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.

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.

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.

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.

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.

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.

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.

Field-Driven Magnetic Phase Diagram and Vortex Stability in Fe Nanometric Square Prisms.

In this work, we deal with the zero temperature hysteretic properties of iron (Fe) quadrangular nanoprisms and the size conditions underlying magnetic vortex states formation. Different aspect ratios of a square base prism of thickness t with free boundary conditions were considered in order to summarize our results in a proposal of a field-driven magnetic phase diagram where such vortex states are stable along the hysteresis loops. To do that, a Hamiltonian consisting of exchange, magnetostatic, Zeeman and cubic anisotropy energies was considered. The time dynamics at each magnetic field step was performed by solving the time-dependent Landau-Lifshitz-Gilbert differential equation. The micromagnetic simulations were performed using the Ubermag package based on the Object Oriented Micromagnetic Framework (OOMMF). Circular magnetic textures were also characterized by means of topological charge calculations. The aspect ratio dependencies of the coercive force, nucleation and annihilation fields are also analyzed. Computations agree with related experimental observations and other micromagnetic calculations.

Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: atomistic simulations.

A dilute ensemble of randomly oriented non-interacting spherical nanomagnets is considered, and its magnetization structure and ensuing neutron scattering response are investigated by numerically solving the Landau-Lifshitz equation. Taking into account the isotropic exchange interaction, an external magnetic field, a uniaxial magnetic anisotropy for the particle core, and in particular the Néel surface anisotropy, the magnetic small-angle neutron scattering cross section and pair-distance distribution function are calculated from the obtained equilibrium spin structures. The numerical results are compared with the well known analytical expressions for uniformly magnetized particles and provide guidance to the experimentalist. In addition, the effect of a particle-size distribution function is modelled.

Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment.

The magnetization profile and the related magnetic small-angle neutron scattering cross section of a single spherical nanoparticle with Néel surface anisotropy are analytically investigated. A Hamiltonian is employed that comprises the isotropic exchange interaction, an external magnetic field, a uniaxial magnetocrystalline anisotropy in the core of the particle and the Néel anisotropy at the surface. Using a perturbation approach, the determination of the magnetization profile can be reduced to a Helmholtz equation with Neumann boundary condition, whose solution is represented by an infinite series in terms of spherical harmonics and spherical Bessel functions. From the resulting infinite series expansion, the Fourier transform, which is algebraically related to the magnetic small-angle neutron scattering cross section, is analytically calculated. The approximate analytical solution for the spin structure is compared with the numerical solution using the Landau-Lifshitz equation, which accounts for the full nonlinearity of the problem. The signature of the Néel surface anisotropy can be identified in the magnetic neutron scattering observables, but its effect is relatively small, even for large values of the surface anisotropy constant.

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.

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.

Spin-transfer and spin-orbit torques in the Landau-Lifshitz-Gilbert equation.

Dynamic simulations of spin-transfer and spin-orbit torques are increasingly important for a wide range of spintronic devices including magnetic random access memory, spin-torque nano-oscillators and electrical switching of antiferromagnets. Here we present a computationally efficient method for the implementation of spin-transfer and spin-orbit torques within the Landau-Lifshitz-Gilbert equation used in micromagnetic and atomistic simulations. We consolidate and simplify the varying terminology of different kinds of torques into a physical action and physical origin that clearly shows the common action of spin torques while separating their different physical origins. Our formalism introduces the spin torque as an effective magnetic field, greatly simplifying the numerical implementation and aiding the interpretation of results. The strength of the effective spin torque field unifies the action of the spin torque and subsumes the details of experimental effects such as interface resistance and spin Hall angle into a simple transferable number between numerical simulations. We present a series of numerical tests demonstrating the mechanics of generalised spin torques in a range of spintronic devices. This revised approach to modelling spin-torque effects in numerical simulations enables faster simulations and a more direct way of interpreting the results, and thus it is also suitable to be used in direct comparisons with experimental measurements or in a modelling tool that takes experimental values as input.

Mapping Magnetic Signals of Individual Magnetite Grains to Their Internal Magnetic Configurations Using Micromagnetic Models.

Micromagnetic tomography (MMT) is a technique that combines X-ray micro computed tomography and scanning magnetometry data to obtain information about the magnetic potential of individual grains embedded in a sample. Recovering magnetic signals of individual grains in natural and synthetic samples provides a new pathway to study the remanent magnetization that carries information about the ancient geomagnetic field and is the basis of all paleomagnetic studies. MMT infers the magnetic potential of individual grains by numerical inversion of surface magnetic measurements using spherical harmonic expansions. The magnetic potential of individual particles in principle is uniquely determined by MMT, not only by the dipole approximation, but also more complex, higher order, multipole moments. Here, we show that such complex magnetic information together with both particle shape and mineral properties severely constrains the internal magnetization structure of an individual grain. To this end, we apply a three dimensional micromagnetic model to predict the multipole signal from magnetization states of different local energy minima. We show that for certain grains it is even possible to uniquely infer the magnetic configuration from the inverted magnetic multipole moments. This result is crucial to discriminate single-domain particles from grains in more complex configurations such as multi-domain or vortex states. As a consequence, our investigation proves that by MMT it is feasible to select statistical ensembles of magnetic grains based on their magnetization states, which opens new possibilities to identify and characterize stable paleomagnetic recorders in natural samples.

Small-angle neutron scattering by spatially inhomogeneous ferromagnets with a nonzero average uniaxial anisotropy.

Micromagnetic small-angle neutron scattering theory is well established for analyzing spin-misalignment scattering data of bulk ferromagnets. Here, this theory is extended to allow for a global uniaxial magnetic anisotropy (texture) of the material, in addition to the already included random zero-average local anisotropy. Macroscopic cross sections and spin-misalignment response functions are computed analytically for several practically relevant mutual anisotropy and external magnetic field orientations in both parallel and perpendicular scattering geometries for field magnitudes both above and below the rotational saturation. Some of these expressions are tested on published experimental data of magnetic-field-annealed Vitroperm and plastically deformed Ni, allowing determination of the corresponding global uniaxial anisotropy quality factors.

Uniaxial polarization analysis of bulk ferromagnets: theory and first experimental results.

On the basis of Brown's static equations of micromagnetics, the uniaxial polarization of the scattered neutron beam of a bulk magnetic material is computed. The approach considers a Hamiltonian that takes into account the isotropic exchange interaction, the antisymmetric Dzyaloshinskii-Moriya interaction, magnetic anisotropy, the dipole-dipole interaction and the effect of an applied magnetic field. In the high-field limit, the solutions for the magnetization Fourier components are used to obtain closed-form results for the spin-polarized small-angle neutron scattering (SANS) cross sections and the ensuing polarization. The theoretical expressions are compared with experimental data on a soft magnetic nanocrystalline alloy. The micromagnetic SANS theory provides a general framework for polarized real-space neutron methods, and it may open up a new avenue for magnetic neutron data analysis on magnetic microstructures.

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.

Two-dimensional characterization of three-dimensional magnetic bubbles in Fe3Sn2 nanostructures.

We report differential phase contrast scanning transmission electron microscopy (TEM) of nanoscale magnetic objects in Kagome ferromagnet Fe3Sn2 nanostructures. This technique can directly detect the deflection angle of a focused electron beam, thus allowing clear identification of the real magnetic structures of two magnetic objects including three-ring and complex arch-shaped vortices in Fe3Sn2 by Lorentz-TEM imaging. Numerical calculations based on real material-specific parameters well reproduced the experimental results, showing that the magnetic objects can be attributed to integral magnetizations of two types of complex three-dimensional (3D) magnetic bubbles with depth-modulated spin twisting. Magnetic configurations obtained using the high-resolution TEM are generally considered as two-dimensional (2D) magnetic objects previously. Our results imply the importance of the integral magnetizations of underestimated 3D magnetic structures in 2D TEM magnetic characterizations.

Ferromagnetic resonance modes of a synthetic antiferromagnet at low magnetic fields.

One key advantage of antiferromagnets over ferromagnets is the high magnetic resonance frequencies that enable ultrafast magnetization switching and oscillations. Among a variety of antiferromagnets, the synthetic antiferromagnet (SAF) is a promising candidate for high-speed spintronic devices design. In this paper, micromagnetic simulations are employed to study the resonance modes in an SAF structure consisting of two identical CoFeB ferromagnetic (FM) layers that are antiferromagnetically coupled via interlayer exchange coupling. When the external bias magnetic field is small enough to ensure the magnetizations of two FM sublayers remain antiparallel alignments, we find that there exist two resonance modes with different precession chirality, namelyy-component synchronized mode andz-component synchronized mode, respectively. These two resonance modes show different features from the conventional in-phase acoustic mode and out-of-phase optic mode. The simulation results are in good agreement with our theoretical analyses.