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Magnetism
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Mathematical Modelling and Physical Applications of Magnetic Systems
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Mathematical Modelling and Physical Applications of Magnetic Systems

A special issue of Magnetism (ISSN 2673-8724).

Deadline for manuscript submissions: 31 July 2025 | Viewed by 17923

Special Issue Editors

Prof. Dr. Roberto Zivieri

E-Mail Website1 Website2
Guest Editor
1. Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 1, 98122 Messina, Italy
2. Istituto Nazionale di Alta Matematica (INdAM), 00185 Rome, Italy
Interests: solid state physics and lattice phonons dynamics; spin waves; ferromagnetic materials and nanostructures; low-dimensional magnetic systems; quantum magnetic models; magnonic crystals; magnetic metamaterials; magnetic signature of ships; quantum magnetic sensors; topological defects; magnetic vortices and antivortices; magnetic skyrmions; spin-transfer torque effect; spin-Hall effect; band structure and mobility calculation of topological semimetals and magnetoresistance; linear and nonlinear seismic metamaterials; statistical thermodynamics of biological systems; entropy of irreversible reactions in living systems; electrical power signals; distribution lines; smart grids
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Giancarlo Consolo

E-Mail Website
Guest Editor
Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Messina, Italy
Interests: mathematical modelling of magnetization and spin-wave dynamics; domain-wall dynamics; magnetoelasticity and magnetostriction; spin-wave pattern formation and stability; magnetization dynamics in confined and unconfined systems; ferromagnetic and antiferromagnetic materials; multiferroic devices; crystal symmetries; parabolic and hyperbolic mathematical models
Special Issues, Collections and Topics in MDPI journals
Dr. Israa Medlej

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Guest Editor
Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
Interests: quantum physics; spintronics; magnonics; microwave magnetics; topological spin textures; neuromorphic computing; nanophotonics; quantum optics; plasmonics; nanofabrication; integrated photonics and quantum technologies; micromagnetic simulations; theoretical calculations; experiments
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

During recent years, magnetic materials have attracted the attention of both experimentalists and theorists for their intriguing properties exhibited at the nanoscale level. During the last two decades, the underlying physics of the complex magnetization dynamics in magnetic systems such as ferromagnetic and antiferromagnetic films and confined magnetic systems of different shapes including nanopillars and waveguides has been widely studied by means of the formulation of sophisticated mathematical models, both in terms of classical and quantum description.  On the other hand, during the same period, there has been an intense experimental activity able to confirm several phenomena predicted by the theoretical models and to discover new effects. These efforts have led to the fabrication of several technological applications such as magnetic memories, microwave oscillators, modulators, magnetic sensors, logic gates, diodes, transistors, etc. The study of the interplay between topology and physics in low-dimensional magnetic systems via the spin-transfer-torque and spin-Hall effects paved the way for the fabrication of spintronic devices. The aim of this Special Issue is to attract world-leading scientists to present the latest exciting theoretical and experimental results in the field of low-dimensional magnetic systems, discussing their underlying physics in different magnetic configurations and suggesting concrete applications. The accepted contributions will include theoretical developments, experimental observations and measurements, and potential applications.

Prof. Dr. Roberto Zivieri
Prof. Dr. Giancarlo Consolo
Dr. Israa Medlej 
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Magnetism is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • ferromagnetic and antiferromagnetic materials
  • low-dimensional magnetic systems
  • spin-wave excitations
  • spin-transfer torque
  • spin-polarized current and spin-Hall effect
  • magnetic solitons
  • magnonic crystals
  • magneto-photonic crystals
  • magnetoelastic effect
  • quantum magnets

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Published Papers (7 papers)

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Research

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9 pages, 2640 KiB  
Article
Can We Still Find an Ideal Memristor?
by Frank Zhigang Wang
Magnetism 2024, 4(3), 200-208; https://doi.org/10.3390/magnetism4030014 - 16 Jul 2024
Viewed by 934
Abstract
In 1971, Chua defined an ideal memristor that links magnetic flux φ and electric charge q. In a magnetic lump with a current-carrying conductor, we found that the direct interaction between physical magnetic flux φ and physical electric charge q is memristive by [...] Read more.
In 1971, Chua defined an ideal memristor that links magnetic flux φ and electric charge q. In a magnetic lump with a current-carrying conductor, we found that the direct interaction between physical magnetic flux φ and physical electric charge q is memristive by nature in terms of a time-invariant φ-q curve being nonlinear, continuously differentiable and strictly monotonically increasing. Although we succeeded in demonstrating that the “ideal/real/perfect/… memristor” needs magnetism, the structure still suffers from two serious limitations: 1. a parasitic “inductor” effect and 2. bistability and dynamic sweep of a continuous resistance range. Then, we discussed how to overcome these two limitations to make a fully functioning ideal memristor with multiple or an infinite number of stable states and no parasitic inductance. We then gave a number of innovations to the current memristor structure, such as an “open” structure, nanoscale size, magnetic materials with cubic anisotropy (or even isotropy) and sequential switching of the magnetic domains. Contrary to the conjecture that “an ideal memristor may not exist or may be a purely mathematical concept”, we remain optimistic that an ideal memristor will be discovered in nature or will be made in the laboratory. Our finding of the memristive flux–charge interaction may advance the development and application of the memristor technology. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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14 pages, 3065 KiB  
Article
Loss Mitigation in Self-Biased Microstrip Circulators
by Lingqi Kong, Alexander Schuchinsky, Sumin Joseph, Taylan Eker and Yi Huang
Magnetism 2023, 3(2), 121-134; https://doi.org/10.3390/magnetism3020010 - 4 May 2023
Viewed by 2228
Abstract
Integration of the ferrite devices in the RF front-end and active antennas is hindered by the need for external magnets, biasing soft microwave ferrites. The hexaferrite-based self-biased nonreciprocal devices can operate without external magnets at mm-wave frequencies but the currently available hexaferrite materials [...] Read more.
Integration of the ferrite devices in the RF front-end and active antennas is hindered by the need for external magnets, biasing soft microwave ferrites. The hexaferrite-based self-biased nonreciprocal devices can operate without external magnets at mm-wave frequencies but the currently available hexaferrite materials inflict high RF losses at lower frequencies, particularly in the wireless communication bands. In this paper, the parameters of La-Co-substituted hexaferrite compounds are used for the self-biased circulators in the low GHz frequency bands, and a means of the dissipation loss reduction are discussed. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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21 pages, 4200 KiB  
Article
Numerically Stable and Computationally Efficient Expression for the Magnetic Field of a Current Loop
by Michael Ortner, Peter Leitner and Florian Slanovc
Magnetism 2023, 3(1), 11-31; https://doi.org/10.3390/magnetism3010002 - 30 Dec 2022
Cited by 1 | Viewed by 2751
Abstract
In this work, it is demonstrated that straightforward implementations of the well-known textbook expressions of the off-axis magnetic field of a current loop are numerically unstable in a large region of interest. Specifically, close to the axis of symmetry and at large distances [...] Read more.
In this work, it is demonstrated that straightforward implementations of the well-known textbook expressions of the off-axis magnetic field of a current loop are numerically unstable in a large region of interest. Specifically, close to the axis of symmetry and at large distances from the loop, complete loss of accuracy happens surprisingly fast. The origin of the instability is catastrophic numerical cancellation, which cannot be avoided with algebraic transformations. All exact expressions found in the literature exhibit similar instabilities. We propose a novel exact analytic expression, based on Bulirsch’s complete elliptic integral, which is numerically stable (15–16 significant figures in 64 bit floating point arithmetic) everywhere. Several field approximation methods (dipole, Taylor expansions, Binomial series) are studied in comparison with respect to accuracy, numerical stability and computation performance. In addition to its accuracy and global validity, the proposed method outperforms the classical solution, and even most approximation schemes in terms of computational efficiency. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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22 pages, 7460 KiB  
Article
Practical Study of Mixed-Core High Frequency Power Transformer
by Arun Kumar Paul
Magnetism 2022, 2(3), 306-327; https://doi.org/10.3390/magnetism2030022 - 1 Sep 2022
Cited by 6 | Viewed by 3980
Abstract
The design of medium- to high-frequency power electronics transformer aims not only to minimize the power loss in the windings and the core, but its heat removal features should also allow optimal use of both core and copper. The heat removal feature (e.g., [...] Read more.
The design of medium- to high-frequency power electronics transformer aims not only to minimize the power loss in the windings and the core, but its heat removal features should also allow optimal use of both core and copper. The heat removal feature (e.g., thermal conduction) of a transformer is complex because there exist multiple loss centers. The bulk of total power loss is concentrated around a small segment of the core assembly where windings are overlaid. The primary winding is most constrained thermally. For superior use of core and copper, the temperature rise in different segments of the transformer should be well below their respective safe operating limits. In practice, cores of same soft-magnetic materials are traditionally used. To achieve superior temperature profile and for better long-term performance, this article proposes to use the mixed-core configuration. The new core(s) would replace the parent ones from the segment where windings are laid. The characteristic features of new cores would share increased burden of heat removal from the transformer. To obtain the qualitative insight of magnetic and thermal performance, the proposed mixed-core transformer would be thoroughly validated practically in two different high-power applications. In the first case, the core is always energized to its rated value, and in the second one, windings are always energized at respective rated current capacity. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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18 pages, 9877 KiB  
Article
Magneto Elasticity Modeling for Stress Sensors
by Gildas Diguet, Joerg Froemel, Hiroki Kurita, Fumio Narita, Kei Makabe and Koichi Ohtaka
Magnetism 2022, 2(3), 288-305; https://doi.org/10.3390/magnetism2030021 - 23 Aug 2022
Cited by 1 | Viewed by 2178
Abstract
In this article, the stress/stress sensing capability of FeSiB thin films is demonstrated and discussed. The sensing relies on the change in permeability by the application of stress, compressive and tensile, and the application of DC magnetic field. This susceptibility/permeability was tested by [...] Read more.
In this article, the stress/stress sensing capability of FeSiB thin films is demonstrated and discussed. The sensing relies on the change in permeability by the application of stress, compressive and tensile, and the application of DC magnetic field. This susceptibility/permeability was tested by the exciting field (AC) being in the same direction with the applied stress. The susceptibility was shown to exhibit a maximal value at a given applied stress, the critical stress. Moreover, this maximal amplitude and position was changing with the application of an external DC magnetic field. For the DC field applied in the direction of the exciting field (AC) and longitudinal to the stress, the critical stress was shifted toward negative values and for the DC field applied perpendicularly, the critical stress was shifted toward larger positive values. This was experimentally demonstrated, and a model was constructed for a better understanding. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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22 pages, 4862 KiB  
Article
Vector-Based Magnetic Circuit Modelling of Induction Motors
by Braden Kidd
Magnetism 2022, 2(2), 130-151; https://doi.org/10.3390/magnetism2020010 - 28 Apr 2022
Cited by 1 | Viewed by 2851
Abstract
Electro-mechanical devices incorporating rotating magnetic fields can be modelled using a wide range of analytical techniques. Choosing a modelling technique usually requires a trade off between computational efficiency and accuracy. Magnetic flux-based models aim to achieve an optimum balance between computational intensity and [...] Read more.
Electro-mechanical devices incorporating rotating magnetic fields can be modelled using a wide range of analytical techniques. Choosing a modelling technique usually requires a trade off between computational efficiency and accuracy. Magnetic flux-based models aim to achieve an optimum balance between computational intensity and accuracy, as required for real time control applications. This paper demonstrates how vector-based magnetic circuit equations can be used to describe the operational characteristics of an induction motor at a more fundamental level than commonly used magnetic flux models. Doing so allows for closed form equations to be derived directly from device-specific geometry. The resultant model has advantages of numerical method-based analytical techniques while retaining the computational efficiency of closed form equations. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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Review

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17 pages, 2570 KiB  
Review
Magnetic Hopfions: A Review
by Konstantin Guslienko
Magnetism 2024, 4(4), 383-399; https://doi.org/10.3390/magnetism4040025 - 20 Nov 2024
Viewed by 583
Abstract
Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge [...] Read more.
Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented. Full article
(This article belongs to the Special Issue Mathematical Modelling and Physical Applications of Magnetic Systems)
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