United States

Single crystals of the triangular lattice Heisenberg antiferromagnet (TLHAF) Ca&lt;sub&gt;3&lt;/sub&gt;NiNb&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;9&lt;/sub&gt; and its non – magnetic analogue Ca&lt;sub&gt;3&lt;/sub&gt;MgNb&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;9&lt;/sub&gt; were grown using the four - mirror optical float zone furnace. Here we have studied the influence of various growth atmospheres and pulling rates on the crystal quality and phase homogeneity. Both the compounds melt congruently and the grown crystal specimens suffer from cracks when the crystal boule is cooled, thus making it difficult to obtain large single crystalline pieces. To overcome this difficulty, an after – heater was used to reduce the formation of cracks. Interestingly, the crystal boule of Ca&lt;sub&gt;3&lt;/sub&gt;NiNb&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;9&lt;/sub&gt; exhibits two regions of distinct colours and optical opacities i.e. opaque black and translucent green. Further, the as - grown, opaque, black specimen was subjected to air annealing at 1200&lt;sup&gt;o&lt;/sup&gt;C for 24hrs, wherein its appearance changed from black to translucent green, without any change of weight. Low temperature specific heat and magnetization measurements carried out on the as - grown black sample (AGO) and the air annealed sample (ANT) revealed contrasting ground state properties. While the as - grown specimen exhibits a broad hump close to 10 K in specific heat measurement, the air annealed sample showcases two transitions at T&lt;sub&gt;N1&lt;/sub&gt; = 4.6 K and T&lt;sub&gt;N2&lt;/sub&gt; = 4.3 K, in agreement with the previous reports by J Ma &lt;i&gt;et al &lt;/i&gt;&lt;sup&gt;1&lt;/sup&gt;. Moreover, room temperature synchrotron XRD further revealed that AGO specimen crystallizes in a higher symmetry orthorhombic space group while the ANT specimen crystallizes in the reported monoclinic space group. Thus, the ground state of this triangular lattice system is very sensitive to the growth conditions and annealing experiments help recover the properties reported for the polycrystalline sample.

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Single crystal growth and low temperature physical properties of triangular lattice antiferromagnet - Ca3NiNb2O9

2022 Joint MMM-INTERMAG

Single crystal growth and low temperature physical properties of triangular lattice antiferromagnet - Ca3NiNb2O9

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Single crystals of the triangular lattice Heisenberg antiferromagnet (TLHAF) Ca3NiNb2O9 and its non – magnetic analogue Ca3MgNb2O9 were grown using the four - mirror optical float zone furnace. Here we have studied the influence of various growth atmospheres and pulling rates on the crystal quality and phase homogeneity. Both the compounds melt congruently and the grown crystal specimens suffer from cracks when the crystal boule is cooled, thus making it difficult to obtain large single crystalline pieces. To overcome this difficulty, an after – heater was used to reduce the formation of cracks. Interestingly, the crystal boule of Ca3NiNb2O9 exhibits two regions of distinct colours and optical opacities i.e. opaque black and translucent green. Further, the as - grown, opaque, black specimen was subjected to air annealing at 1200oC for 24hrs, wherein its appearance changed from black to translucent green, without any change of weight. Low temperature specific heat and magnetization measurements carried out on the as - grown black sample (AGO) and the air annealed sample (ANT) revealed contrasting ground state properties. While the as - grown specimen exhibits a broad hump close to 10 K in specific heat measurement, the air annealed sample showcases two transitions at TN1 = 4.6 K and TN2 = 4.3 K, in agreement with the previous reports by J Ma et al 1. Moreover, room temperature synchrotron XRD further revealed that AGO specimen crystallizes in a higher symmetry orthorhombic space group while the ANT specimen crystallizes in the reported monoclinic space group. Thus, the ground state of this triangular lattice system is very sensitive to the growth conditions and annealing experiments help recover the properties reported for the polycrystalline sample.

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Single crystal growth and low temperature physical properties of triangular lattice antiferromagnet - Ca3NiNb2O9

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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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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.

A Circuit Lattice Representation of a Second-Order Dirac Semimetal

To see the competition between effect of spin fluctuations, e.g. [1] and magnetic ordering the Gd1-xCexNi5 (x=0; 0.2; 0.5; 0.8 and 1) system in a ribbon form was prepared. The XRD results display with the increase of the Ce content, and the unit cell is expanding. The shoulder obtained from the magnetic susceptibility for CeNi5 measured in zero-field cooling and field cooling mode between T = 100 K and T = 150 K corresponds with a maximum presence in polycrystalline CeNi5 compound [2]. The origin of spin fluctuations is possible explained in several ways. The authors of [3, 4] publications suppose that it is an intrinsic material feature. Moreover, the previous study did not show a low-temperature change [5, 6]. The temperature dependencies of the magnetic properties from the rest of the samples besides GdNi5 have a character typical for antiferromagnetic materials. However, the study of other physical properties does not confirm antiferromagnetic ordering. An effective paramagnetic moment for CeNi5 is 3.52 μB/f.u, slightly higher than for free Ce3+ ion and for GdNi5 is 7.52 μB/f.u. The magnetic properties studies show that only a tiny percentage of Gd creates transition temperature in dopped material. This conclusion is partially supported by a negative value of paramagnetic Curie temperature. The paramagnetic region of the M(T) curve under the applied magnetic field fitted with a Curie-Weiss fit. The heat capacity was measured by the 2-τ method in the temperature range from 2 K to 300 K with DC applied magnetic fields from 0 T to 9 T. The obtained results of this method support magnetic measurements analyses. In summary, we will present the preparation, structural, morphological and physical properties analysis of single-phase ribbons of the Gd1-xCexNi5 (x=0; 0.2; 0.5; 0.8 and 1) melt-spun ribbons. The obtained results can bring new knowledge to a group of advanced materials in condensed matter physics. The prepared samples belong to advanced materials and potential magnetic actuators due to their interesting physical properties. This research work was supported partially by VEGA 1/0404/21; VEGA 1/0705/20; VEGA 1/0053/19, and APVV-16-0079.

Experimental Study of Emergent Ground State Behaviour in Gd1-xCexNi5 (x=0; 0.2; 0.5; 0.8 and 1) Melt-Spun Ribbons

Ternary RScGe intermetallics (R = Rare earth) crystallizing in a layered CeScSi-type structure (space group I4/mmm) demonstrate rich physics and a range of diverse magnetic phenomena. For example, PrScGe exhibits multiple magnetic transitions: paramagnetic (PM) to antiferromagnetic (AFM), then AFM to ferrimagnetic (FIM), and finally FiM-I to FiM-II upon cooling.1 GdScGe, in contrast, remains ferromagnetic below its Curie temperature (TC) of 350 K, which is notably higher than the TC (= 293 K) of its only magnetic constituent, Gd.2 These RScGe systems become even more interesting with substitutional alloying or additions of interstitials. Thus, Sm1-xNdxScGe shows an extraordinary large exchange bias3 and GdScGeH exhibits a loss of dimensionality and magnetic order.4 Here, through x-ray magnetic circular dichroism (XMCD) measurements, we report the interplay between Gd and Pr atoms in representatives of pseudo-ternary Pr1-xGdxScGe. We present direct evidence of antiparallel coupling between heavy and light lanthanide ions that occupy the same sublattice resulting in near zero magnetization. We explain how coupling magnetic compensation with small cooling fields can create magnetic memory – possibly opening up a new avenue for magneto-thermal memory devices. Lastly, we discuss the addition of hydrogen and its effects on dimensionality and electronic structure. This work was supported by the Office of Science of the U.S. Department of Energy (DOE), Division of Materials Sciences and Engineering, Office of Basic Energy Sciences. The Ames Laboratory is operated for the U.S. Department of Energy (DOE) by Iowa State University of Science and Technology under contract No. DE-AC02-07CH11358. XMCD research at the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science, under contract DE-AC02-06CH11357.

Magnetic Interplay Between Gd and Pr in the CeScSi-type Layered Structure

The R2TX3 (R = rare-earth, T = transition and X = s and p block element) series of compounds are interesting owing to their fascinating structural and magnetic properties [1-3]. In this present work, we have studied the magnetic properties of the new Pr2AgSi3 polycrystalline compound. The sample was synthesized by arc-melting method and confirmed to crystallize in the tetragonal α-ThSi2 structure with space group I4/amd. The Pr atoms are arranged on a triangular lattice in this crystal structure. The sample was studied by dc– and ac–magnetic susceptibility and specific heat measurements. A ferromagnetic transition was observed at Tc≈15 K which is slightly above the spin freezing temperature Tf ≈ 13 K. The high-temperature dc-magnetic susceptibility exhibit ferromagnetic exchange. The irreversibility observed between zero-field cooled (ZFC) and field cooled (FC) dc-susceptibility data suggests a spin-glass behaviour in the compound. The characteristics of spin-glass behaviour were further confirmed in ac-magnetic susceptibility, aging and memory effect measurements in both ZFC and FC modes. An asymmetric response during heating and cooling of the system is observed in the magnetic relaxation measurement with a positive heating cycle in both ZFC and FC mode. It therefore follows the hierarchical model of spin glass systems. The existence of frustrated moments due to the triangular arrangements of Pr atoms is discussed in terms of the magnetic cluster model observed in Pr2AgSi3.

Ferromagnetic Spin Glass State Behaviour in Pr2AgSi3

The magnetic phase diagram (MPD) of the Cr100-zOsz alloy system exhibits possible quantum critical behavior (QCB), with the commensurate spin-density-wave to paramagnetic (CSDW-PM) phase line terminating at z ≈ 14 in a superconducting dome emerging at z ≈ 12 [1]. The co-existence of SDW antiferromagnetism (AFM) and superconductivity (SC) is also reported for the z = 12.2 sample with bcc structure [1]. Considering the unique behavior in the Cr100-zOsz system [1], the present study reports on the temperature dependence of the thermoelectric power or Seebeck coefficient, S(T), for this system. In general, S(T) is sensitive to changes in the electronic structure as well as to various scattering mechanisms, and can be used to probe the presence of phonon and magnon drag effects [2,3], making it the perfect tool to investigate the magnetic behavior in the mentioned system. S(T) measurements were performed on polycrystalline Cr100-zOsz (2.1 ≤ z ≤ 14.1) samples prepared using arc-melting techniques. Only primary bcc reflections were observed in the x-ray diffraction results. For a magnetic material the absolute thermoelectric power can be approximated as [4]: S = Spd + Smag + Sdiff, where Spd and Smag is the phonon and magnon drag terms and Sdiff is due to the diffusion of electrons. The first two terms dominate at low T and the latter at elavated T. The low-temperature thermoelectric power of Cr and its alloys can be written in the simplified form of [2]: S = aT + bT3, where a and b are constants. Thus, at low T a plot of S/T as a function of T2 should be linear and can be used to obtain a and b. Resulting plots of a(z) and b(z) show anomalies associated with three crucial points in the Cr100-zOsz MPD: (i) z ≈ 7 is associated with the destabilization of the CSDW phase, (ii) z ≈ 12 where SC manifest and (iii) z ≈ 14 linked to QCB [1]. Considering dS/dT where T approaches 0 K, dS/dT│T→0, as function of z, anomalies are also observed at z ≈ 12 and 14, linked to the onset of SC and QCB in this system. Thus, as was previously suggested for selected Cr based alloy systems [5], S can be a decisive parameter that can be utilized in characterizing and understanding the critical behavior reflected in the MPD of Cr100-zOsz.

Anomalous Behaviour in the Seebeck Coefficient of Cr100-zOsz Alloy System

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)

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