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It is shown that micromagnetic and atomistic spin dynamics simulations can use multiple graphical processing units (GPUs) not only to reduce computation time but also to allow for a larger simulation size than is possible on a single GPU. While interactions that depend on neighboring spins, such as exchange interactions, may be implemented efficiently by transferring data between GPUs using halo regions or direct memory accesses, implementing the long-range demagnetizing interaction is the main difficulty in achieving good performance scaling, where the data transfer rate between GPUs is a significant bottleneck. A multi-GPU convolution algorithm is developed here, which relies on single-GPU FFTs executed in parallel. It is shown that even for micromagnetic simulations where the demagnetizing interaction computation time dominates, good performance scaling may be achieved, with speedup factors up to 1.8, 2.5, and 3.1, for two, three, and four GPUs, respectively. The code developed here can be used for any number of GPUs in parallel, with performance scaling strongly dependent on the inter-GPU data transfer rate and connection topology. This is further improved in micromagnetic simulations, which include a spin transport solver, obtaining speedup factors up to 1.96, 2.8, and 3.7, for two, three, and four GPUs, respectively. The best case scenario is obtained for atomistic simulations, where the demagnetizing interaction is implemented with spin-averaged cells. Using a single workstation with four GPUs, it is shown that atomistic spin dynamics simulations with up to 1 × 109 spins and atomistic Monte Carlo simulations with up to 2 × 109 spins are possible, with near-ideal performance scaling. [ABSTRACT FROM AUTHOR]

The storage, transmission, and processing of data become significant problems when large digital data files or databases are involved, as in the case of decentralized online global databases such as blockchain. Here, we propose a novel method that allows for the scalability of digital assets, including blockchain databases in the download, validation, and confidentiality processes, by developing a lightweight blockchain technology called Entropic Blockchain. This is a computer-implemented mathematical method by which to generate an information-entropic numerical barcode representation of a digital asset. Using this technique, a 1–2 Mb block of digital data can be represented by a few bytes, significantly reducing the size of a blockchain. The entropic barcode file can be utilized on its own or as an optically machine-readable entropic barcode for secure data transmission, processing, labeling, identification, and one-way encryption, as well as for compression, validation, and digital tamper-proof checks. The mathematics of this process and all the steps involved in its implementation are discussed in detail in this article. [ABSTRACT FROM AUTHOR]

An efficient method for computing thermodynamic equilibrium states at the micromagnetic length scale is introduced using the Markov chain Monte Carlo method. Trial moves include not only rotations of vectors, but also a change in their magnetization length. The method is parameterized using the longitudinal susceptibility, reproduces the same Maxwell–Boltzmann distribution as the stochastic Landau–Lifshitz–Bloch equation, and is applicable both below and above the Curie temperature. The algorithm is fully parallel, can be executed on graphical processing units, and efficiently includes the long-range dipolar interaction. This method is generally useful for computing finite-temperature relaxation states for both uniform and non-uniform temperature profiles and can be considered as complementary to zero-temperature micromagnetic energy minimization solvers, with comparable computation time. Compared to the dynamic approach, it is shown that the micromagnetic Monte Carlo method is up to almost 20 times faster. Moreover, unlike quasizero temperature approaches that do not take into account the magnetization length distribution and stochasticity, the method is better suited for structures with unbroken symmetry around the applied field axis, granular films, and at higher temperatures and fields. In particular, applications to finite-temperature hysteresis loop modelling, chiral magnetic thin films, granular magnetic media, and artificial spin ices are discussed. [ABSTRACT FROM AUTHOR]

This work discusses the design and testing of a new computational spintronics research software. Boris is a comprehensive multi-physics open-source software, combining micromagnetics modeling capabilities with drift-diffusion spin transport modeling and a heat flow solver in multi-material structures. A multi-mesh paradigm is employed, allowing modeling of complex multi-layered structures with independent discretization and arbitrary relative positioning between different computational meshes. Implemented micromagnetics models include not only ferromagnetic materials modeling, but also two-sublattice models, allowing simulations of antiferromagnetic and ferrimagnetic materials, fully integrated into the multi-mesh and multi-material design approach. High computational performance is an important design consideration in Boris, and all computational routines can be executed on graphical processing units (GPUs), in addition to central processing units. In particular, a modified 3D convolution algorithm is used to compute the demagnetizing field on the GPU, termed pipelined convolution, and benchmark comparisons with existing GPU-accelerated software Mumax3 have shown performance improvements up to twice faster. [ABSTRACT FROM AUTHOR]

As research into magnetic thin films and spintronics devices is moving from single to multiple magnetic layers, there is a need for micromagnetics modeling tools specifically designed to efficiently handle magnetic multilayers. Here, we show an exact method of computing demagnetizing fields in magnetic multilayers, which is able to handle layers with arbitrary spacing, arbitrary thicknesses, and arbitrary relative positioning between them without impacting the computational performance. The multilayered convolution method is a generalization of the well-known fast Fourier transform-based convolution method used to compute demagnetizing fields in a single magnetic body. In typical use cases, such as multilayered stacks used to study skyrmions, we show that the multilayered convolution method can be up to 8 times faster, implemented both for central processors and graphics processors, compared to the simple convolution method. [ABSTRACT FROM AUTHOR]

Pulsed domain wall movement is studied here in Ni80Fe20 nanowires on SiO2, using a fully integrated electrostatic, thermoelectric, and micromagnetics solver based on the Landau-Lifshitz-Bloch equation, including Joule heating, anisotropic magneto-resistance, and Oersted field contributions. During the applied pulse, the anisotropic magneto-resistance of the domain wall generates a dynamic heat gradient, which increases the current-driven velocity by up to 15%. Using a temperature-dependent conductivity, significant differences are found between the constant voltage-pulsed and constant current-pulsed domain wall movement: constant voltage pulses are shown to be more efficient at displacing domain walls whilst minimizing the increase in temperature, with the total domain wall displacement achieved over a fixed pulse duration having a maximum with respect to the driving pulse strength. [ABSTRACT FROM AUTHOR]

An effective field model is introduced here within the micromagnetics formulation, to study roughness in magnetic structures, by considering sub-exchange length roughness levels as a perturbation on a smooth structure. This allows the roughness contribution to be separated, which is found to give rise to an effective configurational anisotropy for both edge and surface roughness, and accurately model its effects with fine control over the roughness depth without the explicit need to refine the computational cell size to accommodate the roughness profile. The model is validated by comparisons with directly roughened structures for a series of magnetization switching and domain wall velocity simulations and found to be in excellent agreement for roughness levels up to the exchange length. The model is further applied to vortex domain wall velocity simulations with surface roughness, which is shown to significantly modify domain wall movement and result in dynamic pinning and stochastic creep effects. [ABSTRACT FROM AUTHOR]

Here, we study the piezoresponse of epitaxial ferroelectric samples excited through top electrode structures with conductive tips in the global excitation mode and compare these results to displacement values obtained using artifact-free laser Doppler vibrometry (LDV) measurements. Substrate bending modes are studied using finite element simulations and LDV measurements and found to be negligible for top electrode diameters below 100 μm. The effect of electrostatic forces on the piezoresponse measurements is analyzed and methods for minimizing these are discussed. Using a resistive tip-electrode contact mode, the piezoresponse measurements are found to be in good agreement with values obtained from calibrations, providing a link between nanometer scale piezoresponse measurements and quantitative LDV measurements. [ABSTRACT FROM AUTHOR]

A heat-assisted multiferroic solid-state memory design is proposed and analysed, based on a PbNbZrSnTiO3 antiferroelectric layer and Ni81Fe19 magnetic free layer. Information is stored as magnetisation direction in the free layer of a magnetic tunnel junction element. The bit writing process is contactless and relies on triggering thermally activated magnetisation switching of the free layer towards a strain-induced anisotropy easy axis. A stress is generated using the antiferroelectric layer by voltage-induced antiferroelectric to ferroelectric phase change, and this is transmitted to the magnetic free layer by strain-mediated coupling. The thermally activated strain-induced magnetisation switching is analysed here using a three-dimensional, temperature-dependent magnetisation dynamics model, based on simultaneous evaluation of the stochastic Landau-Lifshitz-Bloch equation and heat flow equation, together with stochastic thermal fields and magnetoelastic contributions. The magnetisation switching probability is calculated as a function of stress magnitude and maximum heat pulse temperature. An operating region is identified, where magnetisation switching always occurs, with stress values ranging from 80 to 180 MPa, and maximum temperatures normalised to the Curie temperature ranging from 0.65 to 0.99. [ABSTRACT FROM AUTHOR]

In this work, we evaluated the piezoelectric properties of the ZnO nanorods (NRs), subsequently grown by a template-free electrochemical deposition (ECD) approach. The one-step preparation method yielded in a relatively short-time synthesis large arrays of high aspect-ratio ZnO NRs, vertically aligned to the substrate and exhibiting a well-defined hexagonal symmetry coupled with an excellent crystallinity. Piezoresponse force microscopy (PFM) was employed to extract the effective piezoelectric coefficient ( d 33 ) of the ZnO [0 0 0 1]-oriented NRs. A mean effective d 33 coefficient of 11.8 pm/V was measured over several individual NRs. The results have shown an increased piezoelectric response of the ZnO NRs, with ∼18% in respect to the ZnO bulk material, and with a factor ranging from 28% to 167% compared to similar ZnO nanostructures prepared by other counterpart techniques. Both morphology and crystalline quality of the obtained ZnO NRs, as well as the piezoelectric investigations, ranked the ECD as a promising low-cost pathway for possibly producing high quality nanostructured ZnO-based piezoelectric devices with enhanced performance. [ABSTRACT FROM AUTHOR]

The ferroelectric properties of 2-layer Dion-Jacobson compounds ABiNb2O7 (A = Rb and Cs) were studied. Ferroelectricity and piezoelectricity of CsBiNb2O7 were demonstrated for the first time. The ferroelectric domain structure of Dion-Jacobson compounds were imaged using PFM. The Curie points of RbBiNb2 O7 and CsBiNb2 O7 are 1098 ± 5 and 1033 ± 5 °C, respectively. The piezoelectric constant of RbBiNb2O7 and CsBiNb2O7 are approximately 5 and 8 pC N-1. Thermal depoling was also studied to confirm the Curie temperature and the stability of the piezoelectricity. [ABSTRACT FROM AUTHOR]

In this paper we investigate the domain wall pinning positions at parabolic pinning potentials in Gd doped Ni80Fe20 wires. Increasing the Gd doping percentage favors the formation of vortex domain walls, shown to be due to an increase in the out of plane anisotropy, allowing the pinning of a vortex and a transverse domain wall in two similar parabolic pinning potentials. Using pulsed currents to investigate the difference in the depinning characteristics of these two domain wall types, we show that the current density required for steady domain wall motion is smaller than the current density required to set it in motion and estimate this difference to be of the order 1011 A/m². [ABSTRACT FROM AUTHOR]

The dependence of threshold current on applied magnetic field for domain wall depinning from a pinning potential in Gd doped permalloy wires is measured using pulsed current measurements. By increasing the Gd concentration we find a marked reduction in threshold currents. This is shown to arise due to the enhanced non-adiabatic spin-transfer torque: we calculate the non-adiabaticity parameter β to be around 0.11 for 10% Gd concentration. On the other hand we show that the adiabatic spin-transfer torque is largely unaffected by Gd concentrations up to 10%. [ABSTRACT FROM AUTHOR]

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., (© 2023 IOP Publishing Ltd.)

A three-dimensional spin current solver based on a generalised spin drift-diffusion description, including the bulk and interfacial spin Hall effects, is integrated with a magnetisation dynamics solver. The resulting model is shown to simultaneously reproduce the spin-orbit torques generated using the spin Hall effect, spin pumping torques generated by magnetisation dynamics in multilayers, as well as the spin transfer torques acting on magnetisation regions with spatial gradients, whilst field-like and spin-like torques are reproduced in a spin valve geometry. Two approaches to modelling interfaces are analysed, one based on the spin mixing conductance and the other based on continuity of spin currents where the spin dephasing length governs the absorption of transverse spin components. In both cases analytical formulas are derived for the spin-orbit torques in a heavy metal/ferromagnet bilayer geometry, showing in general both field-like and damping-like torques are generated. The limitations of the analytical approach are discussed, showing that even in a simple bilayer geometry, due to the non-uniformity of the spin currents, a full three-dimensional treatment is required. The model is further applied to the analysis of the spin Hall angle in Pt by reproducing published experimental ferromagnetic resonance data in the bilayer geometry.

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 × 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.