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Where the high-performance permanent magnets are needed (e.g. in the area of ‘green’ energy technology, such as electric vehicles and windmills) rare-earth (RE) magnetic materials dominate. At the same time, the heavier RE elements are quite expensive, some of them are rapidly decreasing in availability, and are often mined with the methods that leave an environmental footprint. Additionally, nowadays, there is a gap between the ‘strong’ RE-based magnets and their RE-free alternatives.&lt;br/&gt; We are using the data-mining approach in the search for high (and medium)-performance RE-free/lean magnetic materials. Filtering through a large number of known structures from ICSD database [1], we are looking for materials with high magnetization M &amp;gt; 1 T, uniaxial MAE &amp;gt; 1 MJ/m&lt;sup&gt;3&lt;/sup&gt;, and T&lt;sub&gt;c &lt;/sub&gt;&amp;gt;300 K. Sometimes, additional elements alterations are attempted to tweak the properties that are below the required values or make the material more cost-effective.&lt;br/&gt; Two searches have already been performed – a search amongst the materials containing a 3d- and a 5d-elements [3] and the materials that contain at least two 3d- metals [4]. New material was found (that had not been used as a permanent magnet before) and consequently synthesized by our experimental collaborators – Co&lt;sub&gt;3&lt;/sub&gt;Mn&lt;sub&gt;2&lt;/sub&gt;Ge [4]. From the ab-initio calculations, the defect-free material was predicted to have the saturation magnetization of 1.71 T, the uniaxial magnetocrystalline anisotropy of 1.44 MJ/m&lt;sup&gt;3&lt;/sup&gt;, and the Curie temperature of 700 K. The samples synthesized, however, were found to have a partial disorder of Co and Ge. A saturation polarization of 0.86 T at 10 K was detected, together with a uniaxial magnetocrystalline anisotropy constant of 1.18 MJ/m&lt;sup&gt;3&lt;/sup&gt;, and the T&lt;sub&gt;C&lt;/sub&gt; = 359 K. These magnetic properties make Co&lt;sub&gt;3&lt;/sub&gt;Mn&lt;sub&gt;2&lt;/sub&gt;Ge a very promising material to be considered as a rare-earth free permanent magnet. Its magnetism depends critically on the amount of disorder of the Co and Ge atoms, a further improvement of the magnetism is possible.&lt;br/&gt; The next high-throughput search is being currently performed in collaboration with the experimental colleagues.&lt;br/&gt; We would like to acknowledge the financial support of the SSF and SNIC for the computation resources.

2022 Joint MMM-INTERMAG

High-throughput and Data-mining Search for Novel Rare-Earth-Free Permanent Magnets

Where the high-performance permanent magnets are needed (e.g. in the area of ‘green’ energy technology, such as electric vehicles and windmills) rare-earth (RE) magnetic materials dominate. At the same time, the heavier RE elements are quite expensive, some of them are rapidly decreasing in availability, and are often mined with the methods that leave an environmental footprint. Additionally, nowadays, there is a gap between the ‘strong’ RE-based magnets and their RE-free alternatives. We are using the data-mining approach in the search for high (and medium)-performance RE-free/lean magnetic materials. Filtering through a large number of known structures from ICSD database [1], we are looking for materials with high magnetization M &gt; 1 T, uniaxial MAE &gt; 1 MJ/m3, and Tc &gt;300 K. Sometimes, additional elements alterations are attempted to tweak the properties that are below the required values or make the material more cost-effective. Two searches have already been performed – a search amongst the materials containing a 3d- and a 5d-elements [3] and the materials that contain at least two 3d- metals [4]. New material was found (that had not been used as a permanent magnet before) and consequently synthesized by our experimental collaborators – Co3Mn2Ge [4]. From the ab-initio calculations, the defect-free material was predicted to have the saturation magnetization of 1.71 T, the uniaxial magnetocrystalline anisotropy of 1.44 MJ/m3, and the Curie temperature of 700 K. The samples synthesized, however, were found to have a partial disorder of Co and Ge. A saturation polarization of 0.86 T at 10 K was detected, together with a uniaxial magnetocrystalline anisotropy constant of 1.18 MJ/m3, and the TC = 359 K. These magnetic properties make Co3Mn2Ge a very promising material to be considered as a rare-earth free permanent magnet. Its magnetism depends critically on the amount of disorder of the Co and Ge atoms, a further improvement of the magnetism is possible. The next high-throughput search is being currently performed in collaboration with the experimental colleagues. We would like to acknowledge the financial support of the SSF and SNIC for the computation resources.

technical paper

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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.

Criteria for Permanent-Magnet Materials

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.

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

Abstract: Compared with the widely used industrial production process of sintering, hot deformation (HD) process has many advantages and it was once considered as a candidate technology for the fourth generation rare earth permanent magnets. At present, the research of HD Nd-Fe-B magnets mainly focuses on the magnet preparation and microstructure control[1]. One-step HD can shorten the preparation process of bulk anisotropic magnets to the minimum, which highlights the advantages of simple high-definition process. However, there are still many aspects of this method that have not been systematically studied in depth. In this study, the effects of deformation ratio and temperature on the microstructure and properties of NdFeB magnets were studied by adjusting the one-step HD process. The results show that the optimized magnetic properties with Hcj, Jr and (BH)max of 960 kA/m, 1.2 T and 33 MGOe are obtained at 750 oC with 80% deformation ratio, which are very close to the performance of ordinary hot pressing/hot deformation (HP/HD) magnets, as shown in Fig. 1 (a). The microstructure and corrosion resistance were studied. The results show that with the increase of HD temperature and deformation rate, the corrosion resistance of the magnet first increases and then decreases, and the platelet grains become more obvious. When the HD temperature exceeds 750 oC and the deformation exceeds 80%, the grain growth is too large and the grain boundary thickness decreases sharply. After 90%, there is no grain boundary phase and the grain shape of the two deformed magnets is basically the same, as shown in Fig. 1 (b). It can be considered that one-step HD can replace HP/HD and achieve the simplest process while maintaining the performance [2]. As shown in Figs. 1 (c) (d), with the increase of deformation rate and HD temperature, the magnetic energy product and remanence first increase and then decrease, and the coercivity monotonously decreases.

![](https://assets.underline.io/uploads/markdown_image/1/image/619f224750bb04aa175f6fb5c5df58c9.jpg)

Effects of deformation ratio and temperature on microstructure and properties of NdFeB magnets by one-step hot deformation

Abstract Grain boundary diffusion (GBD) provides a promising way for Nd-Fe-B magnets to obtain high coercivity with less consumption of critical rare earths (RE). With the expansion of application field, the mechanical and anti-corrosion properties of Nd-Fe-B magnets has attracted increasing attention except their magnetic properties. Here, we proposed a strategy to simultaneously enhance these properties by GBD without employing heavy rare earths (HRE). The diffusion sources of Pr70Al20Cu10 (PrAlCu) and Al75Cu25 (AlCu) were prepared by arc melting. The thickness of initial magnet is 4.5 mm. The results show that the coercivity can be enhanced from 1000 to 1346 and 1089 kA/m by diffusion of PrAlCu and AlCu, respectively (Fig. 1(a)). Interestingly, the compression strength of the magnets also increased by 485 and 252 MPa, respectively. In addition, it is found that AlCu diffusion can improve the corrosion resistance of the magnets, which is different from that of PrAlCu [1]. The microstructure analysis showed that PrAlCu diffusion leads to the formation of continuous grain boundary (GB) layers for magnetic decoupling and strong binding between 2:14:1 grains (Fig. 1(b)). Although the non-RE diffusion source of AlCu shows less efficiency in increasing the content of RE-rich GB phases (Fig. 1(c)), it reduces the defects at interfaces, which is helpful for hindering the reversal domain nucleation [2, 3], as shown in Figs. 1(d1) to (d3). The modified GBs by AlCu diffusion also are effective for crack bridging or buffering, and exhibit an enhanced chemical stability. The high-abundance elements La/Ce based diffusion sources are also investigated in this work. The present results indicate that GBD of the HRE-free low-melting alloys can be used to effectively improve both the magnetic and service performance of Nd-Fe-B magnets due to the optimized microstructure.

![](https://assets.underline.io/uploads/markdown_image/1/image/1d95088594a90e4bd612c377f5970c41.jpg)

A strategy to enhance magnetic and service performance of Nd-Fe-B magnets by HRE-free grain boundary diffusion

The theory on exchange spring magnets, published by Kneller and Hawig in 1991, heralded the next big leap forward in the field of advanced permanent magnets. The theory predicted that a magnet prepared by combination of a hard and a soft magnetic phase would exhibit an improved remanent magnetization, Mr, as long as the two phases were mutually exchange coupled [1]. However, accomplishing an actual improvement has proven rather challenging. When large particles of soft phase are strongly exchange coupled to a hard phase, a magnetic softening is induced, instead of the desired hardening [2]. However, moderate Mr enhancements have been detected in exchange-decoupled composites [3]. The dominant magnetic interactions in exchange decoupled systems are magnetodipolar [4]. Therefore, exploiting the dipolar interactions between exchange decoupled hard and soft phases is an alternative strategy to prepare magnetic composites with an enhanced performance [5]. The efficacy of the method relies on controlling the magnitude of the self demagnetizing fields, which strongly depends on the size and shape of the soft phase. Here, exchange decoupled SrFe12O19 (hard)/Fe (soft) composites have been prepared, both in powder and injection moulded magnet dense form. The influence of the size of the soft phase has been experimentally studied, covering a range between 25 nm and 11 µm. Micromagnetic simulations have been carried out for the specific system in order to understand the spin dynamics inside the soft grains (see Figure 1). Regardless of the soft phase dimensions, the composites show a larger Mr than predicted by the theory. In fact, we observe and report here for the first time an increase in remanence in hard-soft injection moulded magnets in the absence of exchange coupling. Micromagnetic simulations point at the existence of a vortex like state at the core of the Fe particles, which orients with the internal field created by the ferrite particles, as the reason for this increase in remanence. Figure 1. (a) experiment; (b) micromagnetic simulations at remanence and (c) at coercivity. The authors would like to thank financial support from the European Commission through the project AMPHIBIAN (H2020 NMBP 2016 720853).

![](https://assets.underline.io/uploads/markdown_image/1/image/feaa7141cd372b61bcc43aab2e22a4ad.jpg)

Remanence Improvement in Exchange-Decoupled Composites Owing to Dipolar Interactions

Exchange spring hard-soft magnetic nanocomposites (NCs) are proposed as potential high-performance magnets [1,2]. Their relatively poor performance [3-6] compared to predicted values [7] is attributed to insufficient control over the size and distribution of the soft phase. In this work e-beam lithography was used to control the size, shape and position of soft magnetic (FeCo) nano-rods embedded in a micro-patterned hard magnetic matrix (25 nm thick FePt-L10). We report a study of samples with different nanorod widths (24 and 120 nm) and comparable volume content. Their global M(H) loops have similar Hc values, but that of the sample with wide nanorods is concave (Fig. 2a), and First Order Reversal Curve diagrams reveal that this sample has some uncoupled soft magnetic phase. Uncoupled soft phase reversal is confirmed by MFM imaging in different remanent states, where hard and soft phase switching can be distinguished owing to the different length scales of the patterns (Fig. 1). Micromagnetic modelling (MuMax3) was performed to simulate magnetization reversal and MFM contrast. Good agreement is obtained between the measured (Fig. 2a) and simulated (Fig. 2b) data. Magnetization distribution cross-sections during reversal indicate that the wide soft rods reverse independently of the hard matrix, while the narrower rods are coupled during the entire reversal process (Fig. 2c-e). Convoluting results of stray field distributions at the experimental scan height with an MFM probe modelled as a monopole, we obtained comparable images with periodic patterns with the same length scale as the nanorods (Fig. 2f-g). The use of MFM remanent imaging combined with simulations to study magnetization reversal will be discussed in the framework of a broader study of model soft in hard nanocomposites.

![](https://assets.underline.io/uploads/markdown_image/1/image/97f767231afaf37c18391fe56fc92af6.jpg)

MFM images of NCs in remanent state, after applied field of 250 mT (left) and 500 mT (right), for rod widths of 24 nm (a,c) and 120 nm (b,d). Inserts - SEM plan view images of the nanorods (1 µm scale bar).

![](https://assets.underline.io/uploads/markdown_image/1/image/0304cf4965480752d8cca3cfd62a8896.jpg)

a) Experimental M(H) loops; b) Simulated demagnetization curves. c-e). Magnetization maps at the height of the rod (numbers indicate position along the demag curve). Simulated (f) and experimental (g) MFM contrast.

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