United States

Additive manufacturing based on selective laser melting (SLM) promises versatile new opportunities for hard magnetic materials as key materials for electrification. However, SLM technology is challenging, especially for today’s strongest permanent magnets based one rare earth (RE) metals. It requires special processing chambers to handle the powders sensitive to oxidation. SLM of RE-based permanent magnet material so far was mainly performed on nanocrystalline Fe-Nd-B powder with overstoichiometric Fe content (e.g. MQP-S from Magnequench). Recently, it has been shown, that due to rapid solidification in SLM, a nanocrystalline microstructure with hard magnetic properties develops in the bulk [1]. In addition, the development of very fine Fe-Nd-B microstructures with directed crystal growth and finely dispersed Nd-rich phase is possible [2].&lt;br/&gt;Material systems such as Co-Sm or Fe-Pr-Cu-B can offer advantages for SLM processing. Due to their solidification process and phase equilibria, they form magnetically advantageous microstructures. Permanent magnet properties can be obtained by annealing, without the need of subsequent powder metallurgical processing or rapid quenching. By a proper choice of processing parameters and post-annealing conditions good permanent magnet properties and partial magnetic anisotropy can be realized for printed parts of both materials. In the case of (CoCuFeZr)&lt;sub&gt;17&lt;/sub&gt;Sm&lt;sub&gt;2&lt;/sub&gt; a coercivity of 2.77 T, remanence of 0.78 T and maximum energy density of 109 kJ/m&lt;sup&gt;3&lt;/sup&gt; have been achieved (Fig. 1). Due to texture of the printed parts the remanence is 24 % higher than for a comparable isotropic sintered magnet. In the case of FePrCuB a coercivity of 0.67 T, remanence of 0.67 T and maximum energy density of 69.8 kJ/m&lt;sup&gt;3&lt;/sup&gt; have been obtained (Fig. 2). Due to higher degree of texturing, the printed parts so far exhibit a 26 % higher remanence compared to identically annealed cast material of the same composition. The paper highlights the correlation between microstructure and related magnetic properties for the processing parameter-sets used.

![](https://assets.underline.io/uploads/markdown_image/1/image/d5437add5e448b415f456c06c19ea099.jpg)

Fig. 1: Microstructural and magnetic properties of (CoCuFeZr)17Sm2 SLM-printed component.

![](https://assets.underline.io/uploads/markdown_image/1/image/a4d614fb9e936909233821d79c9817cc.jpg)

Fig. 2: Microstructural and magnetic properties of FePrCuB SLM-printed component.



2022 Joint MMM-INTERMAG

Selective Laser Melting of Partially Anisotropic Rare Earth-based Permanent Magnets

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Additive manufacturing based on selective laser melting (SLM) promises versatile new opportunities for hard magnetic materials as key materials for electrification. However, SLM technology is challenging, especially for today’s strongest permanent magnets based one rare earth (RE) metals. It requires special processing chambers to handle the powders sensitive to oxidation. SLM of RE-based permanent magnet material so far was mainly performed on nanocrystalline Fe-Nd-B powder with overstoichiometric Fe content (e.g. MQP-S from Magnequench). Recently, it has been shown, that due to rapid solidification in SLM, a nanocrystalline microstructure with hard magnetic properties develops in the bulk [1]. In addition, the development of very fine Fe-Nd-B microstructures with directed crystal growth and finely dispersed Nd-rich phase is possible [2]. Material systems such as Co-Sm or Fe-Pr-Cu-B can offer advantages for SLM processing. Due to their solidification process and phase equilibria, they form magnetically advantageous microstructures. Permanent magnet properties can be obtained by annealing, without the need of subsequent powder metallurgical processing or rapid quenching. By a proper choice of processing parameters and post-annealing conditions good permanent magnet properties and partial magnetic anisotropy can be realized for printed parts of both materials. In the case of (CoCuFeZr)17Sm2 a coercivity of 2.77 T, remanence of 0.78 T and maximum energy density of 109 kJ/m3 have been achieved (Fig. 1). Due to texture of the printed parts the remanence is 24 % higher than for a comparable isotropic sintered magnet. In the case of FePrCuB a coercivity of 0.67 T, remanence of 0.67 T and maximum energy density of 69.8 kJ/m3 have been obtained (Fig. 2). Due to higher degree of texturing, the printed parts so far exhibit a 26 % higher remanence compared to identically annealed cast material of the same composition. The paper highlights the correlation between microstructure and related magnetic properties for the processing parameter-sets used.

![](https://assets.underline.io/uploads/markdown_image/1/image/d5437add5e448b415f456c06c19ea099.jpg)

Fig. 1: Microstructural and magnetic properties of (CoCuFeZr)17Sm2 SLM-printed component.

![](https://assets.underline.io/uploads/markdown_image/1/image/a4d614fb9e936909233821d79c9817cc.jpg)

Fig. 2: Microstructural and magnetic properties of FePrCuB SLM-printed component.

technical paper

In alloy based soft magnetic materials various factors such as alloy composition, phase, synthesis process and annealing conditions affect their magnetic properties. Co, Fe and Ni based alloy thin films exhibit high magnetic moment and high permeability which mark their importance in memory devices and MEMS. The magnetization reversal mechanism in thin films plays a significant role for such technological applications. Here, binary FeCo and ternary (FeCo)(100-x) Nix alloy thin films were deposited on Indium Tin Oxide coated glass substrate by electrochemical deposition. The composition of as deposited alloy was confirmed by EDAX. The surface morphology analysed by SEM, confirmed uniformly dispersed flakes all over the substrate in FeCo films. The increasing content of Ni in the alloy results in the formation of irregular shaped granular structure. Bulk magnetic properties were characterized by VSM hysteresis. As the Ni content increases the coercivity as well as remanence decreases (fig.1) and this is probably due to decrease in anisotropy with added Ni content. The ternary alloy tends to exhibit permalloy like properties but with higher magnetization. The decrease in remanence for higher Ni content marks the change in easy axis orientation from film-plane direction in FeCo to an added minor fraction of out-plane orientation in (FeCo)75Ni25. The plot of coercivity versus angle (θ) between easy axis of magnetization (film plane) and applied field along with the appropriate fitting model to the magnetization reversal is shown in fig.2. It is clear that for lower Ni content, a good fit to the experimental data for angular variation of coercivity is obtained using Kondorsky model, indicating domain reversal mechanism arising due to domain wall depinning from a local defect. The origin of these pinning centres could be the presence of an oxide layer on top of the film surface or at the ITO-alloy film interface. The magnetization reversal mechanism in FeCoNi alloy is predominantly influenced by the Ni concentration. A deeper understanding of this behaviour would be provided by micromagnetic simulation.

![](https://assets.underline.io/uploads/markdown_image/1/image/e2a88a2d12347264f1d1b30df6fbf6b1.jpg)

Change in Hc and Mr/Ms with increasing concentration of Ni


![](https://assets.underline.io/uploads/markdown_image/1/image/4ed8f861136ff255ce3d617ed218ed56.jpg)

Angular variation in Hc fitted with modified Kondorsky Model

Magnetization Reversal Behavior in Electrodeposited FeCoNi Thin Films

Developing a model of magnetic materials, such as electrical steel, that allows to account for both their nonlinear and anisotropic behavior remains a challenge. The approach presented in this paper is based on the use of a Gaussian function whose cumulative distribution function’s shape is very similar to that of a first magnetization curve. This approach has been introduced in the 90s for the study of isothermal remanent magnetization acquired by rock samples containing magnetic minerals [1,2,3]. The main drawback of this approach lies in the fact that a given magnetization curve is derived from one Gaussian function only, which is itself defined by three fixed parameters only [1], leading to non-negligible differences when compared to experimental data. Moreover, this approach has never been adapted to account for the anisotropic behavior of electrical steel. In this paper, we propose to enhance this method by using a function which results from the sum of four Gaussian functions, as illustrated in Fig. 1. To account for the anisotropy, all the parameters used to define the Gaussian functions depend on the angle between the magnetic field H and the rolling direction of the steel, denoted θ. Fig. 2 shows the comparison between first magnetization curves for three different magnetization directions (θ) obtained from experimental data (M530-50A electrical steel), from the original model based on the use of one Gaussian function only and from the proposed enhanced model. The work presented in this paper shows multiple originalities and improvements. Firstly, it shows that using more than one Gaussian function allows for a better approximation of first magnetization curves (Fig. 2). Secondly, it shows that considering θ-dependent parameters to define the Gaussian function allows the method to account for magnetic anisotropy (Fig. 2). Thirdly, it highlights that those parameters follow a polynomial trendline.

![](https://assets.underline.io/uploads/markdown_image/1/image/a840a400f9aa59752141c240e934913c.jpg)

Fig. 1 First magnetization curve derived from a Gaussian function defined as the sum of four subfunctions.

![](https://assets.underline.io/uploads/markdown_image/1/image/553c7c268068ad44177edd6923859cff.jpg)

Fig. 2 Comparison between curves obtained from experimental data (markers), from the original model (dashed) and from the enhanced proposed model (solid).

Modelling of magnetic anisotropy in electrical steel sheet by means of cumulative distribution functions of Gaussians

Additive manufacturing (AM) is becoming an alternative to traditional manufacturing methods [1]. In the most extended AM method (fused deposition modeling, FDM), a polymeric filament is extruded above its melting point for its deposition into thin layers. There is a high interest in the use of composite filaments, formed by a polymeric matrix with functional fillers, for the AM of functional parts [2]. The quality of the FDM printed parts is highly dependent on the uniformity of the filament diameter. In the case of composite filaments, a homogeneous distribution of the fillers is also crucial to have a reproducible and uniform functionality. Homogeneous soft magnetic PLA composite filaments for FDM have been recently reported, in which a customized feedstock of polymeric capsules filled with the functional fillers is employed [3]. Fig. 1 shows that composite filaments exhibit a soft magnetic behavior. Additionally, they all have a demagnetizing factor of ~ 1/3 (spheres, according to the shape of the gas atomized powders) regardless of the concentrations of fillers (up to 52 wt. %, corresponding to 12 vol. %). The addition of the fillers causes a remarkable shift in the thermal degradation temperature of the polymer. Increasing filler content produces an abrupt drop in the complex modulus of the polymer above its glass transition, which shifts to lower temperatures according to the peak of tan(δ) (Fig. 2). A decrease in the viscosity in liquid state is also observed, which causes a reduction of the extrudability and printability of the filaments for filler contents above 30 wt. %. The reduction of the viscosity of the composites requires the lowering of the temperatures for their extrusion and printing with respect to the typical ones for PLA. Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), and Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212.

![](https://assets.underline.io/uploads/markdown_image/1/image/87db25ab60c9820e49c23306bd80571d.jpg)

Fig. 1. Magnetization vs. magnetic field for the raw maraging steel powder and composite filaments.

![](https://assets.underline.io/uploads/markdown_image/1/image/245b4256f10c5e8a2ffe7ab44cd407d4.jpg)

Fig. 2. (a) Complex modulus and (b) tan(δ) of raw PLA and composite filaments.

Manufacturing and Characterization of Soft Magnetic Composite Filaments for Additive Manufacturing

Grain Oriented steels are widely used in transformers and inductors. The materials texture shows an easy magnetization direction adapted to columns and yokes but, at corners when the flux is tilted, the anisotropy must be taken into account. At the quasi-static level, the anisotropy is driven by the crystal grains, demagnetizing field and mechanical stresses, and determines the permeability, the quasi-static hysteresis and the domains orientation at the equilibrium. At the dynamic level, distinct magnetization mechanisms depend on the various domains and walls orientations. It controls the iron losses in any magnetization direction. Numerous scalar models and experimental tools can already describe mainly the unidirectional behavior [1-4]. The extension of scalar models towards tensor models is confronted to unknowns that remain about non-diagonal components and their microscopic physical interpretation explaining the hysteresis cycles in various directions. A dynamic hysteresis model [5] has been chosen. It allows the description of the magnetic behavior related to the anisotropic magnetic structure at equilibrium in quasi-static operating conditions and the anisotropic magnetization mechanisms within domains and walls in dynamic operating conditions. The goal of this work is to identify and determine the tensor properties of an electrical steel, which is necessary to use an anisotropic behavioral model according to two directions of the excitation field, making an angle between 0° (Rolling Direction RD) and 90° (Transverse Direction TD) with RD. The results will be physically discussed considering the main energies that govern the quasi-static domain structure responsible for the slope of the cycles, and those inducing the magnetization mechanisms responsible for the losses, i.e. the cycles area [6]. The experiment uses a conventional GO FeSi steel (R120-27) with a thickness of 0.27mm. Several samples with dimensions 150x150mm2 were laser cut following an accurate angle of respectively 0°, 15°, 30°, 45°, 60°, 75° and 90° with the RD. Measurements were carried out with a Single Sheet Tester which provides data for the magnetic field H and the flux density B in the two directions of the sample’s cut edges.

Experimental identification and physical interpretations of 2D tensor magnetic properties of a grain-oriented electrical steel magnetized between the rolling and the transverse directions.

The large distribution in atomic sizes and masses in high-entropy alloys results in extreme local environments, which manifests strongly in the thermal and magnetic properties. In this work, high-entropy alloys of (Fe,Co,Cr,Ni)Alx, 0 &lt; x &lt; 2, are prepared and their temperature-dependent magnetic and electronic properties determined. Magnetometry results show that all the samples are ferromagnetic, with a high-temperature phase, TC &gt;200 K, and a second low-temperature phase with TC≈20 K. However, the high-temperature phase is not associated with an open hysteresis loop, suggesting superparamagnetic behavior. The closed hysteresis loop suggests the ferromagnetism appears as small clusters, a theory explored with small-angle neutron scattering (SANS). The samples also show downturn in the magnetization at T&lt;10 K which can be associated with an antiferromagnetic phase. Recent works have suggested that extreme strain distributions can induce antiferromagnetic ordering. This research used resources at the High Flux Isotope Reactor and the Spallation Neutron Source, as appropriate, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory, and was funded by the DOE DE-SC0021344.

![](https://assets.underline.io/uploads/markdown_image/1/image/9fbbd3220c653f72e6dbb393fd2fff76.jpg)

2D SANS image from an HEA

![](https://assets.underline.io/uploads/markdown_image/1/image/066093af3816968964a48af8671c86ab.jpg)

M vs T data for HEA.

Mixed magnetic phases in FeCoCrNiAlx high entropy alloys

Rare earth permanent magnets play a key role in view of the increasing market for green energy applications and new materials which can compete with Nd2Fe14B but are environmentally less problematic are highly sought after. Fe-based ThMn12 phases contain less RE material than the commercially used compounds and have attracted quite some interest. An efficient and resource saving way to identify out of this class new phases which have the potential to become permanent magnets is by computational materials design. However, predicting the magnetic properties of 4f systems is challenging because of the localization of the 4f electrons which determines to a large extend the level of theory needed for a reliable description and prediction. We have shown that the 4f electrons in Sm 1:12 can be viewed as fully localized and can be safely treated as core electrons while for CeFe11Ti the correlation effects are smaller and the 4f states can still be viewed as valence states [1,2]. In the case of NdFe11Ti the 4f electrons are partially localized as can be seen from the hybridization function in Fig. 1. The hybridization function serves as a qualitative measure for the interaction of the 4f electrons with the valence electrons in a system [3]. As a consequence of the partial localization, the cone type magnetocrystalline anisotropy (MCA) of the latter system is only observed in a DFT+U description with an intermediate Hubbard U value, see Fig. 2. Assuming full localization (4f in core) results in a uniaxial MCA which contradicts the experimental findings at low temperatures. Plain DFT also fails. It is also discussed in how far the strong dependence of the MCA and related magnetic properties of NdFe11Ti on the theoretical description influences the prediction of new phases. As test case the quaternary system Nd1-xYxFe12-yTiy was chosen. Supported by NOVAMAG (EU686056), the Swedish Foundation for Strategic Research (EM16-0039), and SNIC (Swedish National Infrastructure for Computing).

![](https://assets.underline.io/uploads/markdown_image/1/image/4ef356ea30502b13556ecaaaa8bde227.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d1615ec9348ff3d8df6e838f0771e695.jpg)

New potential materials for rare earth lean permanent magnets from computational design and the challenge of the 4f electrons

New potential materials for rare earth lean permanent magnets from computational design and the challenge of the 4f electrons

Environmental and technological progress in sectors like energy, transportation, robotics requires large amounts of Permanent Magnets (PMs) [1]. However, high demand predictions are difficult to be met by the current supply chain [2]; subsequently there is urgent need for new materials, with less content in critical or expensive resources but compatible with current industrial infrastructure and able to maintain adequate performance. SmCo5 is a well-established PM with excellent properties which come at a high cost and criticality; stoichiometry modification is a path towards improving the overall merit from the applications’ scope [3]. In this work the effect of partially substituting Sm and Co in SmCo5 with less expensive constituents is presented. Sm0.5MM0.5(Co1-x-yFexNiy)5 samples were prepared by arc-melting constituting elements in Ar atmosphere followed by thermal treatment at 1100 - 1200 K in vacuum. Alloys were structurally and magnetically characterized experimentally and DFT calculations were performed within spin polarized rotationally invariant DFT+U framework and the the Perdew-Burke-Ernzerhof derivation of the generalized gradient approximation pseudopontentials by using the VASP code [4-6] confirmed that the desired CaCu5-type phase could be stabilized. Under our experimental conditions single phase hexagonal phase was not formed. X-Ray diffraction plots analyzed with the Rietveld method revealed a three-phase system with the main phase crystallizing in hexagonal CaCu5-type structure (a = b = 0.4877(2) nm, c = 0.4109(2) nm). There were two additional rhombohedral phases, Gd2Co7-type (a = b = 0.5037(2) nm, c = 3.6627(1) nm and Th2Zn17-type (a = b = 0.8449(4) nm, c = 1.2332(3) nm) which are built within the basic hexagonal frame and their main axes are aligned and related (c/a[1:5] = 0.843, c/a[2:7] = 0.808, a1:5 = a2:7=√3.a2:17, c1:5 = 3.c2:17 = 9.c2:7). This relation is evident in Fig. 1 where powder and epoxy-oriented xrd plots are presented. The materials present fairly large magnetization (Ms = 75-90 Am2/kg) and retain the large anisotropy and thermal endurance of the SmCo5 material.

![](https://assets.underline.io/uploads/markdown_image/1/image/d50846a2652e60266aaf2cc374b4ae52.jpg)

Fig.1: X-ray plots of powder and epoxy-oriented samples of Sm0.5MM0.5Co4Ni materials.

Cost effective modification of SmCo5-type alloys

Using molecular beam epitaxy, a nanoscale thin film magnet of c-axis-oriented Sm2Co17 and SmCo5 is stabilized. While typically in the prototype Sm(Co,Fe,Cu, Zr)7.5−8 pinning-type magnets, an ordered nanocomposite is formed by complex thermal treatments, here, a one-step approach to induce controlled phase separation in a binary Sm−Co system is shown. A detailed analysis of the extended X-ray absorption fine-structure confirmed the coexistence of Sm2Co17 and SmCo5 with 65% Sm2Co17 and 35% SmCo5. The SmCo5 phase is stabilized directly on an Al2O3 substrate up to a thickness of 4 nm followed by a matrix of Sm2Co17 intermixed with SmCo5. This structural transition takes place through coherent atomic layers, as revealed by scanning transmission electron microscopy. Highly crystalline growth of well-aligned Sm2Co17 and SmCo5 with coherent interfaces results in strong exchange interaction, leading to enhanced magnetization and magnetic coupling. The arrangement of Sm2Co17 and SmCo5 phases at the nanoscale is reflected in the observed magneto-crystalline anisotropy and coercivity. As next-generation permanent magnets require designing of materials at an atomic level, this work enhances our understanding of self-assembling and functioning of nanophase magnets and contributes to establishing new concepts to engineer the microstructure for beyond state-of-the-art magnets.

Epitaxy Induced Highly Ordered Sm2Co17−SmCo5 Nanoscale Thin Film Magnets

Strong permanent magnets (PMs) are critical for electric vehicle (EV) traction motors to reach high power density levels. Although Nd-Fe-B magnets have superior ambient magnetic strength, Dy additions currently provide thermal stability to enable motor operating temperatures of 150-180C. For sustainable PMs for EV motors, replacement of Dy in Nd-Fe-B magnets is needed since Dy is a scarce heavy rare earth (HRE) and is from (essentially) one source. Fortunately, ultrafine (&lt;4µm) grain size also can improve high temperature magnetic properties and increase ambient temperature coercivity in Dy-free Nd-Fe-B magnets, although not without reduced mechanical properties and only in lab-scale samples [1,2]. Our initial work used commercial Dy-free Nd-Fe-B alloy powders which we ball milled conventionally up to 11h, causing average particle size to decrease to 2.1 µm, but average grain size of resulting sintered magnets grew to 3.8 µm, due to grain growth from high temperature sintering (1080C). Intrinsic coercivity Hcj and maximum energy product (BH)max of the ultrafine grained magnets increased up to 13.7 kOe and 43.6 MGOe. While our new work with high energy milling has further refined feedstock powder size, reduction of sintering temperature also is needed to suppress grain growth in magnets and fully exploit ultrafine grain benefits on magnetics. Thus, an extrinsic transient liquid phase (TLP) sintering aid, Pr-30.2at.%Cu (442C eutectic), was studied for consolidation at reduced sintering temperature with suppression of grain growth. A reduced sintering temperature with full heat treatment (FHT) raised coercivity (Fig 1), presumably from suppression of grain growth. When the 1045C sintered sample with FHT (from Fig 1) was annealed at 480C, 5h (Fig. 2), coercivity also rose, presumably from increased grain defect “smoothing” by penetration of residual liquid TLP further into the magnet microstructure. These improved magnetic properties will be correlated with microstructural analysis. Supported by USDOE-EERE-VTO-EDT through Ames Lab contract no. DE-AC02-07CH11358.

![](https://assets.underline.io/uploads/markdown_image/1/image/57bd2808471f8c67b6f81b15e217de1b.jpg)

Fig 1. Effect of TLP and sintering temperatures on coercivity.

![](https://assets.underline.io/uploads/markdown_image/1/image/6d7fa8eae895d01574b4c2b84a57d45b.jpg)

Fig 2. Effect of 480C anneal with TLP on coercivity (sample sintered at 1045C, 5h).

Magnetic property effects in highly grain-refined Dy-free Nd-Fe-B sintered magnets

The design and discovery of new functional materials has acquired a sense of urgency recently for critical-elements reasons. In the case of permanent magnets, computational and experimental methods are being used synergistically to aid the search for new materials with large values of saturation magnetization Ms, anisotropy K, and Curie temperature Tc [1-3]. Ideally, the materials exhibit μoMs &gt; 0.8 T and K &gt; 1.5 MJ/m3. Another criterion for the evaluation of new permanent-magnet materials before the typically difficult task of synthesis and coercivity development is the hardness parameter κ = (K/μoMs2)1/2 [3]. This parameter can also be written as κ = (Ha/2Ms)1/2, where Ha = 2K/μoMs is the anisotropy field, so that each value of κ yields a straight line when Ha is plotted vs. Ms. Ideally, κ is comparable to or larger than one [3, 4]. Figure 1(a) combines the Ms and κ requirements to yield an area of promising permanent magnets (yellow). However, the main figure of merit in permanent magnets energy product. Figure 1(b) plots K against Ms, which has several advantages: (i) the blue isoenergetic curves show the expected maximum energy product, (ii) real-structure factors such a remanence ratio, Kronmüller factor α, packing fraction, and loop shape easily be included in the isoenergetic curves; and (iii) the primary intrinsic properties are K and Ms, not Ha and Ms. If the boundary of the yellow area and blue curves were physically equivalent, the boundary and the blue curves would be approximately parallel. This in not the case for the ascending branch of the boundary, where the curves are almost perpendicular due to the very different natures of hardness and energy product. Aside from helping to identify promising permanent-magnet materials, this work underlines the long-term aspect of permanent-magnet development. The work in Nebraska is supported by NSF-DMREF (No. 1729288), NSF-EQUATE (OIA-2044049), the NU Collaborative Initiative, and NCMN, whereas the research at Ames is funded by DOE.

![](https://assets.underline.io/uploads/markdown_image/1/image/115daa171706731e49904daa3478c12a.jpg)

Fig. 1. Permanent-magnet performance plots: (a) Ha-Ms plot and (b) K-Ms plot, the axes showing μoH and μoM. The specific model used for the blue curves assume Mr = Ms, a straight M(H) line in the second quarter, and α = 0.4.

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