Boris Livshitz

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle problems of a small or very large size with a high speed. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel Graphics Processing Unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus discretized superposition integrals are computed using a non-uniform grid interpolation method, which evaluates the field from N sources at N collocated observers in ( ) O N operations. This approach allows handling any uniform or non-uniform shapes, allows easily calculating the field outside the magnetized domains, does not require solving linear system of equations, and requires little memory. FastMag is implemented on GPUs with GPU-CPU speed-ups of two orders of magnitude. Simulations are shown of a large array and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

Microwave assisted magnetization reversal in composite media

Magnetic reversal in exchange-coupled composite elements under microwave fields is characterized by several unique properties including reduced reversal fields, microwave fields, microwave resonant frequencies, and reduced sensitivity to anisotropy distributions as compared to homogeneous elements. We find that reversal can occur in uniform and nonuniform regimes. The uniform regime is characterized by coherent spin precession enhancement by the microwave field. In the nonuniform regime domain walls in the soft layer mediate reversal and under linearly polarized microwave fields, can lead to a formation of localized reversal/nonreversal areas in the “applied field-frequency” phase plane.

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N^2) to O(N) in the static and low-frequency regimes, to O(NlogN) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU-CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.

Graphics Processing Unit Accelerated

An efficient micromagnetic solver running on graphics processing units (GPU) is demonstrated. The solver implements a nonuniform grid interpolation method (NGIM) to compute the superposition integral for the magnetostatic field with operations and memory requirements. The NGIM divides the computational domain into a hierarchy of boxes containing sources and observers, and it uses spatial interpolation from sparse nonuniform grids to achieve computational savings. Efficiency of the GPU solver is achieved by using coalesced memory accessing requiring arranging data in contiguous addresses, one-block-per-box computations with a block of threads handling an observation box to achieve the best utilization of the GPU threads, and on-fly computation of all grids and interpolation coefficients leading to reduced memory and increased speed. The GPU-CPU speed-ups are shown to be in the range 40-100 depending on the problem size and accuracy. A simple and inexpensive GPU is shown to handle efficiently problems comprising discretizations of more than 16 million of spins.

O(N)

Patterned media elements comprising coupled magnetically hard and soft sections of different horizontal size, referred to as ledge elements, are characterized by several unique properties. These elements allow for remarkably reduced reversal fields, which are an order of magnitude below the Stoner-Wohlfarth limit. They also allow for precessional reversal to occur for practical field rise times (100–200ps), which are two orders of magnitude larger than those in the case of homogeneous elements (∼2ps). These attractive properties are obtained even for elements of small height (4–8nm). Patterned media implementing such ledge elements can allow for recording densities above 10Tbit∕in2.

Micromagnetic Solver

Magnetization reversal in composite exchange-coupled dual-layer magnetic elements can occur in the regime of precessional reversal. Compared to the regime of damping reversal in composite elements, the regime of precessional reversal exhibits substantially reduced reversal fields with modified angular dependence. Precessional reversal in the composite elements can occur for write field rise times of more than an order larger than those in homogeneous (single-layer) elements. Such long rise times can be achieved in practical writing systems even for materials with an ultrahigh anisotropy. The identified phenomena have potential applications in high density hard drives and magnetic random access memory systems.

Dual-layer patterned media “ledge” design for ultrahigh density magnetic recording

Microwave-assisted magnetic reversal (MAMR) is studied for media comprising exchange-coupled composite elements comprising soft and hard layers. Reversal in such elements occurs under substantially reduced reversal fields, microwave fields, and microwave resonant frequencies as compared to those for homogeneous elements. Reversal can occur in uniform modes as well as nonuniform domain wall assisted modes depending on the soft layer thickness. In addition, a multilevel MAMR scheme is suggested where the recording media comprise multiple levels of elements, with each level having a distinct resonant frequency. These levels are addressed individually by tuning the frequency of the microwave field.

Precessional reversal in exchange-coupled composite magnetic elements

A nonuniform grid (NG) algorithm for rapidly computing magnetostatic field for micromagnetic simulations is described. The algorithm relies on spatial NG representation of the potential from the source boxes and local interpolation. Multilevel implementations of the algorithm result in a linear computational complexity with respect to the number of effective magnetic charges and observers. The algorithm is highly adaptive with respect to structure’s geometry, i.e., it becomes automatically faster for low dimensional configurations such as quasiplanar bit patterned medium arrays.

Microwave-assisted magnetization reversal and multilevel recording in composite media

We report micromagnetic modeling of a bit patterned media where a two-dimensional array of patterned composite islands is antiferromagnetically coupled to a continuous capping layer. This media allows optimization of writability, switching field distributions, and readback response. Lateral and vertical exchange introduced through the coupling with the capping layer compensates the dipolar interactions between islands and antiferromagnetic coupling is employed to modulate the high-density readback response.

Nonuniform grid algorithm for fast calculation of magnetostatic interactions in micromagnetics

Magnetization reversal mechanisms in composite exchange-coupled dual-layer (composite) patterned media are allowed in the regime of precessional reversal, which is characterized by substantially reduced reversal fields. An important property of precessional reversal in composite patterned media is that it can occur for recording field rise times of more than an order larger than those in patterned media comprising homogeneous elements. These longer rise times can be allowed by realistic recording systems even for materials with ultrahigh coercivity. The reversal field and rise times required for precessional reversal can be controlled by varying the soft layer parameters and coupling strength between the layers.