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1. Shape and Topology Optimization of Circular Halbach Array using a Cardinal Basis Function (CBF) Based Parametric Level Set Method

   Gao, Lingfeng; Torrey, David; Luo, Fang; Longtin, Jon; Chen, Shikui (August 2025, American Society of Mechanical Engineers (ASME))

   A Halbach array is a specialized arrangement of permanent magnets designed to generate a strong, uniform magnetic field in the designated region. This unique configuration has been widely utilized in various applications, including magnetic levitation (maglev) systems, electric motors, particle accelerators, and magnetic seals. The advantages of Halbach arrays include high efficiency, reduced weight, and precise directional control of the magnetic field. Halbach arrays are commonly categorized into two configurations: linear and cylindrical. A linear Halbach array produces a concentrated magnetic field on one face and is frequently employed in maglev trains and conveyor systems to ensure stable and efficient operation. In contrast, a cylindrical Halbach array consists of magnets arranged in a ring, generating a uniform magnetic field within the cylinder while suppressing the external field. This configuration is particularly advantageous in applications such as brushless electric motors and magnetic resonance imaging (MRI) systems. Traditionally, the design of electromagnetic systems incorporating Halbach arrays relied on engineers’ expertise and intuition due to the complexity of the permanent magnet configuration. However, advancements in numerical methods, particularly topology optimization, have introduced a systematic approach to optimizing the shape and distribution of permanent magnets within a given design domain. In the context of Halbach array design, topology optimization aims to maximize the total magnetic flux within a designated region while simultaneously determining the optimal material distribution to achieve a specified design objective. This approach enhances the performance and efficiency of Halbach arrays, providing a more precise and automated framework for their development. In this paper, we propose a Cardinal Basis Function (CBF)-based level-set method for designing a circular Halbach array capable of generating a uniform magnetic field within a designated region. The CBF-based level-set method offers significant computational advantages by reducing the computational cost and accelerating the convergence process. This approach enhances the efficiency of the optimization process, making it a promising technique for the systematic design of Halbach arrays. 

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2. Accelerating the discovery of novel magnetic materials using machine learning–guided adaptive feedback

   https://doi.org/10.1073/pnas.2204485119  

   Xia, Weiyi; Sakurai, Masahiro; Balasubramanian, Balamurugan; Liao, Timothy; Wang, Renhai; Zhang, Chao; Sun, Huaijun; Ho, Kai-Ming; Chelikowsky, James R.; Sellmyer, David J.; et al (November 2022, Proceedings of the National Academy of Sciences)

   Magnetic materials are essential for energy generation and information devices, and they play an important role in advanced technologies and green energy economies. Currently, the most widely used magnets contain rare earth (RE) elements. An outstanding challenge of notable scientific interest is the discovery and synthesis of novel magnetic materials without RE elements that meet the performance and cost goals for advanced electromagnetic devices. Here, we report our discovery and synthesis of an RE-free magnetic compound, Fe 3 CoB 2 , through an efficient feedback framework by integrating machine learning (ML), an adaptive genetic algorithm, first-principles calculations, and experimental synthesis. Magnetic measurements show that Fe 3 CoB 2 exhibits a high magnetic anisotropy ( K 1 = 1.2 MJ/m 3 ) and saturation magnetic polarization ( J s = 1.39 T), which is suitable for RE-free permanent-magnet applications. Our ML-guided approach presents a promising paradigm for efficient materials design and discovery and can also be applied to the search for other functional materials. 

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3. Manufacturing of Soft Magnets using the Fused Filament Fabrication Process

   https://doi.org/doi.org/10.13140/RG.2.2.32731.90407  

   Hasanov, Seymur; Fidan, Ismail (January 2020, MatEDU Resource Center)

   Stoebe, Thomas (Ed.)

   Rare-earth (RE) materials are currently used to fabricate permanent magnets through various additive manufacturing (AM) methods. Fused filament fabrication (FFF) is one of the most commonly used polymer-based AM methods and has recently been used to produce metal-matrix composites, known as “green parts,” using a metal powder-infused filament. The FFF method has gained much attention in various industries including the automotive, aerospace, and medical fields. Therefore, involving RE in the FFF process using magnetic powder-infused filaments promises to result in the fabrication of low-cost, efficient, and complex magnetic components based on application areas. This module introduces the FFF process and provides a case study for high school and technical college students to gain a fundamental understanding of how magnetic powders are infused and how parts are fabricated using this method. 

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4. Discovering rare-earth-free magnetic materials through the development of a database

   https://doi.org/10.1103/PhysRevMaterials.4.114408  

   Sakurai, M.; Liao, T.; Wang, R.; Zhang, C.; Sun, H.; Sun, Y.; Wang, H.; Wang, S; Wang, C.Z.; Ho, J.M.; et al (November 2020, Physical review materials)

   We develop an open-access database that provides a large array of datasets specialized for magnetic compounds as well as magnetic clusters. Our focus is on rare-earth-free magnets. Available datasets include (i) crystallography, (ii) thermodynamic properties, such as the formation energy, and (iii) magnetic properties that are essential for magnetic-material design. Our database features a large number of stable and metastable structures discovered through our adaptive genetic algorithm (AGA) searches. Many of these AGA structures have better magnetic properties when compared to those of the existing rare-earth-free magnets and the theoretical structures in other databases. Our database places particular emphasis on site-specific magnetic data, which are obtained by high-throughput first-principles calculations. Such site-resolved data are indispensable for machine-learning modeling. We illustrate how our data-intensive methods promote efficiency of the experimental discovery of new magnetic materials. Our database provides massive datasets that will facilitate an efficient computational screening, machine-learning-assisted design, and the experimental fabrication of new promising magnets. 

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5. Theoretical limits for energy density of aligned ferromagnetic nanoparticles in a nonmagnetic matrix for rare-earth-free permanent magnets

   https://doi.org/10.1063/5.0233620  

   Sarker, Shouvik; Rajib, Md Mahadi; Barua, Radhika; Atulasimha, Jayasimha (March 2025, Applied Physics Letters)

   Developing permanent magnets with fewer critical elements requires understanding hysteresis effects and coercivity through visualizing magnetization reversal. Here, we numerically investigate the effect of the geometry of nanoscale ferromagnetic inclusions in a paramagnetic/nonmagnetic matrix to understand the key factors that maximize the magnetic energy product of such nanocomposite systems. Specifically, we have considered a matrix of “3 μm × 3 μm × 40 nm” dimension, which is a sufficiently large volume, two-dimensional representation considering that the ferromagnetic inclusions' thickness is less than 3.33% of the lateral dimensions simulated. Using this approach, which minimizes edge effects to approximate bulk-like magnetic behavior while remaining computationally tractable for simulation, we systematically studied the effect of the thickness of ferromagnetic strips, separation between the ferromagnetic strips due to the nonmagnetic matrix material, different saturation magnetization values, and the length of these ferromagnetic strips on magnetic coercivity and remanence by simulating the hysteresis loop plots for each geometry. Furthermore, we study the underlying micromagnetic mechanism for magnetic reversal to understand the factors that could help attain the maximum magnetic energy densities for ferromagnetic nanocomposite systems in a paramagnetic/nonmagnetic material matrix. In this study, we have used material parameters of an exemplary Alnico alloy system, a rare-earth-free, thermally stable nanocomposite, which could potentially replace high-strength NdFeB magnets in applications that do not require large energy products. However, we project the energy density (BH)max of materials with higher saturation magnetization to have an ideal theoretical limit of (BH)max ∼94 kJ/m3 (∼12 MGOe), which is ∼(35%–40%) of the energy density of Rare-Earth Free Magnets. This energy density could be higher if exchange bias from antiferromagnets, defects, and pinning is included and could stimulate further experimental work on the fabrication and large-scale manufacturing of RE-free PMs with different nanocomposite systems. 

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