United States

&lt;i&gt;d&lt;/i&gt;-dimensional higher-order topological systems (TS) possess boundary states on (&lt;i&gt;d−n&lt;/i&gt;)-dimensional interfaces where &lt;i&gt;n≥2&lt;/i&gt; [1, 2]. Here, we demonstrate a highly tunable 3-D second-order Dirac semimetal (SODSM) phase on a topolectrical (TE) circuit lattice comprising inductors and capacitors (Fig. 1) [3]. We first construct a 2-D second-order TS on the &lt;i&gt;x−y&lt;/i&gt; plane with four types of sublattice nodes (Fig. 1a). Electrical couplings with negative signs are achieved via a negative impedance converter (NIC) (Fig. 1d). To induce SODSMs, we extend the TE lattice along the &lt;i&gt;z&lt;/i&gt;-direction by stacking the circuit layers in the &lt;i&gt;x−y&lt;/i&gt; plane via the interlayer capacitor &lt;i&gt;C&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt;, which modifies the effective intercell hopping and hence the locations of the gapless points. The presence of both inversion and time-reversal symmetries ensures the existence of pairs of gapless points. The admittance band dispersion at resonant frequency hosts a pair of Dirac points (DPs) along the &lt;i&gt;k&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt; axis under periodic boundary conditions (PBC) along all directions (Fig. 2a). Moreover, two first-order DPs connected by Fermi arc surface edge states emerge under open-boundary conditions (OBC) in the &lt;i&gt;x&lt;/i&gt;-direction and PBC in the &lt;i&gt;y&lt;/i&gt; and &lt;i&gt;z&lt;/i&gt; directions. Interestingly, second-order flat hinge-like states appear in the admittance bandgap and connect the two DPs in the SODSM when PBC is imposed in the &lt;i&gt;z&lt;/i&gt;-direction and OBC in the &lt;i&gt;x&lt;/i&gt; and &lt;i&gt;y&lt;/i&gt; directions (Fig. 2c). Furthermore, the density of states (DOS) vanishes in the vicinity of the DPs. The DPs can be traced via the impedance readout between two terminal nodes. Large impedance peaks exist only near the locations of the DPs, and the impedance falls sharply to nearly zero at other points with finite DOS (Fig. 2d).

![](https://assets.underline.io/uploads/markdown_image/1/image/9ea35d73e7f491a4a7072356e5aa838a.jpg)

Schematic of SODSM TE circuit. Cross-section of TE circuit on a. x-y plane, b. x-z plane, c. y-z plane. d. Schematic of NIC using an op-amp. e. Grounding mechanisms.

![](https://assets.underline.io/uploads/markdown_image/1/image/f92e487050814f6b673b3db6dcaf22ef.jpg)

a. Admittance dispersion under PBC in all directions. b. First-order DPs under PBC in y and z directions and OBC in the z-direction. c. SODSM under PBC in z-direction and OBC in the x and y directions. d. Impedance reading of SODSM.



2022 Joint MMM-INTERMAG

A Circuit Lattice Representation of a Second-Order Dirac Semimetal

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AIP Publishing Horizons - Energy Storage and Conversion

Energy conversion and storage is a critical part of modern society. Applications continue to develop at a fast pace, from the development of new generation battery materials, to environmental sensors, catalytic materials for sustainable energy and solar cells and photodetectors. This conference will cover the latest advances in energy related fields and debate the needs and priorities currently existing or emerging in this field over the next few decades.

d-dimensional higher-order topological systems (TS) possess boundary states on (d−n)-dimensional interfaces where n≥2 [1, 2]. Here, we demonstrate a highly tunable 3-D second-order Dirac semimetal (SODSM) phase on a topolectrical (TE) circuit lattice comprising inductors and capacitors (Fig. 1) [3]. We first construct a 2-D second-order TS on the x−y plane with four types of sublattice nodes (Fig. 1a). Electrical couplings with negative signs are achieved via a negative impedance converter (NIC) (Fig. 1d). To induce SODSMs, we extend the TE lattice along the z-direction by stacking the circuit layers in the x−y plane via the interlayer capacitor Cz, which modifies the effective intercell hopping and hence the locations of the gapless points. The presence of both inversion and time-reversal symmetries ensures the existence of pairs of gapless points. The admittance band dispersion at resonant frequency hosts a pair of Dirac points (DPs) along the kz axis under periodic boundary conditions (PBC) along all directions (Fig. 2a). Moreover, two first-order DPs connected by Fermi arc surface edge states emerge under open-boundary conditions (OBC) in the x-direction and PBC in the y and z directions. Interestingly, second-order flat hinge-like states appear in the admittance bandgap and connect the two DPs in the SODSM when PBC is imposed in the z-direction and OBC in the x and y directions (Fig. 2c). Furthermore, the density of states (DOS) vanishes in the vicinity of the DPs. The DPs can be traced via the impedance readout between two terminal nodes. Large impedance peaks exist only near the locations of the DPs, and the impedance falls sharply to nearly zero at other points with finite DOS (Fig. 2d).

![](https://assets.underline.io/uploads/markdown_image/1/image/9ea35d73e7f491a4a7072356e5aa838a.jpg)

Schematic of SODSM TE circuit. Cross-section of TE circuit on a. x-y plane, b. x-z plane, c. y-z plane. d. Schematic of NIC using an op-amp. e. Grounding mechanisms.

![](https://assets.underline.io/uploads/markdown_image/1/image/f92e487050814f6b673b3db6dcaf22ef.jpg)

a. Admittance dispersion under PBC in all directions. b. First-order DPs under PBC in y and z directions and OBC in the z-direction. c. SODSM under PBC in z-direction and OBC in the x and y directions. d. Impedance reading of SODSM.

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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Recently, SmFe11Ti-based compounds with the ThMn12 crystal structure have been widely studied as a candidate for new permanent magnets due to their excellent intrinsic magnetic properties. Although those compounds have a high anisotropy field (12 T), the actual coercivity is less than 10% of their anisotropy field 1. In general, it is well known that fine precipitates corresponding to the size of the domain wall (several nm to several tens of nm) increase the coercivity of hard magnetic materials by acting as the domain wall pinning site. The addition of C to the SmFe11Ti alloy may result in TiC precipitates in the matrix, and subsequent changes in the coercivity can be expected. In this study, SmFe11Ti alloys containing different amount of C atoms were fabricated by the melt-spinning method to investigate the effects of C atoms on the microstructures and magnetic properties. SmFe11Ti1+xCx (x = 0, 0.05, 0.1, 0.2) alloys with the ThMn12 crystal structure was successfully fabricated by the melt-spinning method and subsequent heat treatment. The optimum heat treatment condition was found to be 850°C for 15 minutes, and the coercivity was shown to be about 6.2 kOe regardless of the C content (Fig. 1). In order to understand these results, the microstructural analysis was performed. It was found that the matrix had the ThMn12 crystal structure and the average grain size was about 30 nm in all samples regardless of the C content (Fig. 2). In these samples, coarse TiC grains (&gt;100 nm) instead of TiC nano-precipitates were formed independently from the matrix. This result explains the reason why the coercivity did not change. Thus, the experimental conditions for obtaining the precipitates are under investigation.


![](https://assets.underline.io/uploads/markdown_image/1/image/75746d30b79db84128662e894a5853fe.jpg)


Fig. 1 Coercivity measured at 2.5 T of SmFe11Ti1+xCx (x = 0, 0.5, 0.1, 0.2) alloys heat treated at 850°C for 15 minutes.


![](https://assets.underline.io/uploads/markdown_image/1/image/4b02a146f9f1f24e4dc7ba739af1ff8b.png)

Fig. 2 Microstructures of SmFe11Ti1.2C0.2 sample heat treated at 850°C for 15 minutes. (a)Bright field image using Transmission Electron Microscopy. (b)Dark field image and corresponding EDS mapping image using Scanning Transmission Electron Microscopy. The grains which was shown in dark contrast on the image was region that Ti and C was concentrated.

The effect of C addition on the magnetic properties and microstructures of nanocrystalline SmFe11Ti alloy

Research on rare-earth-free permanent magnet materials have attracted much attention due to the limited supply and high price of the rare-earth metals used in current state-of-the-art permanent magnets. MnBi and MnBi-based magnets have been investigated as prospective rare-earth-free magnets because the magnetic anisotropy of MnBi increases with increasing temperature reaching a maximum value at 590 K. However, segregation of Bi during synthesis of MnBi is one of the issues which reduces the saturation magnetization. We have found that MnBi synthesized in carbon environment substantially reduces the amount of Bi segregation improving its saturation magnetization. We have synthesized Mn55Bi45 and Mn55Bi45C samples using arc melting and high vacuum annealing. The room temperature x-ray diffraction patterns indicate that both Mn55Bi45 and Mn55Bi45C crystallize in the hexagonal NiAs crystal structure (Low temperature phase, LTP). The X-ray diffraction pattern also indicates that the amount of Bi segregation in Mn55Bi45C is less than that in MnBi. As shown in Fig. 1 below, the high field (3T) magnetization measured at room temperature are 61 emu/g and 66 emu/g for Mn55Bi45 and Mn55Bi45C, respectively. There is small increase in the value of anisotropy constant due to carbon doping. In order to find the possibility of carbon occupying the MnBi lattice, we have carried out first principles calculations of MnBi alloy as well. The conclusions of the first principles calculation and experimental data on structural and magnetic properties of Mn55Bi45 and Mn55Bi45C will be presented. This research is supported by South Dakota-NASA EPSCoR Research Initiation Grant no 80NSSC19M0063.

![](https://assets.underline.io/uploads/markdown_image/1/image/e0f6f2e16ebf3f5ccde46e9f75d13c25.jpg)

Fig. 1: Isothermal magnetization curves M(H) for Mn55Bi45 and Mn55Bi45C measured at 300 K. Inset shows the M(H) curve for Mn55Bi45C after aligning in magnetic field.

Modifying magnetic properties of MnBi with Carbon: An experimental and theoretical study

1.Background Rare earth permanent magnets, i.e., Nd2Fe14B and Sm2Co17, have been used in spacecraft motors. However, the direct atomic displacement in the rare earth permanent magnets’ so-called knock-on damage occurs via cosmic rays [1]. If the knock-on atom does not return to a normal lattice position, the empty lattice point becomes atomic vacancy, so-called a point defect. As a result, the rare earth permanent magnets degrade in magnetic properties and demagnetize, and it could also cause cascade damages. We studied Nd2Fe14B with point defects by first-principle calculation to show how the point defect affects its magnetic properties. 2. Calculation method and models Formation energies and magnetic properties were calculated by the first-principles calculations based on density functional theory, which is implemented in the VASP code with GGA + U method (U = 6 eV) [2]. The cut-off energy was 700 eV, k-point mesh was set to and lattice constants were determined based on the experimental values [3]. A point defect of Nd was assumed to be generated when the interatomic bond in the Nd2Fe14B crystal was cut by the collision of radiation particles with Nd atoms (Fig. 1). The generation processes of point defects of B and Fe were assumed to be the same as Nd. Thus the point defect formation energy was defined as the energy difference before and after the collision as shown in Eq. 1. Eform=(Edef+Eiso)-Eperfect (1) where Eper, Edef and Eiso are the total energies of electrons in a perfect crystal, a crystal with a point defect, and an isolated atom, respectively. 3. Results First, we confirmed that the magnetic moments of the calculation for the perfect crystal and experiment were similar (Table I). Subsequrntly, we found that only the crystal with the point defect of B increased the magnetic moment. We also found that the point defect formation energies of Fe were lower than those of B and Nd and the point defect formation energies of B and Nd were similar.

![](https://assets.underline.io/uploads/markdown_image/1/image/aad867ae5234f598c10ca41a8650f875.jpg)

Fig.1 Calculation models for point defect formation energy of Nd in Nd2Fe17B.


![](https://assets.underline.io/uploads/markdown_image/1/image/590f8f080de1faeb3e880ca5a596de16.jpg)

Table I. Magnetic moments and point defect formation energies

First-principles study of rare earth permanent magnets with point defects created by radiation

Recently, more attention has been paid to developing rare earth free permanent magnets. (Fe0.7Co0.3)2B with tetragonal structure shows good intrinsic hard magnetic properties. It has a large saturation magnetization (Js=13 kGs), a high Curie temperature (Tc=940 K), and a moderate uniaxial magneto-crystalline anisotropy (MCA) field (HA= 7.7 kOe) [1-4]. In addition to the good intrinsic properties, the hard magnetic properties such as coercivity are also sensitive to microstructure. In particular, the coercivity reduces sharply upon the existence of the low MCA regions in microstructure, which favors the nucleation of the magnetic domain for the magnetization reversal. There always exist some local structural defects in real magnets, such as chemical composition fluctuation, local strain, and even the second impurity phase. In this work, the sensitivity of MCA to composition fluctuation and structural defects has been studied by a first-principles DFT calculation. The calculated MCA energy (Emca) of (Fe0.7Co0.3)2B with perfect structure is 0.125 meV/f.u. A fluctuation of cobalt content of 10%, or 1% isotropic lattice strain (Fig.1), or 2% tetragonal distortion will cause a reduction of Emca up to 30% in (Fe0.7Co0.3)2B. The spin-resolved MCA analysis indicates that spin-up and spin-down electrons contribute positively to Emca while the spin mixing has a negative contribution (Fig.1). The interplay of these different contributions results in optimized chemical composition or geometrical structure to maximize MCA. Micromagnetic simulation indicates that the coercivity decrease from 2.2 kOe to 1.0 kOe in an isotropic magnet of (Fe0.7Co0.3)2B with an average grain size of 30nm by considering the existence of randomly distributed local reduction of MCA energy up to 30%. This work is supported by the Critical Materials Institute (CMI), an Energy Innovation Hub funded by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office. Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

![](https://assets.underline.io/uploads/markdown_image/1/image/c11d0f0079ff1d8d06c4d6f00a36a5d9.jpg)

Calculated spin-resolved- and total- magnetocrystalline anisotropy energy as a function of lattice strain in (Fe0.7Co0.3)2B.

Robustness of magneto-crystalline anisotropy and its effect on coercivity in (Fe0.7Co0.3)2B

Magnetic refrigeration (MR), exploiting the adiabatic demagnetization phenomena, is preferable over conventional gas-compression based technology due to its low cost and high efficiency along with environment-friendly method [1-3]. Recently, earth-abundant Mn-based alloy, Mn5Ge3 has emerged as a potential alternative with reasonably high relative cooling power (RCP) which is the centre of the present study [4]. Concerning the technological applications, the role played by the size-reduction (macro to micro-scale) on the engineering of innovative devices is still in its early age. In this context, Mn5Ge3 ribbons are synthesized using the melt spinning technique. The temperature and field-dependent dc magnetization are measured with physical properties measurement system (Quantum design, 8T). The M (T) curve at 1 kOe shows a sharp ferromagnetic ordering at TC ~ 304 K. Furthermore, the M (H) hysteresis loop at 5 K reveal the typical soft ferromagnetic behaviour with saturation magnetisation (MS) of 136 emu/g with approximately zero hysteresis loss which is highly preferential for MR technology. From magnetic isotherms, the magneto-caloric effect is studied in the wide temperature range of 250-360 K. Using the Maxwell equation, Isothermal magnetic entropy change (ΔSM) is calculated as 5 J/Kg-K at 5 T applied field [See Fig 1]. From inset of Fig. 1, It is quite apparent that all the normalized entropy curves with various ΔH values collapse into a single curve, confirms second order magnetic phase transition. Next, we calculate another parameter such as RCP = ΔSm|max × δTFWHM, where δTFWHM is the span for half to maxima of ΔSm (T) curve around a magnetic transition for practical utilization in MR. The RCP value is obtained as 295 (600) J/kg for a field change of 3 (5) T which is significantly larger than 201.3 J/kg (3 T) as observed in an earlier Mn5Ge3 study [5]. Hence, a large RC value makes the Mn5Ge3 ribbon highly promising for magnetic refrigeration application near room temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/b4bb7f645e496a7395e89ca7a488d9ca.jpg)

The temperature dependence of -ΔSm in field range of 0.5 - 3T (ΔH = 0.5 T) and 4 - 8T (ΔH = 1 T). The inset shows normalized -ΔSm as a function of the rescaled temperature (θ).

Enhanced refrigerant capacity in Mn5Ge3 melt spun ribbon near room temperature

Magnetic cooling, based on the magnetocaloric effect (MCE), offers many advantages over traditional compressor-based refrigeration. Among many promising materials, the (Mn,Fe)2(P,Si) family of compounds attracts broad attention due to the non-toxic composition, large magnetocaloric effect, tunable Curie Temperature (Tc) and limited thermal hysteresis (ΔThys). The stoichiometry of the quaternary alloy (Mn,Fe)2(P,Si) has a significant impact on the magnetocaloric performance. Additionally, the magnetocaloric response of the (Mn,Fe)x(P,Si) system is highly sensitive to the heat treatment conditions. For the Fe-rich (Mn,Fe)x(P,Si) (2.00 ≥ x ≥ 1.80) melt-spun ribbons, we investigated the phase purity as a function of starting composition and annealing temperature. For a first batch, annealed for 2h at 1373 K, we found with decreasing M/NM ratio from 2.00/1 to 1.90/1 an increase in Tc from 251.3 to 310.1 K and a decrease in ΔThys from 33.3 to 8.3 K. These changes were accompanied by a decreasing amount of the metal-rich (Mn,Fe)3Si impurity phase. A further decrease of the M/NM ratio leads to a rapid reduction of Tc to 178.5 K and an increase in hysteresis to 75.7 K. Along with these changes, the formation of the non-metal (Mn,Fe)Si impurity phase was observed. In order to investigate the effect of the heat treatment, ribbons were annealed at 1313 and 1433 K. The magnetic entropy change (ΔSm) and ΔThys increase with increasing annealing temperature, indicating the enhancement of the First Order Magnetic Transition (FOMT). The formation and composition of the (Mn,Fe)3Si impurity strongly depend on the annealing conditions, as evidenced by SEM/EDS analysis. The change in the annealing temperature caused a significant change in the composition and amount of the (Mn,Fe)3Si impurity phase. These changes were accompanied by the enlargement of grains and grain boundaries. The (Mn,Fe)Si impurity phase segregated in the form of micro-sized inclusions. Unlike (Mn,Fe)3Si, the (Mn,Fe)Si impurity appeared stable and remained strongly Fe and Si-rich for all annealing temperatures.

Improving the Magnetocaloric Response of Fe-rich (Mn,Fe)2(P,Si) Alloys

Gadolinium is the simplest material with a strong magnetocaloric effect close to room temperature (Tc = 293 K) and no thermal hysteresis [1], making it an ideal test-bench material for magnetic refrigeration and energy harvesting prototypes [2,3]. Gd ribbons of thickness 36-215 μm were prepared by cold-rolling [4] while films of thickness 20-150 μm were deposited by evaporation onto dimpled Hastelloy substrates [5]. More recently, films of thickness in the µm range were made by magnetron sputtering [6,7]. Here we present a study of Gd films of thickness in the range 3.5 - 40 μm, deposited by triode sputtering onto Si substrates at RT or 400°C, with Ta buffer and capping layers. As has been reported in magnetron sputtered films [7], our triode sputtered films can be removed from the substrate to produce free-standing films, and peel-off is easiest for films deposited at elevated temperature. Films were characterized structurally (optical and Scanning Electron Microscopy, XRD), magnetically (VSM-SQUID, extraction magnetometer) and mechanically (interferometer, nanoindenter). An SEM image of the fractured cross section of a 20 µm thick film deposited at 400°C is shown in Fig. 1, together with θ-2θ XRD patterns from the upper and lower surfaces of the film. It can be seen that the film texture changes from (00l) at the lower surface to (103) at the upper surface. A spin-reorientation transition is clearly seen in the M(T) curve of a 3.5 µm thick film, while it becomes smeared in thicker films (Fig. 2), owing to the evolution in crystallographic texture. In this presentation we will report on the influence of film thickness and deposition temperature on the structural, magnetic and mechanical properties of Gd films, which are being developed for integration into micro-scaled thermal energy harvesting devices [3]. Acknowledgement: This research has received funding from the French National Research Agency under the HiPerTherMag project (ANR-18-CE05-0019).

![](https://assets.underline.io/uploads/markdown_image/1/image/dd535808ff17c217e3a7ead00118fb60.jpg)


Fig. 1 Left: SEM image of a 20 µm thick Gd film deposited at 400 °C. Right: θ-2θ XRD spectra from the upper and lower surfaces of the film, following peel-off from the substrate.


![](https://assets.underline.io/uploads/markdown_image/1/image/f29d014564fd1b808054343a926d5a44.jpg)

Fig. 2 Magnetization vs temperature, measured under 50 mT, of Gd films deposited at 400°C.

Structural, magnetic and mechanical properties of Gd films

A recent study shows that the magnetic entropy changes of Gd2O3 nanostructure depend on the morphology and it varies from - 8.7 J kg−1 K−1 for nanotubes to - 20 J kg−1 K−1 for the rod. Several attempts have been made to study the magnetocaloric effect (MCE) on different morphology but comparative study on morphology dependent MCE is missing. Here we investigate the MCE of Gd2O3 nanoparticles of different morphology. Single-phase Gd2O3 nanoparticles were synthesized via the hydrothermal method and a homogeneous precipitation method followed by heat-treated in the air at 1100OC for 12h. Four Gd2O3 nanoparticles of different shapes viz. bulk, rod, spheres, and plate were prepared. The morphology of the samples was analyzed using a scanning electron microscope (SEM). The SEM images of synthesized Gd2O3 showed fine 1D nano-rods, 2D nano-plates-like architecture prepared via hydrothermal method while hollow nanosphere morphology was achieved with a homogeneous precipitation method. The phase identification and lattice parameter of the powders were performed using x-ray diffraction which showed the presence of a highly crystalline single phase cubic crystal structure. Magnetic measurements were performed from 5 to 100K and magnetic field up to 50kOe. The material demonstrated typical paramagnetic behavior in the whole measured temperature region. The M-H data in the temperature range of 3–30 K is used to calculate the isothermal magnetic entropy change. The maximum value of ΔSm for 50 kOe field change at 5K is 11.2 J kg−1 K−1 for the nanoplate sample, 9.4 J kg−1 K−1 for the nano-rod, and 9.2 J kg−1 K−1 for the nano-sphere, and 10.7 J kg−1 K−1 for Bulk. The large ΔSm could be attributed to the surface area and surface geometry of the sample. More surface area indicates more surface spins that enhanced magnetization value. These results show the Gd2O3 nanoplates are promising materials for low-temperature application. Work at SUNY, Buffalo State was supported by the startup fund from SUNY Buffalo State College and the Undergraduate Research Office, Buffalo State.

Study the magnetocaloric properties of shape-dependent nanostructured Gd2O3: Nanoplates, Nanorods, and Nanospheres

Microwave-assisted magnetization recording [1] has been attracting intense research interests for ultra-high-density recording. The mechanism of microwave assisted magnetization switching (MAS) under the DC field applied parallel to the anisotropy direction have been theoretically studied so far [2, 3]. According to the references, the effect of microwave assistance is translated by the equivalent field denoted by ω/γ. Whilst, in the case when DC field is applied non-parallel to the anisotropy axis, the estimation of MAS field is quite complex. In this study, we proposed an approximation for estimating the MAS field when the DC field was applied nonparallel to the anisotropy axis. Fig. 1(a) showed the schematic illustrations for approximating magnetization dynamics by a static system. DC magnetic field (HDC) was applied at θ with respect to the anisotropy axis, and circularly polarized field (HAC) in x-y plane. φ stands for the angle between the procession axis and anisotropy axis. Here we extend the theory [2, 3], where the equivalent field lay in the opposite to the magnetization precession axis, hence the z and x-y plane components of the normalized effective magnetic fields are given by hxy=hDCsinθ-(ω/HkΥ)sinφ+hAC, hz=hDCcosθ-(ω/HkΥ)cosφ (Eq. 1). Fig. 1(b) showed that the field components obtained by micromagnetic calculation agreed with the asteroid curve, which translated the approximation worked even when DC field has an incident angle. The relation between hDC and φ (hDC=(0.5sin2φ-hACcosφ)/sin(θ-φ) Eq. 2) derived from ∂E/∂φ=0 and asteroid curve gave approximated DC MAS field. Fig. 2 compared the approximation and micromagnetic calculation, where hSW were plotted as a function of the DC field incident angles. In the calculation, microwave frequency is lower than critical frequency and hAC is 0.03. The difference between the approximation and micromagnetic simulation were confirmed to be less than 8% and the discrepancy decreased with increase in θ.

Estimation of microwave-assisted magnetization switching field by static energy approximation

This paper deals with a 24-pole segmented rotor in a 3-phase, 36-slot per stator topology of an axial-field double stator switched reluctance machine (AFDSSRM). An axial-field segmental rotor switched reluctance motor with single stator and tooth winding is investigated in [1] achieving higher torque density than the radial SRM. A double stator design of the same motor is presented in [2] to counter the unbalanced force due to the one sided excitation in the single stator version. For radial field SRM, the mutually coupled winding configuration is compared to the conventional one in a number of works [3], [4] but it has never been investigated in the case of an AFDSSRM. Fig.1 (a) shows the classical winding (+A--B++C--A++B--C+) and (b) shows the mutually coupled one (+A-+B-+C-+A-+B-+C-). The topology of the AFDSSRM is made of 2 stators connected in series and a segmented rotor in between. Each stator tooth holds one coil dedicated to one phase. In this paper, The AFDSSRM is modeled using a 2D finite element model (FEM). The 2D-FEM is established at the mean radius of the machine with the hypothesis of radial invariance of local quantities [5]. It is used to achieve calculations of self and mutual inductances, flux-linkage and torque for three different current distributions. The motor is first fed with 3-phase step current in unipolar and bipolar mode. Then a 3-phase sinusoidal current is used. Fig.2 illustrates the variation of self and mutual inductance for both winding configurations. It appears that in the case of the classical winding, the mutual inductance can be neglected and the self-inductance is up to 2.5 times higher than the mutually coupled one. For the mutually coupled configuration, the self and mutual inductance variations follow the same trend with regards to current and they are of the same order of magnitude.

a)
![](https://assets.underline.io/uploads/markdown_image/1/image/04be1c95f8fa36103b4d6d2e3d0d8cb3.png)
b)
![](https://assets.underline.io/uploads/markdown_image/1/image/cb330670f88cd482733a918e33e669ab.png)

Fig.1 Winding configuration of the AFDSSRM, a) Classical winding, b) Mutually coupled.

![](https://assets.underline.io/uploads/markdown_image/1/image/1dda4ef71f1b128f486447cf6a284065.png)

Fig 2. Variation of self and mutual inductance versus current for both winding configuration (Classical and Mutually Coupled)

A Circuit Lattice Representation of a Second-Order Dirac Semimetal

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The effect of C addition on the magnetic properties and microstructures of nanocrystalline SmFe11Ti alloy

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