MagTense: A micromagnetic framework using the analytical demagnetization tensor

Bjørk, Rasmus; Poulsen, E.; Nielsen, Kaspar Kirstein; Insinga, Andrea Roberto

doi:10.1016/j.jmmm.2021.168057

Cited by 20 publications

(10 citation statements)

References 35 publications

(37 reference statements)

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“…To check the performance of our novel method for magnetic field prediction, we introduce a virtual setup, where our open-source micromagnetism and magnetostatic calculation framework MagTense [1] is used to place a 3-D construct of hard magnets around a 2-D area and to compute its resulting magnetic field. As shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…In all of these applications the magnetic field must be optimized for the given technology, and the magnetic field in each device must typically be characterized for this. However, to characterize a magnetic field, this must be determined throughout the volume of interest, regardless of whether the magnetic field is measured using a Hall sensor in an experimental setup or the field is computed using a simulation framework such as analytical modeling [1] or finite element analysis [2]. Determining the magnetic field with increasing resolution is computationally expensive, as is measuring the field in a large number of points for characterizing the field of an experimental setup.…”

Section: Introductionmentioning

confidence: 99%

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Magnetic Field Prediction Using Generative Adversarial Networks

Pollok¹,

Olden-Jørgensen²,

Jørgensen³

et al. 2022

Preprint

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Plenty of scientific and real-world applications are built on magnetic fields and their characteristics. To retrieve the valuable magnetic field information in high resolution, extensive field measurements are required, which are either time-consuming to conduct or even not feasible due to physical constraints. To alleviate this problem, we predict magnetic field values at a random point in space from a few point measurements by using a generative adversarial network (GAN) structure. The deep learning (DL) architecture consists of two neural networks: a generator, which predicts missing field values of a given magnetic field, and a critic, which is trained to calculate the statistical distance between real and generated magnetic field distributions. By minimizing this statistical distance, a reconstruction loss as well as physical losses, our trained generator has learned to predict the missing field values with a median reconstruction test error of 5.14%, when a single coherent region of field points is missing, and 5.86%, when only a few point measurements in space are available and the field measurements around are predicted. We verify the results on an experimentally validated field.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic Field Prediction Using Generative Adversarial Networks

Pollok¹,

Olden-Jørgensen²,

Jørgensen³

et al. 2022

Preprint

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“…When evaluating the Heisenberg exchange parameters (34), one can freely choose a suitable basis representation for the susceptibility and exchange-correlation magnetic field. Here, we present a plane wave implementation based on the transverse magnetic susceptibility module [19] in the GPAW electronic structure code [67,68].…”

Section: B Isotropic Exchange Parameters In a Plane Wave Basismentioning

confidence: 99%

“…The Heisenberg parameters are crucial for predicting spin wave dispersions, but are also important for other properties. For example they constitute the input to micromagnetic modelling [34] and atomistic spin dynamics [35][36][37], which can be applied to unravel more complex dynamical effects such as skyrmion motion [38] and domain wall formation.…”

Section: Introductionmentioning

confidence: 99%

Plane wave implementation of the magnetic force theorem for magnetic exchange constants: Application to bulk Fe, Co and Ni

Durhuus¹,

Skovhus²,

Olsen³

2022

Preprint

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We present a plane wave implementation of the magnetic force theorem, which provides a first principles framework for extracting exchange constants parameterizing a classical Heisenberg model description of magnetic materials. It is shown that the full microscopic exchange tensor may be expressed in terms of the static Kohn-Sham susceptibility tensor and the exchange-correlation magnetic field. This formulation allows one to define arbitrary magnetic sites localized to predefined spatial regions, hence rendering the problem of finding Heisenberg parameters independent of any orbital decomposition of the problem. The susceptibility is calculated in a plane wave basis, which allows for systematic convergence with respect to unoccupied bands and spatial representation. We then apply the method to the well-studied problem of calculating adiabatic spin wave spectra for bulk Fe, Co and Ni, finding good agreement with previous calculations. In particular, we utilize the freedom of defining magnetic sites to show that the calculated Heisenberg parameters are robust towards changes in the definition of magnetic sites. This demonstrates that the magnetic sites can be regarded as well defined and thus asserts the relevance of the Heisenberg model description despite the itinerant nature of the magnetic state.

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“…One important problem in this field is energy minimization, that is finding the quasi-optimal configuration of a magnetic system. The total Gibbs free energy of a magnetic body Ω Ă R 3 is composed of four fundamental energy terms [12], the stray field energy E s , the Zeeman energy E zee , the anisotropy energy E a and the exchange energy E ex , i.e.…”

Section: Introductionmentioning

confidence: 99%

Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization

Schaffer¹,

Schrefl²,

Oezelt³

et al. 2023

Preprint

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We study the full 3d static micromagnetic equations via a physics-informed neural network (PINN) ansatz for the continuous magnetization configuration. PINNs are inherently mesh-free and unsupervised learning models. In our approach we can learn to minimize the total Gibbs free energy with additional conditional parameters, such as the exchange length, by a single low-parametric neural network model. In contrast, traditional numerical methods would require the computation and storage of a large number of solutions to interpolate the continuous spectrum of quasi-optimal magnetization configurations. We also consider the important and computationally expensive stray field problem via PINNs, where we use a basically linear learning ansatz, called extreme learning machines (ELM) within a splitting method for the scalar potential. This reduces the stray field training to a linear least squares problem with precomputable solution operator. We validate the stray field method by means of numerical example comparisons from literature and illustrate the full micromagnetic approach via the NIST µMAG standard problem #3.

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MagTense: A micromagnetic framework using the analytical demagnetization tensor

Cited by 20 publications

References 35 publications

Magnetic Field Prediction Using Generative Adversarial Networks

Magnetic Field Prediction Using Generative Adversarial Networks

Plane wave implementation of the magnetic force theorem for magnetic exchange constants: Application to bulk Fe, Co and Ni

Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization

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