Periodic boundary conditions for demagnetization interactions in micromagnetic simulations

Lebecki, Krzysztof M.; Donahue, Michael J.; Gutowski, M.

doi:10.1088/0022-3727/41/17/175005

Cited by 87 publications

(53 citation statements)

References 19 publications

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“…Consequently, if n image cells are used, the time to compute the BEM matrix will increase by a factor n. However, this does only affect the simulation setup time needed to compute the BEM. This behaviour parallels the PBC extension [1] for OOMMF [6].…”

Section: Macro Geometry Implementationsupporting

confidence: 77%

“…Indeed using a PBC extension [1] for OOMMF with a cubic primary cell of (15nm) 3 , we obtain the correct asymptotic values 0 and 1/2 with an error of less than 10 −8 (i.e. practically zero).…”

Section: Macro Geometry Implementationmentioning

confidence: 81%

“…While no problem arises for structures that are periodic in one or two directions only, micromagnetism requires a modification of the PBC approach for 3d periodic systems, as taking the infinite size limit leaves essential information about the shape of the (now 2d) surface unspecified which here matters for long-range interactions (see also discussion in section 3 in [1]). …”

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confidence: 99%

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A new approach to (quasi) periodic boundary conditions in micromagnetics: The macrogeometry

Fangohr

Bordignon

Franchin

et al. 2009

Journal of Applied Physics

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We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency problem that prevents the naive application of 3d periodic boundary conditions in micromagnetism and (ii) is well suited for the efficient simulation of repetitive systems of any size.Introduction One often wants to quantitatively understand the behaviour of highly regular extended periodic magnetic structures created, for example, by selfassembly methods. As these structures often are too large for full micromagnetic simulation, some physically justifiable assumptions have to be made to reduce the computational complexity.One attractive simplification is to define a 'primary' simulation cell C 0 in the bulk of the sample (which may contain one or multiple elementary lattice cells) and demand that the magnetization in every other 'image' cell C j is constrained to behaving as a translated copy of the magnetization in cell C 0 . While this approximation loses long range multicell structures (such as the domain wall structure of extended materials) and field deviations near surfaces, it is useful in other situations such as magnetic films in strong external fields. This idea is usually described by the term 'periodic boundary conditions' (PBC). We note that there is a conceptual difference between using PBC to remove surface artefacts in multi-particle statistical mechanics simulations (e.g. of a gas of hard spheres) and using PBC to describe real periodic structures with long-range interactions (such as magnetic repulsion).While no problem arises for structures that are periodic in one or two directions only, micromagnetism requires a modification of the PBC approach for 3d periodic systems, as taking the infinite size limit leaves essential information about the shape of the (now 2d) surface unspecified which here matters for long-range interactions (see also discussion in section 3 in [1]).To show why the shape matters, we consider two different structures s A and s B made of one billion individual cells each: s A being a cube of 1000×1000×1000 cells, and s B being a film of 10000 × 10000 × 10 cells. If both structures are homogeneously magnetized, a cell in the center of each experiences a demagnetizing field H = −T M . The demagnetizing tensor T must satisfy (a consequence of the Maxwell equation div B = 0): tr T = 1. For s A , we have T (A) = diag(1/3, 1/3, 1/3), while for s B , we get T (B) = diag(0, 0, 1). The form of T depends on the shape

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Section: Macro Geometry Implementationsupporting

confidence: 77%

Section: Macro Geometry Implementationmentioning

confidence: 81%

mentioning

confidence: 99%

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A new approach to (quasi) periodic boundary conditions in micromagnetics: The macrogeometry

Fangohr

Bordignon

Franchin

et al. 2009

Journal of Applied Physics

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“…The size of the nanoparticles varied from 6 to 1000 nm. We used two-dimensional infinite periodic boundary conditions for the exchange and magnetostatic interactions to eliminate edge effects originating from a non-uniformity of an internal magnetic field in samples of finite sizes [7]. We used the following magnetic parameters in the calculations: the saturation magnetization M s = 955 G (1.2 T), the exchange constant A = 1×10…”

Section: Modeling Detailsmentioning

confidence: 99%

Numerical Simulation of Magnetic Microstructure in Nanocrystalline Thin Films with the Random Anisotropy

Belyaev¹,

Izotov²,

Solovev³

2017

J. Sib. Fed. Univ., Math. phys.

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The magnetic structure of thin nanocrystalline films with a random distribution of magnetization easy axes was studied by means of micromagnetic modeling. The dependences of the correlation function parameters of the non-uniform magnetization on the value of the external in-plane magnetic field were investigated in the wide range (6-1000 nm) of particles sizes. An analysis of the obtained dependences revealed a significant difference between longitudinal (along the field) and transversal (perpendicular to the field) correlation radii of a stochastic magnetic structure. The blocking effect of a fine magnetic structure-a magnetization ripple-was observed during magnetization reversal of the films.

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“…3) and is subject to a variable applied field (0, 0, H) as well as the calculated stray field, (H x stray , H y stray , H z stray ), of the nanoplatelets which would surround and be contained within the lateral calculation region. The domain wall moves in the x-direction and periodic boundary conditions 64 were used in the y direction. The following simulation parameters were used.…”

Section: Appendix A: Micromagnetic Simulationmentioning

confidence: 99%

Spatially periodic domain wall pinning potentials: Asymmetric pinning and dipolar biasing

Metaxas

Zermatten

Novak

et al. 2013

Journal of Applied Physics

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Domain wall propagation has been measured in continuous, weakly disordered, quasi-two-dimensional, Isinglike magnetic layers that are subject to spatially periodic domain wall pinning potentials. The potentials are generated non-destructively using the stray magnetic field of ordered arrays of magnetically hard [Co/Pt] m nanoplatelets which are patterned above and are physically separated from the continuous magnetic layer. The effect of the periodic pinning potentials on thermally activated domain wall creep dynamics is shown to be equivalent, at first approximation, to that of a uniform, effective retardation field, H ret , which acts against the applied field, H. We show that H ret depends not only on the array geometry but also on the relative orientation of H and the magnetization of the nanoplatelets. A result of the latter dependence is that wall-mediated hysteresis loops obtained for a set nanoplatelet magnetization exhibit many properties that are normally associated with ferromagnet/antiferromagnet exchange bias systems. These include a switchable bias, coercivity enhancement and domain wall roughness that is dependent on the applied field polarity.

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Periodic boundary conditions for demagnetization interactions in micromagnetic simulations

Cited by 87 publications

References 19 publications

A new approach to (quasi) periodic boundary conditions in micromagnetics: The macrogeometry

A new approach to (quasi) periodic boundary conditions in micromagnetics: The macrogeometry

Numerical Simulation of Magnetic Microstructure in Nanocrystalline Thin Films with the Random Anisotropy

Spatially periodic domain wall pinning potentials: Asymmetric pinning and dipolar biasing

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