Magnetic states of small cubic particles with uniaxial anisotropy

Rave, Wolfgang; Fabian, Karl; Hubert, A.

doi:10.1016/s0304-8853(98)00328-x

Cited by 153 publications

(132 citation statements)

References 15 publications

Supporting

Mentioning

123

Contrasting

Unclassified

Order By: Relevance

“…The approach of HK on the other hand, was similar to ours for the interior mesh, but had a different treatment of the outer-space problem, based on a nonlinear mapping to a finite region, and a variational formulation based on optimizing over all solenoidal fields. This can possibly explain the small but noticeable difference in evaluating the magnetostatic energies (our values are systematically lower by about 5 × 10 −3 than In summary, our results lie well within the range of already published values, being in particularly good agreement with those of Rave, Fabian and Hubert [21].…”

Section: Phase Diagram Of the Standard Cubesupporting

confidence: 80%

“…Other numerical techniques mainly based on the fast Fourier transform technique on regular grids have been employed (see e.g. [5,21,22]). Several benchmarks (one of which is studied in the next section) may be found on the NIST webpage [18].…”

Section: Methodsmentioning

confidence: 99%

“…This consists in estimating the size of a cube at which the ground state changes from a quasi-uniform (flower) to a vortex state, in the presence of uniaxial anisotropy with K u = 0.1. The problem had been proposed by A. Hubert, and a first solution has been published by Rave, Fabian and Hubert (RFH) [21]. Hertel and Kronmüller (HK) [15] in a successive solution, with a different method, discovered the presence of an additional "twisted flower" state, which is a modification of the symmetric flower breaking inversion symmetry, with lower energy than the flower in the region of interest.…”

Section: Phase Diagram Of the Standard Cubementioning

confidence: 99%

“…As a first application of our method, we consider the Micromagnetic Standard Problem 3 [15,18,21]. This consists in estimating the size of a cube at which the ground state changes from a quasi-uniform (flower) to a vortex state, in the presence of uniaxial anisotropy with K u = 0.1.…”

Section: Phase Diagram Of the Standard Cubementioning

confidence: 99%

“…A precise determination of the critical size at which the assumption of a quasi-uniform magnetization breaks down is, however, a nontrivial task. Indeed, starting from the pioneering work of Shabes and Bertram [23], a large numerical literature has developed on the subject ( [15,16,21] and references therein), and a specific set of parameters has been chosen as Standard Problem No. 3 [18] for the validation of numerical micromagnetic algorithms.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Energetics and switching of quasi-uniform states in small ferromagnetic particles

Alouges¹,

Conti²,

DeSimone³

et al. 2004

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract. We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.Mathematics Subject Classification. 65L60, 78M10, 82D40.

show abstract

Section: Phase Diagram Of the Standard Cubesupporting

confidence: 80%

Section: Methodsmentioning

confidence: 99%

Section: Phase Diagram Of the Standard Cubementioning

confidence: 99%

Section: Phase Diagram Of the Standard Cubementioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Energetics and switching of quasi-uniform states in small ferromagnetic particles

Alouges¹,

Conti²,

DeSimone³

et al. 2004

ESAIM: M2AN

View full text Add to dashboard Cite

show abstract

Systematic Analysis of Micromagnetic Switching Processes

Hubert

Rave²

1999

phys. stat. sol. (b)

Self Cite

View full text Add to dashboard Cite

show abstract

The Special Role of Magnetization Curling in Nanoparticles

Aharoni

2002

phys. stat. sol. (a)

View full text Add to dashboard Cite

A qualitative change can occur, in a certain particle size, if the magnetization reverses by the curling mode, as demonstrated by superparamagnetic spheres, and by the initial susceptibility of ideally-soft spheres and disks. The theory of exchange resonance modes in small ferromagnetic spheres is extended to the case of a sphere whose centre is not ferromagnetic, as is the case when the magnetic particle is grown around a non-magnetic nucleus, such as the fine particles of the alloys of Fe, Co, and Ni that are made around a nucleus of a noble metal. A first-order calculation leads to a negligible modification of the eigenvalues for the inner radius used in the experiments. For larger holes, the change can be measurably large for some modes. IntroductionThe theory of micromagnetics has never been able [1] to account for the magnetization processes in bulk ferromagnets. It is commonly believed that these processes are mostly governed by crystalline imperfections in hard materials, and by surface roughness and internal voids in soft materials. Both types help the nucleation of reversed domains on the one hand, and hinder the motion of the walls on the other hand. In both cases, however, the mechanisms are not sufficiently clear, and there is no satisfactory theory for them. There are many numerical simulations, but the results always look as if something is still missing there [2], so that they do not even seem promising yet, and it is not really known how to proceed.The situation is much better with fine ferromagnetic particles, for which it is energetically unfavorable to subdivide into domains, thus eliminating the most difficult theoretical problem of nucleation and growth of reversed domains. Theoretical nucleation fields are [3] close to the experimental coercivities of nearly-perfect whiskers for small whisker radius, but are off by several orders of magnitude for larger radii, thus indicating that the effect of body and surface imperfections is less important in fine particles than it is in larger ones. The computer resources necessary for numerical study of particles, by subdividing them into a sufficiently fine mesh, is also manageable when the particles are not too large. Moreover, there are now several experimental studies of individual particles, with which it should be easy to compare the theoretical results, without the problem of interactions between particles that complicated the analysis of older experiments. And there are some analytic results for ideal particles that can be used as a start and a guidance for the study of less perfect particles.It should thus seem natural for numerical micromagnetics to concentrate on extending the analytic results, by studying the effects of imperfections, and of other phenomena neglected in the old theory, such as surface anisotropy, magnetostriction, etc. For some historical reasons, however, numerical computations have been [2] mostly search-

show abstract

Magnetic states of small cubic particles with uniaxial anisotropy

Cited by 153 publications

References 15 publications

Energetics and switching of quasi-uniform states in small ferromagnetic particles

Energetics and switching of quasi-uniform states in small ferromagnetic particles

Systematic Analysis of Micromagnetic Switching Processes

The Special Role of Magnetization Curling in Nanoparticles

Contact Info

Product

Resources

About