Dipolar-stabilized first and second-order antiskyrmions in ferrimagnetic multilayers.

Skyrmions and antiskyrmions are topologically protected spin structures with opposite vorticities. Particularly in coexisting phases, these two types of magnetic quasi-particles may show fascinating physics and potential for spintronic devices. While skyrmions are observed in a wide range of materials, until now antiskyrmions were exclusive to materials with D2d symmetry. In this work, we show first and second-order antiskyrmions stabilized by magnetic dipole-dipole interaction in Fe/Gd-based multilayers. We modify the magnetic properties of the multilayers by Ir insertion layers. Using Lorentz transmission electron microscopy imaging, we observe coexisting antiskyrmions, Bloch skyrmions, and type-2 bubbles and determine the range of material properties and magnetic fields where the different spin objects form and dissipate. We perform micromagnetic simulations to obtain more insight into the studied system and conclude that the reduction of saturation magnetization and uniaxial magnetic anisotropy leads to the existence of this zoo of different spin objects and that they are primarily stabilized by dipolar interaction.

Microscopic Origin of Magnetization Reversal in Nanoscale Exchange-Coupled Ferri/Ferromagnetic Bilayers: Implications for High Energy Density Permanent Magnets and Spintronic Devices.

Giant exchange bias shifts of several Tesla have been reported in ferrimagnetic/ferromagnetic bilayer systems, which could be highly beneficial for contemporary high energy density permanent magnets and spintronic devices. However, the lack of microscopic studies of the reversal owing to the difficulty of measuring few nanometer-wide magnetic structures in high fields precludes the assessment of the lateral size of the inhomogeneity in relation to the intended application. In this study, the magnetic reversal process of nanoscale exchange-coupled bilayer systems, consisting of a ferrimagnetic TbFeCo alloy layer and a ferromagnetic [Co/Ni/Pt] N multilayer, was investigated. In particular, minor loop measurements, probing solely on the reversal characteristics of the softer ferromagnetic layer, reveal two distinct reversal mechanisms, which depend critically on the thickness of the ferromagnetic layer. For thick layers, irreversible switching of the macroscopic minor loop is observed. The underlying microscopic origin of this reversal process was studied in detail by high-resolution magnetic force microscopy, showing that the reversal is triggered by in-plane domain walls propagating through the ferromagnetic layer. In contrast, thin ferromagnetic layers show a hysteresis-free reversal, which is nucleation-dominated due to grain-to-grain variations in magnetic anisotropy of the Co/Ni/Pt multilayer and an inhomogeneous exchange coupling with the magnetically hard TbFeCo layer, as confirmed by micromagnetic simulations.

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory.

In this paper, the thermal stability of skyrmion bubbles and the critical currents to move them over pinning sites were investigated. For the used pinning geometries and the used parameters, the unexpected behavior is reported that the energy barrier to overcome the pinning site is larger than the energy barrier of the annihilation of a skyrmion. The annihilation takes place at boundaries by current driven motion, as well as due to the excitation over energy barriers, in the absence of currents, without forming Bloch points. It is reported that the pinning sites, which are required to allow thermally stable bits, significantly increase the critical current densities to move the bits in skyrmion-like structures to about jcrit = 0.62 TA/m². The simulation shows that the applied spin transfer model predicts experimentally obtained critical currents to move stable skyrmions at room temperature well, which is in contrast to simulations based on spin orbit torque that predict significantly too low critical currents. By calculating the thermal stability, as well as the critical current, we can derive the spin torque efficiency η = ΔE/Ic = 0.19 kBT300/µA, which is in a similar range to the simulated spin torque efficiency of MRAM structures. Finally, it is shown that the stochastic depinning process of any racetrack-like device requires an extremely narrow depinning time distribution smaller than ~6% of the current pulse length to reach bit error rates smaller than 10-9.

3D Printing of Polymer-Bonded Rare-Earth Magnets With a Variable Magnetic Compound Fraction for a Predefined Stray Field.

Additive manufacturing of polymer-bonded magnets is a recently developed technique, for single-unit production, and for structures that have been impossible to manufacture previously. Also, new possibilities to create a specific stray field around the magnet are triggered. The current work presents a method to 3D print polymer-bonded magnets with a variable magnetic compound fraction distribution. This means the saturation magnetization can be adjusted during the printing process to obtain a required external field of the manufactured magnets. A low-cost, end-user 3D printer with a mixing extruder is used to mix permanent magnetic filaments with pure polyamide (PA12) filaments. The magnetic filaments are compounded, extruded, and characterized for the printing process. To deduce the quality of the manufactured magnets with a variable magnetic compound fraction, an inverse stray field framework is developed. The effectiveness of the printing process and the simulation method is shown. It can also be used to manufacture magnets that produce a predefined stray field in a given region. This opens new possibilities for magnetic sensor applications. This setup and simulation framework allows the design and manufacturing of polymer-bonded permanent magnets, which are impossible to create with conventional methods.

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method.

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated.

A self-consistent spin-diffusion model for micromagnetics.

We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.

A three-dimensional spin-diffusion model for micromagnetics.

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.

Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations.

Magnetostatic Maxwell equations and the Landau-Lifshitz-Gilbert (LLG) equation are combined to a multiscale method, which allows to extend the problem size of traditional micromagnetic simulations. By means of magnetostatic Maxwell equations macroscopic regions can be handled in an averaged and stationary sense, whereas the LLG allows to accurately describe domain formation as well as magnetization dynamics in some microscopic subregions. The two regions are coupled by means of their strayfield and the combined system is solved by an optimized time integration scheme.

Removal of earth's magnetic field effect on magnetoelastic resonance sensors by an antisymmetric bias field.

Magnetoelastic sensors are used in a wide field of wireless sensing applications. The sensing element is a low-cost magnetostrictive ribbon whose resonant frequency depends on the measured quantity. The accuracy of magnetoelastic sensors is limited by the fact that the resonant frequency is also affected by the earth's magnetic field. In this paper we present a technique to minimize this effect by applying an antisymmetric magnetic bias field to the ribbon. The ribbon's response to external perturbation fields was measured and compared to a conventional sensor design. Our results show that the influence of the earth's magnetic field could be reduced by 77%.