16 research outputs found
Computation of the magnetostatic interaction between linearly magnetized polyhedrons
In this paper we present a method to accurately compute the energy of the
magnetostatic interaction between linearly (or uniformly, as a special case)
magnetized polyhedrons. The method has applications in finite element
micromagnetics, or more generally in computing the magnetostatic interaction
when the magnetization is represented using the finite element method (FEM).
The magnetostatic energy is described by a six-fold integral that is singular
when the interaction regions overlap, making direct numerical evaluation
problematic. To resolve the singularity, we evaluate four of the six iterated
integrals analytically resulting in a 2d integral over the surface of a
polyhedron, which is nonsingular and can be integrated numerically. This
provides a more accurate and efficient way of computing the magnetostatic
energy integral compared to existing approaches.
The method was developed to facilitate the evaluation of the demagnetizing
interaction between neighouring elements in finite-element micromagnetics and
provides a possibility to compute the demagnetizing field using efficient fast
multipole or tree code algorithms
Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
In the finite difference method which is commonly used in computational
micromagnetics, the demagnetizing field is usually computed as a convolution of
the magnetization vector field with the demagnetizing tensor that describes the
magnetostatic field of a cuboidal cell with constant magnetization. An
analytical expression for the demagnetizing tensor is available, however at
distances far from the cuboidal cell, the numerical evaluation of the
analytical expression can be very inaccurate.
Due to this large-distance inaccuracy numerical packages such as OOMMF
compute the demagnetizing tensor using the explicit formula at distances close
to the originating cell, but at distances far from the originating cell a
formula based on an asymptotic expansion has to be used. In this work, we
describe a method to calculate the demagnetizing field by numerical evaluation
of the multidimensional integral in the demagnetization tensor terms using a
sparse grid integration scheme. This method improves the accuracy of
computation at intermediate distances from the origin.
We compute and report the accuracy of (i) the numerical evaluation of the
exact tensor expression which is best for short distances, (ii) the asymptotic
expansion best suited for large distances, and (iii) the new method based on
numerical integration, which is superior to methods (i) and (ii) for
intermediate distances. For all three methods, we show the measurements of
accuracy and execution time as a function of distance, for calculations using
single precision (4-byte) and double precision (8-byte) floating point
arithmetic. We make recommendations for the choice of scheme order and
integrating coefficients for the numerical integration method (iii)
Frequency-based nanoparticle sensing over large field ranges using the ferromagnetic resonances of a magnetic nanodisc
Using finite element micromagnetic simulations, we study how resonant
magnetisation dynamics in thin magnetic discs with perpendicular anisotropy are
influenced by magnetostatic coupling to a magnetic nanoparticle. We identify
resonant modes within the disc using direct magnetic eigenmode calculations and
study how their frequencies and profiles are changed by the nanoparticle's
stray magnetic field. We demonstrate that particles can generate shifts in the
resonant frequency of the disc's fundamental mode which exceed resonance
linewidths in recently studied spin torque oscillator devices. Importantly, it
is shown that the simulated shifts can be maintained over large field ranges
(here up to 1T). This is because the resonant dynamics (the basis of
nanoparticle detection here) respond directly to the nanoparticle stray field,
i.e. detection does not rely on nanoparticle-induced changes to the magnetic
ground state of the disk. A consequence of this is that in the case of small
disc-particle separations, sensitivities to the particle are highly mode- and
particle-position-dependent, with frequency shifts being maximised when the
intense stray field localised directly beneath the particle can act on a large
proportion of the disc's spins that are undergoing high amplitude precession.Comment: 9 pages, 9 figures. Updated version from 31.7.2016 includes minor
changes in introduction and sections III.C and III.D (additional information
linking the results to real-world bio-sensing devices
Magnon-Driven Domain-Wall Motion with the Dzyaloshinskii-Moriya Interaction
We study domain wall (DW) motion induced by spin waves (magnons) in the
presence of Dzyaloshinskii-Moriya interaction (DMI). The DMI exerts a torque on
the DW when spin waves pass through the DW, and this torque represents a linear
momentum exchange between the spin wave and the DW. Unlike angular momentum
exchange between the DW and spin waves, linear momentum exchange leads to a
rotation of the DW plane rather than a linear motion. In the presence of an
effective easy plane anisotropy, this DMI induced linear momentum transfer
mechanism is significantly more efficient than angular momentum transfer in
moving the DW
Ground state search, hysteretic behaviour, and reversal mechanism of skyrmionic textures in confined helimagnetic nanostructures
Magnetic skyrmions have the potential to provide solutions for low-power,
high-density data storage and processing. One of the major challenges in
developing skyrmion-based devices is the skyrmions' magnetic stability in
confined helimagnetic nanostructures. Through a systematic study of equilibrium
states, using a full three-dimensional micromagnetic model including
demagnetisation effects, we demonstrate that skyrmionic textures are the lowest
energy states in helimagnetic thin film nanostructures at zero external
magnetic field and in absence of magnetocrystalline anisotropy. We also report
the regions of metastability for non-ground state equilibrium configurations.
We show that bistable skyrmionic textures undergo hysteretic behaviour between
two energetically equivalent skyrmionic states with different core orientation,
even in absence of both magnetocrystalline and demagnetisation-based shape
anisotropies, suggesting the existence of Dzyaloshinskii-Moriya-based shape
anisotropy. Finally, we show that the skyrmionic texture core reversal dynamics
is facilitated by the Bloch point occurrence and propagation.Comment: manuscript: 14 pages, 7 figures; supplementary information: 8 pages,
7 figure
Skyrmions in thin films with easy-plane magnetocrystalline anisotropy
We demonstrate that chiral skyrmionic magnetization configurations can be
found as the minimum energy state in B20 thin film materials with easy-plane
magnetocrystalline anisotropy with an applied magnetic field perpendicular to
the film plane. Our observations contradict results from prior analytical work,
but are compatible with recent experimental investigations. The size of the
observed skyrmions increases with the easy-plane magnetocrystalline anisotropy.
We use a full micromagnetic model including demagnetization and a
three-dimensional geometry to find local energy minimum (metastable)
magnetization configurations using numerical damped time integration. We
explore the phase space of the system and start simulations from a variety of
initial magnetization configurations to present a systematic overview of
anisotropy and magnetic field parameters for which skyrmions are metastable and
global energy minimum (stable) states.Comment: 5 pages, 3 figure
Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics
A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar)
equation, which could be viewed as the combination of Landau-Lifshitz (LL)
equation and an extra "exchange damping" term, was derived by Baryakhtar using
Onsager's relations. We interpret the origin of this "exchange damping" as
nonlocal damping by linking it to the spin current pumping. The LLBar equation
is investigated numerically and analytically for the spin wave decay and domain
wall motion. Our results show that the lifetime and propagation length of
short-wavelength magnons in the presence of nonlocal damping could be much
smaller than those given by LL equation. Furthermore, we find that both the
domain wall mobility and the Walker breakdown field are strongly influenced by
the nonlocal damping.Comment: 10 pages, 6 figure
Computational methods in micromagnetics
With the continued growth of computational power, computational modelling has become an increasingly important part of modern science. The field of micromagnetism has benefited from the increase of computational power, leading in recent decades to the development of many important micromagnetic methods. This thesis aims to address some computational challenges relevant to the field of micromagnetism today.The computation of the demagnetising field is often the most time-consuming part of a micromagnetic simulation. In the finite difference method, this computation is usually done using the Fourier transform method, in which the demagnetising field is computed as the convolution of the magnetisation field with the demagnetising tensor. An analytical formula for the demagnetising tensor is available, however due to numerical cancellation errors it can only be applied for close distances between the interacting cells. For far distances between the interacting cells other approaches, such as asymptotic expansion, have to be used. In this thesis, we present a new method to compute the demagnetising tensor by means of numerical integration. The method offers improved accuracy over existing methods for the intermediate range of distances.In the finite element method, the computation of the demagnetising field is commonly done using the hybrid FEM/BEM method. The fast multipole method offers potential theoretical advantages over the hybrid FEM/BEM method particularly for the current and future generations of computing hardware. In micromagnetics, it has been applied to compute the demagnetising field in the finite difference setting and to compute the magnetostatic interaction between nanoparticles, however no implementation of the fast multipole method in finite elements is yet available. As one of the steps towards it, in this thesis we develop a new formula for the energy of the magnetostatic interaction between linearly magnetized polyhedrons. This formula can be used to compute the direct interaction between finite element cells in the fast multipole method.Ferromagnetic resonance is a popular experimental technique for probing the dynamical properties of magnetic systems. We extend the eigenvalue method for the computation of resonance modes to the computation of the FMR spectrum, and apply it to compute ferromagnetic resonance for a proposed FMR standard reference problem
Joule heating in nanowires
We study the effect of Joule heating from electric currents flowing through ferromagnetic nanowires on the temperature of the nanowires and on the temperature of the substrate on which the nanowires are grown. The spatial current density distribution, the associated heat generation, and diffusion of heat is simulated within the nanowire and the substrate. We study several different nanowire and constriction geometries as well as different substrates: (thin) silicon nitride membranes, (thick) silicon wafers, and (thick) diamond wafers. The spatially resolved increase in temperature as a function of time is computed. For effectively three-dimensional substrates (where the substrate thickness greatly exceeds the nanowire length), we identify three different regimes of heat propagation through the substrate: regime (i), where the nanowire temperature increases approximately logarithmically as a function of time. In this regime, the nanowire temperature is well-described analytically by You et al. [APL89, 222513 (2006)]. We provide an analytical expression for the time tc that marks the upper applicability limit of the You model. After tc, the heat flow enters regime (ii), where the nanowire temperature stays constant while a hemispherical heat front carries the heat away from the wire and into the substrate. As the heat front reaches the boundary of the substrate, regime (iii) is entered where the nanowire and substrate temperature start to increase rapidly. For effectively two-dimensional substrates (where the nanowire length greatly exceeds the substrate thickness), there is only one regime in which the temperature increases logarithmically with time for large times. We provide an analytical expression, valid for all pulse durations, that allows one to accurately compute this temperature increase in the nanowire on thin substrate
Supplementary Information For: Computation Of The Magnetostatic Interaction Between Linearly Magnetized Polyhedrons
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