing. We find that samples with the top Co/Pt layers grown at 250 degrees C exhibit a local maximum in roughness-intermixing and that the interface quality is better for lower or higher deposition temperatures, up to 400 degrees C, above which the interface quality degrades. Imaging the expansion of magnetic domains in an in-plane field using wide-field Kerr microscopy, we determine the interfacial Dzyaloshinskii-Moriya interaction (DMI) in films in the deposition temperature range 100 degrees C to 300 degrees C. The net DMI is linked to the difference in top and bottom Co interface qualities; the net DMI increases as the difference between top and bottom Co interface quality increases. Furthermore, for sufficiently low base pressures, the net DMI increases linearly with the deposition temperature, indicating that fine-tuning of the DMI may be achieved via the deposition conditions., Comment: 8 pages, 9 figures

In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetisation energy contribution or ignoring the magnetisation variation in the out-of-film direction - although not changing the eigenmode's magnetisation dynamics significantly - changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures., Comment: manuscript: 17 pages, 9 figures; supplementary information: 10 pages, 8 figures

Domain walls in ferromagnetic nanowires are potential building-blocks of future technologies such as racetrack memories, in which data encoded in the domain walls are transported using spin-polarised currents. However, the development of energy-efficient devices has been hampered by the high current densities needed to initiate domain wall motion. We show here that a remarkable reduction in the critical current density can be achieved for in-plane magnetised coupled domain walls in CoFe/Ru/CoFe synthetic ferrimagnet tracks. The antiferromagnetic exchange coupling between the layers leads to simple N\'{e}el wall structures, imaged using photoemission electron and Lorentz transmission electron microscopy, with a width of only $\sim 100$~nm. The measured critical current density to set these walls in motion, detected using magnetotransport measurements, is $1.0 \times 10^{11}$~Am$^{-2}$, almost an order of magnitude lower than in a ferromagnetically coupled control sample. Theoretical modelling indicates that this is due to nonadiabatic driving of anisotropically coupled walls, a mechanism that can be used to design efficient domain-wall devices., Comment: Supplmentary Information as ancillary file