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Because the degree of vibration in the permanent magnet synchronous motor (PMSM) is dependent on the magnetization distribution in the permanent magnet. The accurate estimation of magnetization distribution at the previous stage of the practical design eliminates the manufacturing of PMSM with poor performance.&lt;br/&gt;To nondestructively estimate the magnetization distribution in the permanent magnet, some numerical methods using the magnetic flux density measured on the outside region of the permanent magnet have been proposed [1], [2]. Because there are countless combinations of magnetization distribution in the permanent magnet, these methods can effectively remove the non-physical distributions. However, since those performances depend on the parameter tunings, the non-physical distributions cannot be completely removed. Then, the deep learning-based estimation method is proposed.&lt;br/&gt;In this paper, the deep feedforward neural network is applied to the estimation method. The network is configured by the framework of Keras [3], which is the python-based library of deep learning. The number of network layers is set to 9 layers. The number of neurons in the input layer is set to 344, which is identical to the summation of &lt;i&gt;x&lt;/i&gt;- and &lt;i&gt;y&lt;/i&gt;- direction of magnetic flux density on 172 measuring points on the outside of the 2-D permanent magnet model. The number of neurons in the output layer is set to 816, which is identical to the number of cells for the magnetization. The target distribution of magnetization is focused on the parallel orientation. The training data are generated by changing the angle of parallel direction every 0.01 degree within [0, 360] with the uniform intensity of magnetization. The weighted coefficients are determined by AdaGrad [4].&lt;br/&gt;The input data (magnetic flux density) is generated by Biot-Savart law, and the 5 % error of the magnetization intensity is superposed on all data, as shown in Fig. 1. While the non-physical distribution tends to be estimated using the conventional methods [1], [2], the practical distribution is estimated using the proposed deep learning system, as shown in Fig. 2. The complicated magnetization distributions in 3D field will be estimated in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/7c8243f47a10aa08684a096da45db3f1.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/37d9c1618dae2eb45dea4d383d086e70.jpg)

2022 Joint MMM-INTERMAG

Deep Learning-based Estimation Method of Magnetization Distribution in Permanent Magnet

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INTERMAG 2021

Because the degree of vibration in the permanent magnet synchronous motor (PMSM) is dependent on the magnetization distribution in the permanent magnet. The accurate estimation of magnetization distribution at the previous stage of the practical design eliminates the manufacturing of PMSM with poor performance. To nondestructively estimate the magnetization distribution in the permanent magnet, some numerical methods using the magnetic flux density measured on the outside region of the permanent magnet have been proposed [1], [2]. Because there are countless combinations of magnetization distribution in the permanent magnet, these methods can effectively remove the non-physical distributions. However, since those performances depend on the parameter tunings, the non-physical distributions cannot be completely removed. Then, the deep learning-based estimation method is proposed. In this paper, the deep feedforward neural network is applied to the estimation method. The network is configured by the framework of Keras [3], which is the python-based library of deep learning. The number of network layers is set to 9 layers. The number of neurons in the input layer is set to 344, which is identical to the summation of x- and y- direction of magnetic flux density on 172 measuring points on the outside of the 2-D permanent magnet model. The number of neurons in the output layer is set to 816, which is identical to the number of cells for the magnetization. The target distribution of magnetization is focused on the parallel orientation. The training data are generated by changing the angle of parallel direction every 0.01 degree within [0, 360] with the uniform intensity of magnetization. The weighted coefficients are determined by AdaGrad [4]. The input data (magnetic flux density) is generated by Biot-Savart law, and the 5 % error of the magnetization intensity is superposed on all data, as shown in Fig. 1. While the non-physical distribution tends to be estimated using the conventional methods [1], [2], the practical distribution is estimated using the proposed deep learning system, as shown in Fig. 2. The complicated magnetization distributions in 3D field will be estimated in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/7c8243f47a10aa08684a096da45db3f1.jpg)

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poster

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.

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Magnetocaloric refrigeration has emerged as an attractive candidate to replace conventional compression-based refrigeration systems in virtue of its higher Carnot efficiency and eco-friendlier refrigeration thereby replacing potent CFCs. This solid-state refrigeration can be exploited mainly for compact devices such as micro refrigerators, thermal diodes, regulators, and electronics where heat extraction is challenging. To facilitate the usage of magnetocalorics for such applications, 2D printing of magnetocaloric nanoparticle inks is versatile approach to generate custom structures. Among magnetocaloric materials, the FeRh alloy system demonstrates the largest magnetocaloric effect at first order (AFM-FM) phase transition at near-to-equimolar composition. Previous studies reveal that the synthesis of FeRh nanoparticles using conventional processes leads to undesired Fe/Rh core-shell structures and for a magnetocaloric response, a uniform near-to-equiatomic distribution of Fe and Rh within nanoparticles is critical. Here, we demonstrate a laser-based approach for the synthesis of FeRh nanoparticles1 and 2D sintering of a developed ink2. A Fe50Rh50 bulk target was ablated using an infrared picosecond-pulsed laser in organic solvents (acetone, acetonitrile, and ethanol) leading to the formation of paramagnetic solid solution Fe50Rh50 nanoparticles with reduced oxygen content (up to 5 at. %).1 The generated nanoparticles were used to formulate an ink (up to 1 wt.%) in ethanol and dispersed on PVP-coated glass substrates and were patterned using 532 nm CW laser. The 2D laser sintering facilitates the formation of pore-free custom structures and induces ultrafast partial phase transition from paramagnetic to ferromagnetic and antiferromagnetic phases.2

Synthesis and printing of Fe50Rh50 nanoparticle inks– a laser-based route to generate magnetocaloric structures

The development of the electric vehicle makes a higher requirement to the torque/power density of the traction motors. It has been difficult to meet the requirements by using conventional silicon steels. Therefore, the application of “new” materials could become a breakthrough. In this paper, we research the properties and the application in traction motors of the Fe-Co-V alloy 1J22. Compared with conventional silicon steels, 1J22 has a higher saturation flux density, which enables the motor to have a higher torque density. However, the impact of stamping and shear stress during the processing progress greatly reduces the magnetic properties, which means the annealing processes is necessary and will change the magnetic performance significantly[1]. According to the Fe-Co binary alloy phase diagram[2], it can be seen that the annealing temperature cannot be higher than 910 degrees. For our experiment, the annealing temperature of 850 degrees is adopted. At the same time, hydrogen protection is applied to avoid the oxidation reaction. R. S. Sundar found that the magnetic performance with a holding time of 4 hours can reach an excellent level and when the temperature is above 750 degrees during cooling, slowly lower the temperature at a rate of 50 degrees/hour. At 730 degrees, an ordered phase will be produced [3], the short-range order in the disordered phase will grow up to form a long-range order which makes the dislocations difficult and leads to the poor ductility and the brittleness of the alloy. The saturated flux density (Bs) of Fe-Co binary alloy increases with the increase of Co content. When the Co content is 35%, Bs is 2.45T. When the Fe-Co atom ratio is close to 1:1, the magnetocrystalline anisotropy constant is about 0, which has the highest magnetic permeability. Dr. White’s team [2] added 2% V to the alloy to improve its brittleness. We use 1J22 material to develop a prototype with a rated power of 6kW and a rated speed of 4500rpm. The torque density of the prototype is increased by 14% compared with the conventional motor used silicon steel. This paper is divided into 4 parts: Magnetic properties test and metallographic observation; Motor design; Prototype manufacturing and test and conclusion.

![](https://assets.underline.io/uploads/markdown_image/1/image/114336f638aef64cff3a088076af1427.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/f0e907f6b5e4ded7acbe9650d566bc60.jpg)

Research and Application of the Fe-Co-V Soft Magnetic Alloy to The High Torque Density Electric Machine

With the rapid improvement of electromagnetic (EM) equipment, the high-frequency (HF) soft magnetic films have been studied intensively as HF components such as a film type inductor, an electromagnetic noise suppressor sheet, and so on.[1, 2] In particular, the nano-granular films are well-known as one of the best choices as HF components, which can prevent the ensuing plunge in electrical resistivity as ferromagnetic resonance frequency (fFMR) increases. Herein, we select Co-Sr-F nano-granular films as the material of HF components and investigate their structure and magnetic properties in detail. The structure is nanocomposite, that is, Co nano-granules are evenly dispersed in a ceramic matrix. TEM observations indicate Co nano-granules change from a spherical to a columnar shape as the Co content increases. The electrical resistivity decreases from 109 to 104 μΩ*cm with a steep around 50~55 at.% of Co content as the Co content increases because of the change in the morphology of the film. In the range of Co content above 50 at.%, their coercivities are obtained and their saturation magnetizations (Ms) increase linearly(Fig.1). These results indicate that the films are ferromagnetic in the range of Co content above 50 at.%. To clarify fFMR of these films, the change in permeability of these films with frequency is measured, and the observed fFMR is summarized in Fig. 2 as a function of Co content. For Co content between 51~55 at.% (stage I), fFMR remains constant around 4.8 GHz, while, for Co content above 55 at.% (stage II), fFMR increases to 12 GHz monotonically. These behaviors can be explained by the change in the morphology of Co nano-granules. Namely, in stage I, as Co nano-granules are spherical, Kittel formula[3] is expressed as fFMR=γHz (γ is the gyromagnetic ratio). In stage II, as Co nano-granules are columnar, Kittel formula is described as fFMR=γ(Hz+1/2MS) and fFMR increases linearly with the increase of Ms. Therefore, these results demonstrate fFMR and film morphology correlates each other apparently, and suggest that Co-Sr-F nano-granular films are one of the candidates for HF components.

![](https://assets.underline.io/uploads/markdown_image/1/image/95284d1c80b5b322b200c42bcb5efff8.jpg)

Fig. 1 Magnetization curves of Co-Sr-F nano-granular thin film.


![](https://assets.underline.io/uploads/markdown_image/1/image/bfe412a99934f4776922a184262e4281.jpg)

Fig. 2 The dependence of fFMR on Co content.

Relationship between morphology and soft-magnetic properties of Co-Sr-F nano-granular films

The magnetization switching in glass-coated amorphous nanowires with cylindrical symmetry is presented and discussed. We studied the coercive field dependence of the nanowires dimensions in order to understand the main aspects of the magnetization reversal processes in amorphous nanowires with cylindrical symmetry. The considered samples were two alloys with representative compositions: (1) the alloy (Co0,94Fe0,06)72,5Si12,5B15, with very small negative magnetostriction, considered, from this reason, almost zero; and (2) the alloy Fe77,5Si7,5B15, with a positive magnetostriction. In order to substantiate the approach taken, we simulated the axial hysteresis loops for amorphous nanowires with various diameters, whilst keeping a constant sample length. The results, illustrated in Figure 1, reveal the fact that the coercive field decreases when the diameter is larger. This dependence is related to the value of the shape anisotropy, which increases with the ratio between length and diameter. The simulated loops allowed us to understand the effect of anisotropy on coercivity. For the magnetoelastic contribution, we used a simple anisotropy distribution to calculate the axial hysteresis loops in the case of glass-coated Fe77.5Si7.5B15 amorphous nanowires. The results, for different magnitudes of the magnetoelastic anisotropy, are shown in Fig.2. One observes that the magnetoelastic contribution clearly affects the remanence of the axial hysteresis loops. A smaller squareness also shows an easier nucleation of a domain with reversed magnetization. The use of such cylindrical nanowires in magnetic logic gates is straightforward, given their bistable behavior which paves the way for application in new miniaturized devices [1]. Acknowledgement: Work supported by the Executive Unit for Financing Higher Education, Research, Development and Innovation (UEFISCDI) under the project PN-III-P4-ID-PCE-2020-1856 (contract no. PCE 1/2021).

![](https://assets.underline.io/uploads/markdown_image/1/image/197b3e03e30de3198a8693848bcd624e.jpg)

Fig. 1 Hysteresis loops of cylindrical amorphous nanowires with different diameters and compositions.

![](https://assets.underline.io/uploads/markdown_image/1/image/4884a95693a04dfe9ca0274e826a4e4a.jpg)

Fig. 2 Hysteresis loops for different anisotropy distributions: (i) monotonous distribution (MD) with various amplitudes; and (ii) nonlinear distribution (NLD).

Micromagnetic study of anisotropy in cylindrical amorphous nanowires

Bayesian optimization is a well-developed machine learning field for black box function optimization. In Bayesian optimization a surrogate predictive model, here a Gaussian process, is used to approximate the black box function. The estimated mean and uncertainty of the surrogate model are paired with an acquisition function to decide where to sample next. Bayesian optimization with Gaussian processes can be used for structure-property relationship optimization in materials systems with second order phase transitions or gradual disordering without a distinct phase transition. In this study we applied this technique to known ferromagnetic thin film materials such as ferromagnetic (Fe100−y Gay)1−xBx (x=0–21 & y=9–17) and (Fe100−y Gay)1−xCx (x=1–26 and y=2–18) to demonstrate optimization of structure-property relationships, specifically the dopant concentration or stoichiometry effect on magnetostriction and ferromagnetic resonance linewidth. These systems both experience gradual disordering without distinct phase transition with increase in boron and carbon concentration, thus are great case systems for Bayesian optimization with Gaussian processes. We have shown that using simulated Bayesian optimization methods to guide experiments, the number of samples required to statistically determine the optimum was reduced by 50% compared with traditional research methods. Our results suggest that Bayesian optimization can be used to save time and resources to optimize ferromagnetic films. This method is transferrable to other ferromagnetic material structure-property relationships, providing an accessible implementation of machine learning to magnetic materials development.

Application of Bayesian Optimization and Regression Analysis to Ferromagnetic Materials Development

Currently, anisotropic magnetoresistive (AMR) sensors are actively used in many promising areas, such as automotive industry, geomagnetic navigation, biomedicine, etc. This is due to the fact that AMR sensors have quite good sensitivity to the magnetic field, high reliability, thermal stability, resistance to harsh environment and low cost. An important role in the fabrication of magnetoresistive elements of AMR sensors is played by the magnetic characteristics of thin ferromagnetic films at the nanoscale, which, in turn, depends on their internal crystal structure, controlled by the parameters of the technological process [1]. In this work, we experimentally analyzed the dependence of the key magnetic properties (coercivity, AMR coefficient, and magnetic anisotropy field) of a 30 nm permalloy (Ni80Fe20) thin film on its grain size controlled by the substrate temperature during magnetron sputtering (Figure 1). It was shown that both the AMR coefficient and the magnetic anisotropy field tend to reach a constant level of 2.25% and 5 Oe, respectively, with an increase in the grain size. In turn, the dependence of the permalloy film coercivity on the grain size has a minimum in the region of about 8 nm and sharply increases at a smaller thickness, which corresponds to the assumed behavior of NiFe from previous studies [2]. The results obtained are important for the development of magnetic nanostructures for a new generation of highly sensitive magnetoresistive sensors based on the AMR effect [3]. This work was performed with the financial support of the Foundation for Assistance to Small Innovative Enterprises in Science and Technology (FASIE) (contract No. AAAA-A20-120111290020-5) using the equipment of MIET Core Facilities Center «MEMSEC».

![](https://assets.underline.io/uploads/markdown_image/1/image/a8ea0939bc9bcdd7c425fcf114f38ae9.jpg)

Figure 1. (a) Coercivity (anisotropy field) and (b) AMR coefficient as a function of the grain size of 30 nm permalloy film.

Study of the magnetic properties of nano-thin permalloy films depending on the grain size

Vibration of the core during the operation of medium-frequency transformer is the main electromagnetic noise source, which will cause environmental noise pollution and even influence the reliability of the transformer [1-2]. At present, the research on vibration and noise of silicon steel under multiple conditions is developing rapidly. However, the measurement of magnetic properties, vibration and noise of ultra-thin oriented silicon steel are not complete [3]. Therefore, a real-time vibration and noise measurement platform based on a triaxial acceleration sensor is built in this paper to measure the magnetic properties, vibration and noise of ultra-thin oriented silicon steel simultaneously, as shown in Fig.1. The vibration and noise of amorphous, GT-050 and GT-100 ultra-thin grain-oriented silicon steel core under sinusoidal, square and rectangular waveforms are compared and analyzed. The calculation formula of the vibration acceleration under non-sinusoidal excitation is also deduced. In addition, the effect of dead time on vibration and noise is analyzed. Part of the results are shown in Fig. 2. It can be seen that the vibration of the core increases with the increase of frequency and magnetic flux density. The vibration and noise under non-sinusoidal excitation are much greater than that under sinusoidal excitation. The vibration amplitude in the lamination direction is larger than other directions. By comparison, ultra-thin oriented silicon steel has higher saturation magnetic flux density, lower loss and lower vibration noise than amorphous alloys. The measurement data in this paper can provide a basis for material selection for medium-frequency electrical equipment designers.

![](https://assets.underline.io/uploads/markdown_image/1/image/e21eaf43663686cf2289451e7a3f2600.jpg)

Fig. 1. Real-time measurement platform for transformer core vibration and noise

![](https://assets.underline.io/uploads/markdown_image/1/image/33cf023dda74693ab975e58f0efc3c3b.jpg)

Fig. 2. Vibration acceleration of GT-100 under different excitations and directions

Measurement and Analysis of Vibration and Noise Characteristics of Medium-Frequency Transformer Core Under Non-Sinusoidal Voltage Excitation

Rapidly solidified amorphous wires with diameters below 1 μm have opened up new miniaturization opportunities for sensing devices and created new application possibilities [1]. Here we report on an in-depth study of magnetization switching in nearly zero magnetostrictive (Co0.94Fe0.06)72.5Si12.5B15 amorphous wires with diameters between 300 and 450 nm, prepared by an improved variant of glass-coated melt spinning. Hysteresis loops were measured using a method developed specifically for thin wires [2]. All samples were magnetically bistable, exhibiting a rectangular axial loop. Hence, magnetization reversal takes place by depinning and subsequent propagation of a single domain wall when the applied field H reaches the value of the switching field, H*. We measured the domain wall velocity at various values of H, starting from H = H* up to the maximum employed value, Hmax = 10 000 A/m. The most remarkable results are shown in Fig. 1, which illustrates both the switching field and the domain wall velocity vs. sample diameter. Both exhibit strongly nonlinear variations with the diameter. Also, the slopes of the curves are always opposite to one another. The nonlinear shape of wall velocity vs. sample diameter is maintained even at larger fields, up to H = Hmax. The maximum wall velocity at H = H*, i.e. 1450 m/s, was observed for a sample with 410 nm in diameter. Domain wall velocity increases monotonically with applied field for all samples. Fig. 2 shows the field dependence of domain wall velocity for the 410 nm sample, with a maximum of nearly 4000 m/s at H = Hmax. The nonlinear effects have been attributed to the nonlinear distribution of intrinsic frozen-in stresses, that are inherent to the rapid solidification preparation process. The results allow one to accurately control and tailor the magnetic behavior of these ultrathin magnetic wires for specific applications. Work supported by the Romanian Executive Unit for Financing Higher Education, Research, Development and Innovation (UEFISCDI) through project PN-III-P4-ID-PCE-2020-1856 MaDWallS (contract no. PCE1/01.02.2021).

![](https://assets.underline.io/uploads/markdown_image/1/image/a970aba3063dffb28164de150a42efa1.jpg)

Fig. 1. Switching field & wall velocity vs. sample diameter.

![](https://assets.underline.io/uploads/markdown_image/1/image/00e3b06de01dbc5ecfa81be5b8357d0f.jpg)

Fig. 2. Domain wall velocity vs. applied field for a 410 nm in diameter sample.

Nonlinear Effects in the Magnetization Switching of Nearly Zero Magnetostrictive Amorphous Submicron Wires

NdFeB sintered magnet shows the highest energy product ((BH)max) at room temperature of all developed magnetic materials, but the drastic decrease in magnetic anisotropy field (HA) of Nd2Fe14B (2:14:1) phase with rising temperature limits its application at high temperature [1]. In recent years, the grain boundary diffusion (GBD) has been reported to be an effective method to significantly enhance coercivity (iHc) with minor sacrificing remanence (Br), and also to reduce the usage of heavy rare earth (HRE) elements simultaneously [2]. The formation of core-shell structure, the distribution of HRE only at the surface of 2:14:1 phase, through GBD of HRE-containing alloys, could inhibit the nucleation of reverse domain, and thus enhance iHc [3]. In this work, the dual-alloy (DA) sintering method together with GBD treatment are adopted to further enhance coercivity and modify the magnetic properties of NdFeB sintered magnets. (BH)max of 51.4 MGOe and iHc of 14.9 kOe are obtained for the original NdFeB magnet made by sintering Ce85Al15 doped NdFeB powders. Magnetic isolation due to the distribution of Ce and Al at grain boundary increases of the coercivity effectively, yet few Ce entering into grain interior decreases Br, (BH)max, and Curie temperature slightly. In addition, coercivity of the above magnets can be further enhanced to 22.7-25.1 kOe by GBD with different amount of Tb70Cu30 powders. The clear core-shell structure, which consists of (Nd, Tb)2Fe14B phase with higher HA as the shell and Nd2Fe14B phase as the core, is observed. CeAl helps to form continuous and smooth grain boundary. The diffusion source of TbCu could infiltrate into the magnet along such smooth grain boundary and form homogeneous core-shell structure. As a result, coercivity are remarkably enhanced from 14.9 kOe for DA sintered magnet with 2 wt.% CeAl to 25.1 kOe for the magnet GBD with TbCu. Most importantly, various levels of the NdFeB magnets, such as 52M, 35-50SH, and 45UH, could be attained by simply modifying the amounts of CeAl for DA sintered magnets and/or GBD with TbCu powders.

Magnetic properties of Ce85Al15 doped NdFeB sintered magnet by grain boundary diffusion of Tb70Cu30 powders

In order to reveal the demagnetization mechanism of NdFeB magnets and establish the relationship between microstructure and magnetic property, this paper focuses on the structural change of magnetic domain and the demagnetization behavior of NdFeB magnets under various demagnetization factors. Temperature, constant demagnetizing field and alternating demagnetizing field are applied to NdFeB magnets by high and low temperature alternating test chamber, demagnetization test device, programmable DC power supply and programmable AC power supply. Demagnetization test device is made up of 2000 turns copper winding winded on a laminated hollow rectangular steel core. Magnetic properties of the studied material are determined by magnetic domain size, amplitude and open-circuit remanence. The magnetic domain structure and open-circuit remanence are measured by atomic force microscope and Tesla meter. When the sample is demagnetized, the open-circuit remanence of the measuring point in the magnetization direction decreases, and the open-circuit remanence of the measuring point perpendicular to the magnetization direction increases. In the domain imaging, the domain size in the magnetization direction becomes fine and the amplitude decreases, while the domain size perpendicular to the magnetization direction expands and the amplitude increases. The change of magnetic domain structure is consistent with the macroscopic demagnetization law. As the domain size decreases, the number of domains increases and the area of domain wall increases. As a transition region with weak magnetism, the increase of domain wall area will lead to the decrease of macro magnetic properties. When the alternating demagnetizing field is 1000Hz at 140 °C, the remanence losses in the magnetization direction reaches 47.9%, and the domain size increases from 2.35 μm reduced to 1.15 μm. This work is helpful to understand the demagnetization mechanism of NdFeB magnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/6e029230f24bf115f2a0be497a2d004f.jpg)

Magnetic domain of NdFeB magnet demagnetized by an alternating magnetic field with frequency of 1000Hz at 140 °C.

![](https://assets.underline.io/uploads/markdown_image/1/image/a78fa86255ef22db4c513685daf75636.jpg)

Open-circuit remanence losses and domain size of NdFeB magnets demagnetized by multiple levels of alternating fields and temperatures.




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Synthesis and printing of Fe50Rh50 nanoparticle inks– a laser-based route to generate magnetocaloric structures

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