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Recently, Co&lt;sub&gt;2&lt;/sub&gt;TiSi Heusler alloy is theoretically predicted that is one of the Weyl semimetal (WSM) candidates, and also the half-metal [1, 2, 3]. Since it is expected that a large anomalous Hall effect (AHE) can be observed in the WSM materials, Co&lt;sub&gt;2&lt;/sub&gt;TiSi is an attractive material showing both a large AHE and a large spin polarization. And it is also expected that the AHE can be enhanced by the Fermi level tuning in Co&lt;sub&gt;2&lt;/sub&gt;TiSi with V doping [4, 5]. In this research, we optimized the fabrication conditions for producing Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;1-x&lt;/sub&gt;V&lt;sub&gt;x&lt;/sub&gt;Si thin films, and investigated their AHE.&lt;br/&gt;The ultra-high vacuum magnetron co-sputtering method was used for the preparation of thin films using Co&lt;sub&gt;2&lt;/sub&gt;TiSi and Co&lt;sub&gt;2&lt;/sub&gt;VSi targets. The structure of the sample was MgO (001) sub. / Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;1-x&lt;/sub&gt;V&lt;sub&gt;x&lt;/sub&gt;Si (50 nm) / Ta (5 nm). For the preparation of Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;1-x&lt;/sub&gt;V&lt;sub&gt;x&lt;/sub&gt;Si films, we changed the doping amount of x, and the post annealing temperature (&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;a&lt;/sub&gt;) was changed in the range of 300 to 700°C. We characterized the crystal structure, magnetic properties, and anomalous Hall effect by XRD, SQUID, and PPMS, respectively.&lt;br/&gt;Four-hold symmetric (111) superlattice diffractions from Co&lt;sub&gt;2&lt;/sub&gt;TiSi and Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;0.84&lt;/sub&gt;V&lt;sub&gt;0.16&lt;/sub&gt;Si are observed, shown in Fig.1, meaning that the &lt;i&gt;L2&lt;sub&gt;1&lt;/sub&gt;&lt;/i&gt; ordered epitaxial films were successfully fabricated. High magnitude of saturation magnetization was also confirmed at low measurement temperature for both films. By the plot of anomalous Hall conductivity vs electric conductivity, all samples show that the intrinsic mechanism dominates over the extrinsic mechanism which is also expected in WSM. The anomalous Hall conductivity of Co&lt;sub&gt;2&lt;/sub&gt;TiSi sample was only 53 S/cm at low temperature and it was enhanced to 98 S/cm by the Fermi level tuning in Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;0.84&lt;/sub&gt;V&lt;sub&gt;0.16&lt;/sub&gt;Si, shown in Fig.2. We infer that the Fermi level for the prepared Co&lt;sub&gt;2&lt;/sub&gt;TiSi is not cross the Weyl points and it is expected that the AHE can be huge enhanced by the Fermi level tuning in Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;0.61&lt;/sub&gt;V&lt;sub&gt;0.39&lt;/sub&gt;Si.&lt;br/&gt;This research was conducted by participating in the GP-Spin, Tohoku University, and supported by CSIS Organization for Advanced Studies and the CSRN.

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2022 Joint MMM-INTERMAG

Enhancement of Anomalous Hall Effect in Magnetic Weyl Semimetal Co2TiSi Heusler Alloy Thin Films with V doping

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

Recently, Co2TiSi Heusler alloy is theoretically predicted that is one of the Weyl semimetal (WSM) candidates, and also the half-metal [1, 2, 3]. Since it is expected that a large anomalous Hall effect (AHE) can be observed in the WSM materials, Co2TiSi is an attractive material showing both a large AHE and a large spin polarization. And it is also expected that the AHE can be enhanced by the Fermi level tuning in Co2TiSi with V doping [4, 5]. In this research, we optimized the fabrication conditions for producing Co2Ti1-xVxSi thin films, and investigated their AHE. The ultra-high vacuum magnetron co-sputtering method was used for the preparation of thin films using Co2TiSi and Co2VSi targets. The structure of the sample was MgO (001) sub. / Co2Ti1-xVxSi (50 nm) / Ta (5 nm). For the preparation of Co2Ti1-xVxSi films, we changed the doping amount of x, and the post annealing temperature (Ta) was changed in the range of 300 to 700°C. We characterized the crystal structure, magnetic properties, and anomalous Hall effect by XRD, SQUID, and PPMS, respectively. Four-hold symmetric (111) superlattice diffractions from Co2TiSi and Co2Ti0.84V0.16Si are observed, shown in Fig.1, meaning that the L21 ordered epitaxial films were successfully fabricated. High magnitude of saturation magnetization was also confirmed at low measurement temperature for both films. By the plot of anomalous Hall conductivity vs electric conductivity, all samples show that the intrinsic mechanism dominates over the extrinsic mechanism which is also expected in WSM. The anomalous Hall conductivity of Co2TiSi sample was only 53 S/cm at low temperature and it was enhanced to 98 S/cm by the Fermi level tuning in Co2Ti0.84V0.16Si, shown in Fig.2. We infer that the Fermi level for the prepared Co2TiSi is not cross the Weyl points and it is expected that the AHE can be huge enhanced by the Fermi level tuning in Co2Ti0.61V0.39Si. This research was conducted by participating in the GP-Spin, Tohoku University, and supported by CSIS Organization for Advanced Studies and the CSRN.

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poster

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

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.

![](https://assets.underline.io/uploads/markdown_image/1/image/85de8c1c92d82b2319726be39907dba1.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/7eae1aa5f12df7726cd9f06806846048.jpg)

Single crystal growth and low temperature physical properties of triangular lattice antiferromagnet - Ca3NiNb2O9

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

Half-metallic Heusler alloys have attracted much attention due to their potential application in spin-transport-based devices. We have synthesized one such alloy, CoFeV0.5Mn0.5Si, using arc melting and high-vacuum annealing. The vacuum annealing was done at 600oC for 24 hours. First principles calculation indicates that CoFeV0.5Mn0.5Si shows nearly half-metallic band structure with the degree of spin polarization of about 93%. The room temperature x-ray diffraction patterns are indexed with the cubic crystal structure without disorder and secondary phases. The annealed sample show ferromagnetic order with the Curie temperature well above room temperature (Tc = 657 K) and the high-field (3T) magnetization at room temperature of about 83 emu/g. Figure 1 below shows the magnetization as a function of temperature of CoFeV0.5Mn0.5Si measured at 1 kOe which shows a smooth magnetic transition at the Curie temperature. The observed structural and magnetic properties are consistent with the theoretical results and these results indicate that CoFeV0.5Mn0.5Si has a potential for room temperature spin-transport-based devices. This research is supported by the National Science Foundation (NSF) under Grant Numbers 2003828 and 2003856 via DMR and EPSCoR.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd63234b2eeb383951e6554ddc76dd14.jpg)

Figure 1: Thermomagnetic curve M(T) of CoFeV0.5Mn0.5Si alloy. The inset shows the dM/dT versus T curve

Electronic band structure and magnetism of CoFeV0.5Mn0.5Si

A gap opening in the surface state bands via breaking of TRS in topological insulators (TI) is needed for realization of dissipationless Quantum Anomalous Hall Effect (QAH) and other fascinating topological properties [1-5]. Here, we report formation of an antiferromagnetic (AFM) phase at the interface of sputter grown crystalline textured TI, Bi2Te3 when coupled with ferromagnetic metal (FM), Ni80Fe20 (Permalloy, Py). We grew samples of 40 nm c-axis oriented Bi2Te3 at 250 degC followed by 20 nm of Py at room temperature. Diffusion of Ni from Py and formation of distinct Ni-doped Bi2Te3 interfacial phase was observed. Zero Field Cooled (ZFC) magnetic hysteresis loop measurements at low temperatures showed a large spontaneous exchange bias of ~80 Oe at 6 K which suggests presence of strong FM/AFM coupling in the samples (Figure. 1). Location of the antiferromagnetic phase at Ni intercalated Bi2Te3 interfacial layer was identified using Polarized Neutron Reflectometry (PNR) (Figure 2) at 7 K. The magnetic scattering length density (MSLD) has a value of ~0.26 at 1T saturation field but is ~0 at a low field of 50 Oe when the magnetic moments in the interfacial layer are antiferromagnetically ordered. The large exchange bias in the Ni intercalated Bi2Te3 interfacial layer clearly suggests a large exchange energy which is characteristic of super-exchange mediated coupling of moments in Ni, Bi and Te based Van der Waals (VdW) MTI compounds [8]. This large exchange bias raises the possibility of formation of topologically nontrivial magnetic material at the interface. The observation of magnetic phase at the interface layer further raises the possibility of QAH state and paves the way for further exploration of TI/FM based heterostructures and applications for energy efficient spintronic devices which are compatible with industrial CMOS processes.

![](https://assets.underline.io/uploads/markdown_image/1/image/8270706ca20995363a54b4e33edb73db.jpg)

ZFC hysteresis loop measured at 300 K and 6 K. At 6 K a large exchange bias of ~80 Oe emerges because of coupling of AFM interface layer with FM Py layer.

![](https://assets.underline.io/uploads/markdown_image/1/image/683d74f2557c122585bafe57a4a52001.jpg)

PNR measurement at 7 K showing finite moments at 1 T saturation and AFM ordering at the Ni intercalated interface at 50 Oe. Inset: STEM-HAADF image with clear indication of the AFM Ni-intercalated Bi2Te3 layer.

Antiferromagnetic Phase in Sputtered Topological Insulator/Ferromagnetic Heterostructure Interface

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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A Circuit Lattice Representation of a Second-Order Dirac Semimetal

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