Exchange energy formulations for 3D micromagnetics

Donahue, Michael J.; Porter, Donald G.

doi:10.1016/j.physb.2003.08.090

Cited by 48 publications

(34 citation statements)

References 10 publications

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“…Further discussions regarding the dependence of micromagnetic simulation results on cell size may be found elsewhere. 27,28 The change in relative energy error as cell size reduces well below the exchange length is generally not significant compared to the increase in the required computation time. Details on doing micromagnetic simulations with OOMMF may be found elsewhere.…”

Section: Methodsmentioning

confidence: 99%

Dynamic dephasing of magnetization precession in arrays of thin magnetic elements

Barman

2009

Phys. Rev. B

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We present a systematic micromagnetic simulation to demonstrate how the static and dynamic behaviors of single nanomagnets are modified in an array. We examine the precessional frequency and damping as a function of the width to separation ͑w / s͒ ratio in arrays of square and circular magnetic elements and compare it with the single nanomagnet dynamics. Both frequency and damping are significantly modified by the interelement interaction. The precessional frequency shows a general trend of increase with w / s ratio due to the increase in the dipolar magnetic field in the array and split into multiple modes when the w / s ratio becomes greater than 1. The damping of precession increases with increase in w / s ratio, i.e., with decrease in the separation between the elements. The increase in damping is found to be due to the mutual dephasing of precession of elements in an array. For larger square nanomagnets, ͑width= 150 nm, thickness= 50 nm͒, where the single nanomagnet dynamics is inherently nonuniform, the effect of the array only increases the incoherence in the precession. For larger circular nanomagnets, ͑width= 150 nm, thickness= 50 nm͒, where the single nanomagnet shows slow vortex core oscillation, the array modifies the dynamics into incoherent spin-wave dynamics whose coherence increases with the increase in w / s ratio. Analysis of static and dynamic magnetic images reveals that the dynamics is strongly dependent on the static magnetization in the arrays. The results presented here show that the dynamics of arrays of nanomagnets is significantly or entirely different from that of individual elements, and hence measurements from arrays may not be considered as the single nanomagnet dynamics. We also evaluate the role of dynamic dephasing in the increased damping coefficient.

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Section: Methodsmentioning

confidence: 99%

Dynamic dephasing of magnetization precession in arrays of thin magnetic elements

Barman

2009

Phys. Rev. B

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“…The nm case was simulated with 5 nm and 2 nm cubic cells, while the nm case was simulated with 2 nm and 1 nm cubic cells. It is noted that all cell sizes are less than the magnetostatic exchange length, nm ( in meters and SI units for soft magnetic material [17]). The appendage width for elements of , and nm increased or decreased slightly off dimension when the shape's image was imported in order to fill or unfill whole cells.…”

Section: Micromagnetic Computer Simulationmentioning

confidence: 99%

Micromagnetic Computer Simulated Scaling Effect of S-Shaped Permalloy Nano-Element on Operating Fields for and or or Logic

et al. 2012

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The scaling effect of permalloy s-shaped element, a rectangular element with appendages, on operating fields, x and y , was investigated by micromagnetic computer simulations for AND or OR logic. The optimized combination of operating fields ( x y ) was found to be (27 7 9 9 16 7 8 8) (37 9 12 4 25 9 6 0), and (42 2 8 8 23 9 4 0) in kA/m for the 100, 50, and 30 nm long s-shaped elements, respectively. As the s-shaped element is scaled down, the allowable deviation from the optimized operating fields becomes smaller and optimized operating fields shift to higher field.Index Terms-Micromagnetic computer simulation, s-shaped element, spin logic.

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“…H exch , the effective field due to the exchange interaction is commonly implemented using a six‐neighbor formulation :

\begin{matrix} H (i, j, k) = \frac{2 A}{Δ^{2}} (m (i + 1, j, k) + m (i - 1, j, k) + \\ m (i, j + 1, k) + m (i, j - 1, k) + \\ m (i, j, k + 1) + m (i, j, k - 1) - 6 m (i, j, k)) \end{matrix}

where A is the exchange stiffness and Δ the finite difference discretization length. This formula could be efficiently implemented on the GPU using the methods described in .…”

Section: Effective Field Computationmentioning

confidence: 99%

Implementation of a finite‐difference micromagnetic model on GPU hardware

Vansteenkiste

Wiele

Dupré

et al. 2012

Int J Numerical Modelling

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SUMMARY We have developed a micromagnetic simulator for graphical processing units (GPU), using the CUDA framework. In this paper, we discuss the optimization of the effective field calculation, both from a mathematical and from a hardware‐specific point of view. By using a finite‐difference discretization scheme, the long‐range magnetostatic field can be calculated using fast Fourier transforms, an approach well suited for the GPU. We show how the implementation can be tuned to the GPU hardware and how the performance can be further increased by dealing with the large number of zeros that typically occurs in the micromagnetic field computation. Additionally, we show how the ferromagnetic exchange interaction can be readily included in the magnetostatic field calculation without any additional computational cost. The resulting high‐performance software can be used to run large‐scale simulations that would have been very time‐consuming on regular CPU hardware. As an example, we present a case study on the de‐pinning of domain walls in racetrack memory devices. Copyright © 2012 John Wiley & Sons, Ltd.

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Exchange energy formulations for 3D micromagnetics

Cited by 48 publications

References 10 publications

Dynamic dephasing of magnetization precession in arrays of thin magnetic elements

Dynamic dephasing of magnetization precession in arrays of thin magnetic elements

Micromagnetic Computer Simulated Scaling Effect of S-Shaped Permalloy Nano-Element on Operating Fields for and or or Logic

Implementation of a finite‐difference micromagnetic model on GPU hardware

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