Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque.

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 one 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 that inclusion of the interfacial spin-transfer torque results in reduced skyrmion Hall angles, with values close to experimental results. 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 is included. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which helps to explain the low skyrmion Hall angles and velocities observed in experiment. We conclude that the interfacial spin-transfer torque should be considered in numerical modelling for reproduction of experimental results.

Switching between Magnetic Bloch and Néel Domain Walls with Anisotropy Modulations.

It has been shown previously that the presence of a Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films stabilizes Néel 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 Néel walls in the absence of a Dzyaloshinskii-Moriya interaction. It is possible to abruptly switch between Bloch and Néel walls via a small modulation of the in plane, but also the perpendicular, magnetic anisotropy. This opens up a route toward electric field control of the domain wall type with small applied voltages through electric field controlled anisotropies.

Controlled Individual Skyrmion Nucleation at Artificial Defects Formed by Ion Irradiation.

Magnetic skyrmions are particle-like deformations in a magnetic texture. They have great potential as information carriers in spintronic devices because of their interesting topological properties and favorable motion under spin currents. A new method of nucleating skyrmions at nanoscale defect sites, created in a controlled manner with focused ion beam irradiation, in polycrystalline magnetic multilayer samples with an interfacial Dzyaloshinskii-Moriya interaction, is reported. This new method has three notable advantages: 1) localization of nucleation; 2) stability over a larger range of external field strengths, including stability at zero field; and 3) existence of skyrmions in material systems where, prior to defect fabrication, skyrmions were not previously obtained by field cycling. Additionally, it is observed that the size of defect nucleated skyrmions is uninfluenced by the defect itself-provided that the artificial defects are controlled to be smaller than the inherent skyrmion size. All of these characteristics are expected to be useful toward the goal of realizing a skyrmion-based spintronic device. This phenomenon is studied with a range of transmission electron microscopy techniques to probe quantitatively the magnetic behavior at the defects with applied field and correlate this with the structural impact of the defects.

Author Correction: Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Diameter-independent skyrmion Hall angle observed in chiral magnetic multilayers.

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, characterised by an angle with respect to the applied force direction. This skyrmion Hall angle is predicted to be skyrmion diameter-dependent. In contrast, our experimental study finds that the skyrmion Hall angle is diameter-independent for skyrmions with diameters ranging from 35 to 825 nm. At an average velocity of 6 ± 1 ms-1, the average skyrmion Hall angle was measured to be 9° ± 2°. In fact, the skyrmion dynamics is dominated by the local energy landscape such as materials defects and the local magnetic configuration.

Magnetization dynamics of weakly interacting sub-100 nm square artificial spin ices.

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. We have observed that they follow an Arrhenius-type Néel-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 computed with micromagnetic simulations.

Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice.

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.

Deterministic Field-Free Skyrmion Nucleation at a Nanoengineered Injector Device.

Magnetic skyrmions are topological solitons promising for applications as encoders for digital information. A number of different skyrmion-based memory devices have been recently proposed. 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, possibly in the absence of external applied magnetic fields, which would needlessly complicate the device design. While the skyrmion displacement and detection have both been thoroughly investigated, much less attention has been dedicated to the study of the skyrmion nucleation process and its sub-nanosecond dynamics. In this study, we investigate the nucleation of magnetic skyrmions from a dedicated nanoengineered injector, demonstrating the reliable magnetic skyrmion nucleation at the remnant state. The sub-nanosecond dynamics of the skyrmion nucleation process were also investigated, allowing us to shine light on the physical processes driving the nucleation.

Tuning spin-orbit torques at magnetic domain walls in epitaxial Pt/Co/Pt1-x Au x trilayers.

Magnetic domain walls (DWs) in perpendicularly magnetised thin films are attractive for racetrack memories, but technological progress still requires further reduction of the operationing currents. To efficiently drive these objects by the means of electric current, one has to optimize the damping-like torque which is caused by the spin Hall effect (SHE). This not only requires a high net spin Hall angle but also the presence of a Dzyaloshinskii-Moriya interaction (DMI) to produce magnetic textures sensitive to this type of the torque. In this work, we explore the coexistence and importance of these two phenomena in epitaxial Pt/Co/Pt1-x Au x films in which we control the degree of inversion symmetry-breaking between the two interfaces by varying x. Gold is used as a material with negligible induced magnetic moment and SHE and the interface between Co/Au as a source of a small DMI. We find no current-induced DW motion in the symmetric Pt/Co/Pt (x = 0) trilayer. By fitting a one-dimensional model to the DW velocity as a function of drive current density and in-plane applied field in samples with non-zero values of x, we find that both net DMI strength and spin Hall angle rise monotonically as Au is introduced. They reach values of 0.75 ± 0.05 mJ m-2 and 0.10 ± 0.01, respectively, for Pt/Co/Au (x = 1).

Domain-wall motion and interfacial Dzyaloshinskii-Moriya interactions in Pt/Co/Ir(t Ir)/Ta multilayers.

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 layers. There is 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 DW velocity across the creep and depinning regimes. Asymmetric bubble expansion shows that DWs in all of the samples have the left-handed Néel form. The value of in-plane magnetic 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 (BLS) 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, namely a lack of symmetry about the velocity minimum and no difference in velocities at high in-plane fields. These features are explained by the use of a new 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 the velocity minimum underestimates the DMI field, consistent with BLS giving 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.

Dynamic Imaging of the Delay- and Tilt-Free Motion of Néel Domain Walls in Perpendicularly Magnetized Superlattices.

We report on the time-resolved investigation of current- and field-induced domain wall motion in the flow regime in perpendicularly magnetized microwires exhibiting antisymmetric exchange interaction by means of scanning transmission X-ray microscopy with a 200 ps time step. The sub-ns time step of the dynamical images allowed us to observe the absence of incubation times for the motion of the domain wall within an uncertainty of 200 ps, together with indications for a negligible inertia of the domain wall. Furthermore, we observed that, for short current and magnetic field pulses, the magnetic domain walls do not exhibit a tilting during their motion, providing a mechanism for the fast, tilt-free, current-induced motion of magnetic domain walls.

Superferromagnetism and Domain-Wall Topologies in Artificial "Pinwheel" Spin Ice.

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° 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, 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 one- or two-dimensional avalanches. This property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.

Discrete Hall resistivity contribution from Néel skyrmions in multilayer nanodiscs.

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. The read-out operation of skyrmion-based spintronic devices will rely on the electrical detection of a single magnetic skyrmion within a nanostructure. Here we present Pt/Co/Ir nanodiscs that support skyrmions at room temperature. We measured the Hall resistivity and simultaneously imaged the spin texture using magnetic scanning transmission X-ray microscopy. 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 magnetization over the entire disc. We observed a resistivity contribution that only depends on the number and sign of skyrmion-like objects present in the disc. Each skyrmion gives rise to 22 ± 2 nΩ cm irrespective of its size. This contribution needs to be considered in all-electrical detection schemes applied to skyrmion-based devices. Not only the area of Néel skyrmions but also their number and sign contribute to their Hall resistivity.

Effect of FePd alloy composition on the dynamics of artificial spin ice.

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 Néel-Brown two-state model and find a large discrepancy which we attribute to activation volumes much smaller than the island volume.

Quantitative TEM imaging of the magnetostructural and phase transitions in FeRh thin film systems.

Equi-atomic FeRh is a very interesting material as it undergoes a magnetostructural transition from an antiferromagnetic (AF) to a ferromagnetic (FM) phase between 75-105 °C. Its ability to present phase co-existence separated by domain walls (DWs) above room temperature provides immense potential for exploitation of their DW motion in spintronic devices. To be able to effectively control the DWs associated with AF/FM coexistence in FeRh thin films we must fully understand the magnetostructural transition and thermomagnetic behaviour of DWs at a localised scale. Here we present a transmission electron microscopy investigation of the transition in planar FeRh thin-film samples by combining differential phase contrast (DPC) magnetic imaging with in situ heating. We perform quantitative measurements from individual DWs as a function of temperature, showing that FeRh on NiAl exhibits thermomagnetic behaviour consistent with the transition from AF to FM. DPC imaging of an FeRh sample with HF-etched substrate reveals a state of AF/FM co-existence and shows the transition from AF to FM regions proceeds via nucleation of small vortex structures, which then grow by combining with newly nucleated vortex states into larger complex magnetic domains, until it is in a fully-FM state.

Synthetic ferrimagnet nanowires with very low critical current density for coupled domain wall motion.

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 Néel wall structures, imaged using photoemission electron and Lorentz transmission electron microscopy, with a width of only ~100 nm. The measured critical current density to set these walls in motion, detected using magnetotransport measurements, is 1.0 × 1011 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.

Sputter growth and characterization of metamagnetic B2-ordered FeRh epilayers.

Chemically ordered alloys are useful in a variety of magnetic nanotechnologies. They are most conveniently prepared at an industrial scale using sputtering techniques. Here we describe a method for preparing epitaxial thin films of B2-ordered FeRh by sputter deposition onto single crystal MgO substrates. Deposition at a slow rate onto a heated substrate allows time for the adatoms to both settle into a lattice with a well-defined epitaxial relationship with the substrate and also to find their proper places in the Fe and Rh sublattices of the B2 structure. The structure is conveniently characterized with X-ray reflectometry and diffraction and can be visualised directly using transmission electron micrograph cross-sections. B2-ordered FeRh exhibits an unusual metamagnetic phase transition: the ground state is antiferromagnetic but the alloy transforms into a ferromagnet on heating with a typical transition temperature of about 380 K. This is accompanied by a 1% volume expansion of the unit cell: isotropic in bulk, but laterally clamped in an epilayer. The presence of the antiferromagnetic ground state and the associated first order phase transition is very sensitive to the correct equiatomic stoichiometry and proper B2 ordering, and so is a convenient means to demonstrate the quality of the layers that can be deposited with this approach. We also give some examples of the various techniques by which the change in phase can be detected.

Linear magnetoresistance in n-type silicon due to doping density fluctuations.

We report the observation of a large linear magnetoresistance in the ohmic regime in commonplace commercial n-type silicon wafer with a P dopant density of (1.4±0.1) ×10(15) cm(-3), and report measurements of it in the temperature range 30-200 K. It arises from the deformation of current paths, which causes a part of the Hall field to be detected at the voltage probes. In short, wide samples we found linear magnetoresistance as large as 4707% in an 8 tesla field at 35 K. Sample geometry effects like these are commonplace in commercial Hall sensors. However, we found that the effect persisted in long, thin samples where the macroscopic current flow should be uniform between the voltage probes: we observed a magnetoresistance of 445% under the same conditions as above. We interpret this result as arising due to spatial fluctuations in the donor density, in the spirit of the Herring model.

Single electron spintronics.

Single electron electronics is now well developed, and allows the manipulation of electrons one-by-one as they tunnel on and off a nanoscale conducting island. In the past decade or so, there have been concerted efforts in several laboratories to construct single electron devices incorporating ferromagnetic components in order to introduce spin functionality. The use of ferromagnetic electrodes with a non-magnetic island can lead to spin accumulation on the island. On the other hand, making the dot also ferromagnetic introduces new physics such as tunnelling magnetoresistance enhancement in the cotunnelling regime and manifestations of the Kondo effect. Such nanoscale islands are also found to have long spin lifetimes. Conventional spintronics makes use of the average spin-polarization of a large ensemble of electrons: this new approach offers the prospect of accessing the quantum properties of the electron, and is a candidate approach to the construction of solid-state spin-based qubits.