Intrinsic high frequency permeability of magnetic nanocomposites: uncertainty principle.

The intrinsic high frequency permeability spectra of ferromagnetic conductive nanocomposites containing different volume fractions of nanoscale iron and cobalt have been simulated. A law is proposed to explain the simulated results by assuming that there are plenty of Landau-Lifshitz-Gilbert (LLG) type natural resonances contributing to the intrinsic permeability spectra. The results clearly show that the spectra strongly depend on the distribution of local effective magnetic field, the interaction between the magnetic particles, the inhomogeneous damping constant of LLG precession, and the initial equilibrium states. Especially, the effect of particles shape distribution in each sampling on the local effective magnetic field. In view of this fact: it is absolutely impossible to have the same effect from these factors when someone prepares several measurement samples, an uncertainty principle is believed to hold for measuring the intrinsic permeability of an electromagnetic (EM) composite. Therefore, this law tells us that it should be cautious when comparing or evaluating the EM properties of composites (for instance, EM wave absorbing composites). Memory effect can be used to restore the intrinsic high frequency permeability for a specific defunct composite sample.

Controlled evolution of three-dimensional magnetic states in strongly coupled cylindrical nanowire pairs.

Cylindrical magnetic nanowires are promising systems for the development of three-dimensional spintronic devices. Here, we simulate the evolution of magnetic states during fabrication of strongly-coupled cylindrical nanowires with varying degrees of overlap. By varying the separation between wires, the relative strength of exchange and magnetostatic coupling can be tuned. Hence, we observe the formation of six fundamental states as a function of both inter-wire separation and wire height. In particular, two complex three-dimensional magnetic states, a 3D Landau Pattern and a Helical domain wall, are observed to emerge for intermediate overlap. These two emergent states show complex spin configurations, including a modulated domain wall with both Néel and Bloch character. The competition of magnetic interactions and the parallel growth scheme we follow (growing both wires at the same time) favours the formation of these anti-parallel metastable states. This works shows how the engineering of strongly coupled 3D nanostructures with competing interactions can be used to create complex spin textures.

Terahertz permeability of hard ferromagnetic L10-FePt alloy nanowire.

It is commonly thought that ferromagnetic materials can not find applications in terahertz domain because of their very weak dynamic magnetic responses. However, our results in this paper show that the terahertz (THz) permeability of an isolated L10-FePt alloy nanowire with super hard ferromagnetic properties is significant at 0.348 THz, as long as it is at proper remanent states (for instance, Mr/Ms = 1.0), which are ever thought only possible in some metamaterials. Compared to the gigahertz (GHz) permeability of single Fe nanowire, the THz permeability spectra of L10-FePt are shown obviously different. Unusual negative imaginary parts of permeability (µâ€³ < 0) is found related to the equivalent negative damping constant, which is explained from the perspective of abnormal precession of natural resonance at THz for FePt nanowire.

Thermomagnetic recording fidelity of nanometer-sized iron and implications for planetary magnetism.

Paleomagnetic observations provide valuable evidence of the strength of magnetic fields present during evolution of the Solar System. Such information provides important constraints on physical processes responsible for rapid accretion of the protoplanetesimal disk. For this purpose, magnetic recordings must be stable and resist magnetic overprints from thermal events and viscous acquisition over many billions of years. A lack of comprehensive understanding of magnetic domain structures carrying remanence has, until now, prevented accurate estimates of the uncertainty of recording fidelity in almost all paleomagnetic samples. Recent computational advances allow detailed analysis of magnetic domain structures in iron particles as a function of grain morphology, size, and temperature. Our results show that uniformly magnetized equidimensional iron particles do not provide stable recordings, but instead larger grains containing single-vortex domain structures have very large remanences and high thermal stability-both increasing rapidly with grain size. We derive curves relating magnetic thermal and temporal stability demonstrating that cubes (>35 nm) and spheres (>55 nm) are likely capable of preserving magnetic recordings from the formation of the Solar System. Additionally, we model paleomagnetic demagnetization curves for a variety of grain size distributions and find that unless a sample is dominated by grains at the superparamagnetic size boundary, the majority of remanence will block at high temperatures ([Formula: see text]C of Curie point). We conclude that iron and kamacite (low Ni content FeNi) particles are almost ideal natural recorders, assuming that there is no chemical or magnetic alteration during sampling, storage, or laboratory measurement.

Propagation of Spin Waves in a 2D Vortex Network.

Efficient propagation of spin waves in a magnetically coupled vortex is crucial to the development of future magnonic devices. Thus far, only a double vortex can serve as spin-wave emitter or oscillator; the propagation of spin waves in the higher-order vortex is still lacking. Here, we experimentally realize a higher-order vortex (2D vortex network) by a designed nanostructure, containing four cross-type chiral substructures. We employ this vortex network as a waveguide to propagate short-wavelength spin waves (∼100 nm) and demonstrate the possibility of guiding spin waves from one vortex to the network. It is observed that the spin waves can propagate into the network through the nanochannels formed by the Bloch-Néel-type domain walls, with a propagation decay length of several micrometers. This technique paves the way for the development of low-energy, reprogrammable, and miniaturized magnonic devices.

Confinement and Protection of Skyrmions by Patterns of Modified Magnetic Properties.

Magnetic skyrmions are versatile topological excitations that can be used as nonvolatile information carriers. The confinement of skyrmions in channels is fundamental for any application based on the accumulation and transport of skyrmions. Here, we report a method that allows effective position control of skyrmions in designed channels by engineered energy barriers and wells, which is realized in a magnetic multilayer film by harnessing the boundaries of patterns with modified magnetic properties. We experimentally and computationally demonstrate that skyrmions can be attracted or repelled by the boundaries of areas with modified perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. By fabricating square and stripe patterns with modified magnetic properties, we show the possibility of building reliable channels for confinement, accumulation, and transport of skyrmions, which effectively protect skyrmions from being destroyed at the device edges. Our results are useful for the design of spintronic applications using either static or dynamic skyrmions.

Discovery and Implications of Hidden Atomic-Scale Structure in a Metallic Meteorite.

Iron and its alloys have made modern civilization possible, with metallic meteorites providing one of the human's earliest sources of usable iron as well as providing a window into our solar system's billion-year history. Here highest-resolution tools reveal the existence of a previously hidden FeNi nanophase within the extremely slowly cooled metallic meteorite NWA 6259. This new nanophase exists alongside Ni-poor and Ni-rich nanoprecipitates within a matrix of tetrataenite, the uniaxial, chemically ordered form of FeNi. The ferromagnetic nature of the nanoprecipitates combined with the antiferromagnetic character of the FeNi nanophases gives rise to a complex magnetic state that evolves dramatically with temperature. These observations extend and possibly alter our understanding of celestial metallurgy, provide new knowledge concerning the archetypal Fe-Ni phase diagram and supply new information for the development of new types of sustainable, technologically critical high-energy magnets.

Magnetic Vortex States in Toroidal Iron Oxide Nanoparticles: Combining Micromagnetics with Tomography.

Iron oxide nanorings have great promise for biomedical applications because of their magnetic vortex state, which endows them with a low remanent magnetization while retaining a large saturation magnetization. Here we use micromagnetic simulations to predict the exact shapes that can sustain magnetic vortices, using a toroidal model geometry with variable diameter, ring thickness, and ring eccentricity. Our model phase diagram is then compared with simulations of experimental geometries obtained by electron tomography. High axial eccentricity and low ring thickness are found to be key factors for forming vortex states and avoiding net-magnetized metastable states. We also find that while defects from a perfect toroidal geometry increase the stray field associated with the vortex state, they can also make the vortex state more energetically accessible. These results constitute an important step toward optimizing the magnetic behavior of toroidal iron oxide nanoparticles.

Stability of equidimensional pseudo-single-domain magnetite over billion-year timescales.

Interpretations of paleomagnetic observations assume that naturally occurring magnetic particles can retain their primary magnetic recording over billions of years. The ability to retain a magnetic recording is inferred from laboratory measurements, where heating causes demagnetization on the order of seconds. The theoretical basis for this inference comes from previous models that assume only the existence of small, uniformly magnetized particles, whereas the carriers of paleomagnetic signals in rocks are usually larger, nonuniformly magnetized particles, for which there is no empirically complete, thermally activated model. This study has developed a thermally activated numerical micromagnetic model that can quantitatively determine the energy barriers between stable states in nonuniform magnetic particles on geological timescales. We examine in detail the thermal stability characteristics of equidimensional cuboctahedral magnetite and find that, contrary to previously published theories, such nonuniformly magnetized particles provide greater magnetic stability than their uniformly magnetized counterparts. Hence, nonuniformly magnetized grains, which are commonly the main remanence carrier in meteorites and rocks, can record and retain high-fidelity magnetic recordings over billions of years.

Electric Field-Induced Creation and Directional Motion of Domain Walls and Skyrmion Bubbles.

Magnetization dynamics driven by an electric field could provide long-term benefits to information technologies because of its ultralow power consumption. Meanwhile, the Dzyaloshinskii-Moriya interaction in interfacially asymmetric multilayers consisting of ferromagnetic and heavy-metal layers can stabilize topological spin textures, such as chiral domain walls, skyrmions, and skyrmion bubbles. These topological spin textures can be controlled by an electric field and hold promise for building advanced spintronic devices. Here, we present an experimental and numerical study on the electric field-induced creation and directional motion of topological spin textures in magnetic multilayer films and racetracks with thickness gradient and interfacial Dzyaloshinskii-Moriya interaction at room temperature. We find that the electric field-induced directional motion of chiral domain wall is accompanied by the creation of skyrmion bubbles at certain conditions. We also demonstrate that the electric field variation can induce motion of skyrmion bubbles. Our findings may provide opportunities for developing skyrmion-based devices with ultralow power consumption.

Room-Temperature Current-Induced Generation and Motion of sub-100 nm Skyrmions.

Magnetic skyrmions are nanoscale windings of the spin configuration that hold great promise for technology due to their topology-related properties and extremely reduced sizes. After the recent observation at room temperature of sub-100 nm skyrmions stabilized by interfacial chiral interaction in magnetic multilayers, several pending questions remain to be solved, notably about the means to nucleate individual compact skyrmions or the exact nature of their motion. In this study, a method leading to the formation of magnetic skyrmions in a micrometer-sized track using homogeneous current injection is evidenced. Spin-transfer-induced motion of these small electrical-current-generated skyrmions is then demonstrated and the role of the out-of-plane magnetic field in the stabilization of the moving skyrmions is also analyzed. The results of these experimental observations of spin torque induced motion are compared to micromagnetic simulations reproducing a granular type, nonuniform magnetic multilayer in order to address the particularly important role of the magnetic inhomogeneities on the current-induced motion of sub-100 nm skyrmions for which the material grains size is comparable to the skyrmion diameter.

Finite Difference Micromagnetic Solvers with the Object Oriented MicroMagnetic Framework (OOMMF) on Graphics Processing Units.

A micromagnetic solver using the Finite Difference method on a Graphics Processing Unit (GPU) and its integration with the Object Oriented MicroMagnetic Framework (OOMMF) are presented. Two approaches for computing the magnetostatic field accelerated by the Fast Fourier Transform (FFT) are implemented. The first approach, referred to as the tensor approach, is based on the tensor spatial convolution to directly compute the magnetostatic field from magnetic moments. The second approach, referred to as the scalar potential approach, uses differential operator evaluation through finite differences (divergence for magnetic charge and gradient for magnetostatic field) and spatial convolution for magnetic scalar potential. Comparisons of implementation details, speed, memory consumption and accuracy are provided. The GPU implementation of OOMMF shows up to 32x GPU-CPU speed-up.

Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator.

We propose and analyze a decoupled time-marching scheme for the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation for the spin accumulation. This model describes the interplay of magnetization and electron spin accumulation in magnetic and nonmagnetic multilayer structures. Despite the strong nonlinearity of the overall PDE system, the proposed integrator requires only the solution of two linear systems per time-step. Unconditional convergence of the integrator towards weak solutions is proved.

Advanced Modeling and Simulation of Multilayer Spin-Transfer Torque Magnetoresistive Random Access Memory with Interface Exchange Coupling.

In advancing the study of magnetization dynamics in STT-MRAM devices, we employ the spin drift-diffusion model to address the back-hopping effect. This issue manifests as unwanted switching either in the composite free layer or in the reference layer in synthetic antiferromagnets-a challenge that becomes more pronounced with device miniaturization. Although this miniaturization aims to enhance memory density, it inadvertently compromises data integrity. Parallel to this examination, our investigation of the interface exchange coupling within multilayer structures unveils critical insights into the efficacy and dependability of spintronic devices. We particularly scrutinize how exchange coupling, mediated by non-magnetic layers, influences the magnetic interplay between adjacent ferromagnetic layers, thereby affecting their magnetic stability and domain wall movements. This investigation is crucial for understanding the switching behavior in multi-layered structures. Our integrated methodology, which uses both charge and spin currents, demonstrates a comprehensive understanding of MRAM dynamics. It emphasizes the strategic optimization of exchange coupling to improve the performance of multi-layered spintronic devices. Such enhancements are anticipated to encourage improvements in data retention and the write/read speeds of memory devices. This research, thus, marks a significant leap forward in the refinement of high-capacity, high-performance memory technologies.

Self-consistent computation of spin torques and magneto-resistance in tunnel junctions and magnetic read-heads with metallic pinhole defects.

A three-dimensional self-consistent spin transport model is developed, which includes both tunnelling transport, leading to tunnelling magneto-resistance, as well as metallic transport, leading to giant magneto-resistance. An explicit solution to the drift-diffusion model is also derived, which allows analysing the effect of both the reference and free layer thickness on the spin-transfer torque polarization and field-like coefficient. It is shown the model developed here can be used to compute the signal-to-noise ratio in realistic magnetic read-heads, where spin torque-induced fluctuations and instabilities limit the maximum operating voltage. The effect of metallic pinhole defects in the insulator layer is also analysed. Increasing the area covered by pinholes results in a rapid degradation of the magneto-resistance, following an inverse dependence. Moreover, the spin torque angular dependence becomes skewed, similar to that obtained in fully metallic spin valves, and the spin-transfer torque polarization decreases. The same results are obtained when considering tunnel junctions with a single pinhole defect, but decreasing cross-sectional area, showing that even a single pinhole defect can significantly degrade the performance of tunnel junctions and magnetic read-heads below the 40 nm node.

Encoding and Multiplexing Information Signals in Magnetic Multilayers with Fractional Skyrmion Tubes.

Tailored magnetic multilayers (MMLs) provide skyrmions with enhanced thermal stability, leading to the possibility of skyrmion-based devices for room-temperature applications. At the same time, the search for additional stable topological spin textures has been under intense research focus. Besides their fundamental importance, such textures may expand the information encoding capability of spintronic devices. However, fractional spin texture states within MMLs in the vertical dimension are yet to be investigated. In this work, we demonstrate numerically fractional skyrmion tubes (FSTs) in a tailored MML system. We subsequently propose to encode sequences of information signals with FSTs as information bits in a tailored MML device. Micromagnetic simulations and theoretical calculations are used to verify the feasibility of hosting distinct FST states within a single device, and their thermal stability is investigated. A multilayer multiplexing device is proposed, where multiple sequences of the information signals can be encoded and transmitted based on the nucleation and propagation of packets of FSTs. Finally, pipelined information transmission and automatic demultiplexing are demonstrated by exploiting the skyrmion Hall effect and introducing voltage-controlled synchronizers and width-based track selectors. The findings indicate that FSTs can be potential candidates as information carriers for future spintronic applications.

A Comprehensive Study of Temperature and Its Effects in SOT-MRAM Devices.

We employ a fully three-dimensional model coupling magnetization, charge, spin, and temperature dynamics to study temperature effects in spin-orbit torque (SOT) magnetoresistive random access memory (MRAM). SOTs are included by considering spin currents generated through the spin Hall effect. We scale the magnetization parameters with the temperature. Numerical experiments show several time scales for temperature dynamics. The relatively slow temperature increase, after a rapid initial temperature rise, introduces an incubation time to the switching. Such a behavior cannot be reproduced with a constant temperature model. Furthermore, the critical SOT switching voltage is significantly reduced by the increased temperature. We demonstrate this phenomenon for switching of field-free SOT-MRAM. In addition, with an external-field-assisted switching, the critical SOT voltage shows a parabolic decrease with respect to the voltage applied across the magnetic tunnel junction (MTJ) of the SOT-MRAM cell, in agreement with recent experimental data.

Finite Element Approach for the Simulation of Modern MRAM Devices.

Because of their nonvolatile nature and simple structure, the interest in MRAM devices has been steadily growing in recent years. Reliable simulation tools, capable of handling complex geometries composed of multiple materials, provide valuable help in improving the design of MRAM cells. In this work, we describe a solver based on the finite element implementation of the Landau-Lifshitz-Gilbert equation coupled to the spin and charge drift-diffusion formalism. The torque acting in all layers from different contributions is computed from a unified expression. In consequence of the versatility of the finite element implementation, the solver is applied to switching simulations of recently proposed structures based on spin-transfer torque, with a double reference layer or an elongated and composite free layer, and of a structure combining spin-transfer and spin-orbit torques.

Unveiling the Emergent Traits of Chiral Spin Textures in Magnetic Multilayers.

Magnetic skyrmions are topologically wound nanoscale textures of spins whose ambient stability and electrical manipulation in multilayer films have led to an explosion of research activities. While past efforts focused predominantly on isolated skyrmions, recently ensembles of chiral spin textures, consisting of skyrmions and magnetic stripes, are shown to possess rich interactions with potential for device applications. However, several fundamental aspects of chiral spin texture phenomenology remain to be elucidated, including their domain wall (DW) structure, thermodynamic stability, and morphological transitions. Here the evolution of these textural characteristics are unveiled on a tunable multilayer platform-wherein chiral interactions governing spin texture energetics can be widely varied-using a combination of full-field electron and soft X-ray microscopies with numerical simulations. With increasing chiral interactions, the emergence of Néel helicity, followed by a marked reduction in domain compressibility, and finally a transformation in the skyrmion formation mechanism are demonstrated. Together with an analytical model, these experiments establish a comprehensive microscopic framework for investigating and tailoring chiral spin texture character in multilayer films.

Terahertz magnetic excitation in antiferromagnets: atomistic spin simulations versus a coupled pendulum model.

Understanding and manipulating of the antiferromagnetic (AF) ultrafast spin dynamics in antiferromagnets (AFMs) is a crucial importance issue because of the promising applications in terahertz spintronic devices. In this study, an analytical theory extended from the classic coupled pendulum model has been developed to describe the intrinsic magnetic excitation of AFMs. The derived frequency dispersion of the AF resonances has been further checked by using the atomistic-level Landau-Lifshitz-Gilbert simulations. We show that the rutile crystalline AFM MnF2possess two separate resonance modes at low magnetic fields: high frequency mode with right-handed polarization and low frequency mode with left-handed polarization. In the absence of magnetic field, these two resonance modes could degenerate into a single resonance state. When the applied magnetic field is higher than the spin-flip field, the system behaves a quasi-ferromagnetic mode. Both quantitative and qualitative agreement with atomistic simulation results confirm the theoretical picture of the AF resonance dynamics. This study provides a simple but physical understanding of the ultrafast dynamics of AF excitations.