Effective field model of roughness in magnetic nano-structures

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

Accelerating micromagnetic and atomistic simulations using multiple GPUs

It is shown micromagnetic and atomistic spin dynamics simulations can use multiple GPUs in order to reduce computation time, but also to allow for a larger simulation size than is possible on a single GPU. Whilst interactions which depend on neighbouring spins, such as exchange interactions, may be implemented efficiently by transferring data between GPUs using halo regions, or alternatively using 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 2, 3, and 4 GPUs respectively. The code developed here can be used for any number of GPUs in parallel, with performance scaling strongly dependent on 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 2, 3, and 4 GPUs respectively. The best case scenario is obtained for atomistic spin dynamics simulations, where the demagnetizing interaction is implemented with spin-averaged cells. Using a single workstation with 4 GPUs, it is shown atomistic spin dynamics simulations with up to 1 billion spins, and atomistic Monte Carlo simulations with up to 2 billion spins are possible, with a near-ideal performance scaling

Emergence of transient domain wall skyrmions after ultrafast demagnetization

It is known that ultrafast laser pulses can be used to deterministically switch magnetization and createskyrmions; however, the deterministic creation of a single Néel skyrmion after ultrafast demagnetization remainsan open question. Here we show domain wall skyrmions also emerge in systems with broken inversion symmetryafter exposure to an ultrafast laser pulse, carrying an integer topological charge. While domain wall skyrmionsdo not appear in the relaxed state due to quick thermal decay following an Arrhenius law, they play a key role incontrolling the final skyrmion population through annihilations with skyrmions of opposite topological charge,with the resultant skyrmion states following a Poisson distribution. Using single-shot linearly polarized laserpulses, as well as a train of circularly polarized laser pulses, we show that when a high degree of disorder iscreated, the possibility of nucleating a single Néel skyrmion is accompanied by the possibility of nucleating askyrmion with domain wall skyrmion pair, which results in a self-annihilation collapse

All-optical magneto-thermo-elastic skyrmion motion

It is predicted magnetic skyrmions can be controllably moved on surfaces using a focused laser beam. Here an absorbed power of the order 1 mW, focused to a spot-size of the order 10 $\mu$m, results in a local temperature increase of around 50 K, and a local perpendicular strain of the order 10$^{-3}$ due to the thermo-elastic effect. For positive magneto-elastic coupling this generates a strong attractive force on skyrmions due to the magneto-elastic effect. The resultant motion is dependent on forces due to i) gradients in the local strain-induced magnetic anisotropy, ii) gradients in the effective anisotropy due to local temperature gradients, and magnetic parameters temperature dependences, and iii) Magnus effect acting on objects with non-zero topological number. Using dynamical magneto-thermo-elastic modelling, it is predicted skyrmions can be moved with significant velocities (up to 80 m/s shown), both for ferromagnetic and antiferromagnetic skyrmions, even in the presence of surface roughness. This mechanism of controllably moving single skyrmions in any direction, as well as addressing multiple skyrmions in a lattice, offers a new approach to constructing and studying skyrmionic devices with all-optical control

Effect of inter-layer spin diffusion on skyrmion motion in magnetic multilayers

It is well known that skyrmions can be driven using spin-orbit torques due to the spin-Hall effect. Here we show an additional contribution in multilayered stacks arises from vertical spin currents due to inter- layer diffusion of a spin accumulation generated at a skyrmion. This additional interfacial spin torque is similar in form to the in-plane spin transfer torque, but is significantly enhanced in ultra-thin films and acts in the opposite direction to the electron flow. The combination of this diffusive spin torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles even with moderate magnetisation damping values. Further, the effect of material imperfections on threshold currents and skyrmion Hall angle is also investigated. Topographical surface roughness, as small as a single monolayer variation, is shown to be an important contributing factor in ultra-thin films, resulting in good agreement with experimental observations

BORIS – Micromagnetic, Spin Transport and Multiscale Atomistic Software for Modelling Magnetic Information Storage

A brief review of BORIS is given here, together with a review of recent works using this software, including applications to modelling magnetic hard-disk-drive read heads, ultrafast magnetization processes, computation of thermodynamic equilibrium states using Monte Carlo algorithms, and modelling skyrmions as information carriers. BORIS is a state-of-the-art multi-physics and multi-scale research software designed to solve three-dimensional magnetization dynamics problems, coupled with a self-consistent charge and spin transport solver, heat flow solver with temperature-dependent material parameters, and elastodynamics solver including thermoelastic and magnetoelastic/magnetostriction effects, in arbitrary multi-layered structures and shapes. Both micromagnetic and atomistic models are implemented, also allowing multi-scale modelling where computational spaces may be configured with multiple simultaneous micromagnetic and atomistic discretization regions. The software allows multi-GPU computations on any number of GPUs in parallel, in order to accelerate simulations and allow for larger problem sizes compared to single-GPU computations – this is the first magnetization dynamics software to allow multi-GPU computations, enabling large problems encompassing billions of cells to be simulated with unprecedented performance

Boris computational spintronics—High performance multi-mesh magnetic and spin transport modeling software

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

Speeding up explicit numerical evaluation methods for micromagnetic simulations using demagnetizing field polynomial extrapolation

The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are in common use. Higher order methods call for evaluation of all effective field terms, including the demagnetizing field, at all sub-steps. Here a general method of speeding up such explicit evaluation methods is discussed, by skipping the demagnetizing field computation at sub-steps, and instead approximating it using polynomial extrapolation based on stored previous exact computations. This approach is tested for a large number of explicit evaluation methods, both adaptive and fixed time-step, ranging from 2nd order up to 5th order. The polynomial approximation order should be matched to the evaluation method order. In this case we show higher order methods with polynomial extrapolation are more accurate than lower order methods with full evaluation of the demagnetizing field. Moreover, for higher order methods we show it is possible to achieve a factor of 2 or more computation speedup with no decrease in solution accuracy

Evidence of substrate roughness surface induced magnetic anisotropy in Ni80Fe20 flexible thin films

Experimental and computational evidence of a surface roughness induced magnetic anisotropy in NiFe thin films coated onto substrates of various surface roughnesses is reported. Magnetic coercive fields of 15 nm NiFe thin films coated on substrates with approximately 7 nm average roughness were remarkably 233% larger than identical thin films coated onto smooth substrates with < 1 nm average roughness. The NiFe films coated onto rough substrates developed hard and easy axes, normally non-existent in NiFe Permalloy. A linear correlation of the incline angles of the hard axis hysteresis loops to the average roughness values of the individual substrates was observed, with 99% correlation level. Using a modified micromagnetics theory that incorporates the effects of surface roughness, it is shown the observed magnetic anisotropy arises due to the spatial anisotropy of the surface roughness, resulting in an effective in-plane uniaxial magnetic anisotropy with energy density up to 15 kJ/m3

Heat-Assisted Multiferroic Solid-State Memory

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