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High-Frequency Signal injection (HFSW)method is a technology to obtain the rotor position information from the high-frequency response of the injected voltage or current signal. While this method is quite sensitive to the motor parameters, the correct parameter decides the rotor position estimation accuracy. In traditional scheme, the d-q axis inductance is set as a constant value under the rated conditions in the high-frequency mathematical models, while the d-q axis inductance varies in different operating conditions exactly. Even in the same operating conditions, the d-q axis inductance also changes due to the magnetic field saturation caused by phase current. JMAG simulation verifies the assumption, as shown in Fig.1. However, very little about that has been discussed in the published papers corresponding to HFSW method. Inspired by current linkage harmonics and torque ripple [1], a modified motor model considering non-linear change of inductance is proposed in this paper, where motor parameter is changing with magnetic field saturation. With the adoption of new model, the traditional HFSW injection equation is also modified in the paper. Compared with the traditional scheme, the modified model takes the dynamic change of d-q axis inductance into consideration and reduced the influence of the induction variation. Simulation in matlab Simulink shows a good performance in rotor error suppression and steady state error depression. The proposed method has also been employed in a 4p-24s permanent magnet synchronous motor. Fig.2 exhibits the high frequency incremental current in α-β axis while Fig.2 shows the incremental current with the modified high frequency square wave injection equation. (The variation of inductance is reflected as 5th and 7th current harmonics in α-β axis). It can be verified that the proposed method can not only compensate the HFI current harmonics caused by non-linear changes in d-q axis inductance but also maintain the good steady-state and dynamic performance of traditional systems.References: [1] Ponomarev, P. , Petrov, I. , &amp; Pyrhonen, J. . (2014). Influence of travelling current linkage harmonics on inductance variation, torque ripple and sensorless capability of tooth-coil permanent-magnet synchronous machines. IEEE Transactions on Magnetics, 50(1), 1-8.

MMM 2020

Sensorless Control Scheme for PMSM Based on High-Frequency Square-Wave Voltage Injection considering Non-linear Change of Inductance in D-Q Axis

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INTERMAG 2021

High-Frequency Signal injection (HFSW)method is a technology to obtain the rotor position information from the high-frequency response of the injected voltage or current signal. While this method is quite sensitive to the motor parameters, the correct parameter decides the rotor position estimation accuracy. In traditional scheme, the d-q axis inductance is set as a constant value under the rated conditions in the high-frequency mathematical models, while the d-q axis inductance varies in different operating conditions exactly. Even in the same operating conditions, the d-q axis inductance also changes due to the magnetic field saturation caused by phase current. JMAG simulation verifies the assumption, as shown in Fig.1. However, very little about that has been discussed in the published papers corresponding to HFSW method. Inspired by current linkage harmonics and torque ripple [1], a modified motor model considering non-linear change of inductance is proposed in this paper, where motor parameter is changing with magnetic field saturation. With the adoption of new model, the traditional HFSW injection equation is also modified in the paper. Compared with the traditional scheme, the modified model takes the dynamic change of d-q axis inductance into consideration and reduced the influence of the induction variation. Simulation in matlab Simulink shows a good performance in rotor error suppression and steady state error depression. The proposed method has also been employed in a 4p-24s permanent magnet synchronous motor. Fig.2 exhibits the high frequency incremental current in α-β axis while Fig.2 shows the incremental current with the modified high frequency square wave injection equation. (The variation of inductance is reflected as 5th and 7th current harmonics in α-β axis). It can be verified that the proposed method can not only compensate the HFI current harmonics caused by non-linear changes in d-q axis inductance but also maintain the good steady-state and dynamic performance of traditional systems.References: [1] Ponomarev, P. , Petrov, I. , & Pyrhonen, J. . (2014). Influence of travelling current linkage harmonics on inductance variation, torque ripple and sensorless capability of tooth-coil permanent-magnet synchronous machines. IEEE Transactions on Magnetics, 50(1), 1-8.

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The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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The present work reports the synthesis of Fe3O4 nanotubes (NTs), nanorods (NRs), and nanodiscs (NDs) prepared by microwave-hydrothermal route with varying ratio of sodium phosphate/sodium sulfate ions. The Rietveld refinement analysis of the X-ray diffraction patterns divulges the presence of a metallic iron phase decreasing gradually from NTs ~16 %, NRs ~11 % to NDs ~ 0% with increasing concentration of phosphate ions as confirmed later by Mossbauer data. A sharp drop in the coercive field from NTs (~252 Oe) to NDs (~182 Oe) indicates clearly a magnetic vortex state in NDs as also reported by Lorenz microscopy and micromagnetic simulation [1]. Further, a reduction in Verwey transition temperature (NTs to NDs) is observed in zero fields cooled magnetization measurement (Figure 1(a)) related to a gradual loss of stoichiometry for Fe3O4 nanostructures. The obtained results are understood based upon a core-shell structure consist of stoichiometric Fe3O4 surrounded by a non-stoichiometric one. The magnetic vortex NDs are further analyzed for their utilization in magnetic hyperthermia applications [2,3]. The specific absorption rate (SAR) for NDs is calculated by orientation-dependent hysteresis loss through micromagnetic simulation and found to be 16 % higher at θ = 15o as compared to randomly oriented NDs, where q is the angle between magnetization (M) and applied field (H). Interestingly, the switching field (HS) of magnetic vortex NDs is responsible for a larger hysteresis loss at θ = 15o which is understood by developing a relationship with anisotropy constant (K). The theoretical SAR (~ 182 W/gNPs) of NDs is almost constant for aspect ratio β( = t/d) ≤ 0.13 whereas it is dramatically enhanced by ~5 times (~ 862 W/gNPs) at β = ~ 0.26, which is assigned due to the contribution of shape anisotropy. Our results indicate the implication of switching field (HS), orientation, anisotropy (K), and geometrical parameters (d & t) for improving the heating performance of Fe3O4 nanodiscs.References: 1. H. M. Fan, J. B. Yi, Y. Yang. ACS Nano 3:2798–2808 (2009). DOI: 10.1021/nn9006797 2 Y. Yang, X. Liu, and Y. Lv, Adv Funct Mater 25:812–820(2015) . DOI: 10.1002/adfm.201402764 3. D. H. Kim, E.A. Rozhkova, and I. V. Ulasov. Nat Mater 9:165–171(2010). DOI: 10.1038/nmat2591

Switching Field, Orientation and Shape Anisotropy Contribution on the Magnetic Heating of Fe3O4 Nanodisc

With the development of AC/DC UHV grid, large capacity transformer is widely used in power grid. After DC resistance measurement, no-load test and other operations of power transformer, mainly due to hysteresis phenomenon of ferromagnetic materials, a certain magnetic flux is left in the core, which is called residual flux. When transformer switching on without load, residual flux will lead to inrush current which is several times of the rated current. Inrush current endangers the mechanical stability and insulation strength of power transformer windings, and affects the normal operation of power system, resulting in many adverse effects. In this paper, an improved method is proposed to establish the relationship between residual flux and transient current characteristics by analyzing the transient current waveform of winding under different residual flux with different polarity DC voltage. DC voltage amplitude is determined by a criterion that the residual flux in the core should not change over 10% after the DC voltage unloaded. Based on the previous studies on positive and negative transient current, the relationship between transient characteristics and residual flux is further studied and analyzed. Combined with theory and experiment, the form of empirical formula and parameter calculation flow are determined. Compared with directly using transient current amplitude at a certain moment to calculate, using waveform characteristics to calculate residual flux is more accurate and less susceptible to measurement error and noise.References: C. Huo, Y. Wang, S. Wu, Y. Yang, and Z. Zhao, "Residual Flux Density Measurement Method for Transformer Core Considering Relative Differential Permeability," IEEE Trans. Magn., pp. 1-1, 2020. G. Wenqi, W. Youhua, Z. Zhenghan, Y. Xiaoguang, and L. Yongjian, "Residual Flux in the Closed Magnetic Core of a Power Transformer," IEEE Trans. Appl. Supercond., vol. 24, no. 3, pp. 1-4, 2014. W. Ge, J. Zhao, and Y. Wang, "Analysis of the residual flux influence on inrush current and electromagnetic force in large power transformer," The Journal of Engineering, vol. 2019, no. 16, pp. 2426-2429, 2019.

Improved Residual Flux Measurement Method based on Transient Current Characteristics used in Single-Phase Power Transformer

Spintronic with garnets materials is an emerging field that promises the use of pure spin currents to realize low power electronics thanks to the insulating character and low Gilbert dampings of this family of materials. The recent demonstration of the possibility to control the magnetization dynamics with a DC current through spin-orbit-torques (SOT) provides some great perspectives in tunable spin wave devices for magnonic applications. An example illustrating these opportunities is the auto-oscillations that can be induced in YIG/Pt bilayers using SOT [1] or compensate the damping of propagating spin-waves [2]. In Bi doped YIG/Pt that shows a perpendicular anisotropy, coherent spin-waves emission can be generated by SOT [3]. However, SOT induced irreversible switching of magnetization has only been observed so far in Tm3Fe5O12 (TmIG) thin films covered with Pt, with the disadvantage that TmIG has a much larger Gilbert damping than YIG and BiYIG [4], which limits the scope of applications. In this study, we grew some series of epitaxial TmIG with different thicknesses (from 6 to 50nm) by pulsed laser deposition (PLD) on sGGG(111)-oriented substrate. Their structural characterization demonstrated the high epitaxial strain of the films up to a thickness of 25nm. Epitaxial strain could be maintained up to films thickness of 50 nm as shown in the XRD pattern in Figure 1. Kerr microscopy was used to image the magnetics domains of the samples and their hysteresis loops. The results attest the strong perpendicular magnetic anisotropy of these TmIG samples as depicted in Figure 2. Magnetic dynamical properties were probed by broadband ferromagnetic resonance with a coplanar waveguide. We hence found that the Gilbert damping of TmIG can still be improved for very thin films by tailoring the growth parameter to achieve a ferromagnetic linewidth of 72 Oe at 12 GHz, narrower than recent results in literature [5,6]. This work has been funded by the European Union’s Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under grant agreement No. 801055.References: [1] V. E. Demidov, S. Urazhdin, G. De Loubens, et al., Physics Reports, 673, 1-31 (2017) [2] V. E. Demidov, S. Urazhdin, A. Anane, et al., Journal of Applied Physics, 127, 170901 (2020) [3] M. Evelt, L. Soumah, A. B. Rinkevich, et al., Physical Review Applied, 10 (4), 041002 (2018) [4] L. Soumah, N. Beaulieu, L. Qassym, et al., Nature Communications, 9, 3355 (2018) [5] C. Tang, P. Sellappan, Y. Liu et al., Physical Review B, 94, 140403(R) (2016) [6] O. Ciubotariu, A. Semisalova, K. Lenz et al., Scientific Reports, 9, 17474 (2019)

Narrow Ferromagnetic Resonance Linewidth in Perpendicularly Magnetized Tm3Fe5O12 Thin Films Grown by Pulsed Laser Deposition

Magnetite, Fe3O4, is a frequently studied magnetic oxide growing in the inverse spinel structure Fe3O4 exhibits a ferrimagnetic ground state which stems from the interplay of its three cation species due to super exchange and double exchange depending on site and oxidation state: Octahedrally coordinated Fe2+ and Fe3+ ions, and tetrahedrally coordinated Fe3+ ions. The coupling among octahedral sites is ferromagnetic, while tetrahedral and octahedral sites couple antiferromagnetically. One of the most successful ways to discriminate between the magnetic contributions of these cations are X-Ray Magnetic Circular Dichroism (XMCD) experiments across the Fe L2,3 edges, making use of a slight difference of their L edge energies and the easily resolvable antiferromagnetic coupling between the tetrahedral and the octahedral sites (c.f. Fig. 1).On the other side, X-Ray Resonant Magnetic Reflectivity(XRMR) is a technique combining the depth resolution of X-Ray Reflectivity and the site- and magnetism-sensitivity of XMCD. This enables us to determine the magnetooptical depth profiles at the energies characteristic for Fe2+oct, Fe3+tet, and Fe3+oct in the XMCD of Fe3O4/MgO(100) ultrathin films (c.f. Fig. 2). We find a ~3.9Å layer of enhanced magnetooptical absorption at the surface for both Fe3+ species but not for Fe2+ [1]. The magnetically enhanced Fe3+tet layer is additionally shifted about 3±1.5 Å into the sample compared to the Fe3+oct layer. We attribute this to the first unit cell from the surface containing an excess to Fe3+ cations.References: [1] T. Pohlmann et al., arXiv:2005.01657 [2] S. Macke and E. Goering, J. Phys.: Cond. Matter 26, 363201 (2014).

Cation-Specific Magnetic Depth Profiles of Ultrathin Fe3O4 Films Obtained by X-Ray Resonant Magnetic Reflectivity (XRMR)

Nanostructured Ni-Zn ferrite (NZF) thin film, deposited by a CMOS-compatible microwave-assisted solvothermal (MAS) process, exhibits ‘far-from-equilibrium’ arrangement of cations in the spinel structure with significant anisotropy, thus promising for miniaturized passive devices in GHz regime [1, 2]. Achieving extreme cationic distribution at sub-200oC is the hallmark of this process [3] where, selected metal precursors dissolved in a solvent transform into metal oxide and nucleate on an immersed substrate under microwave heating at 2.45 GHz interacting with solvents of high loss-tangent (tanδ). The objective here is to study the impact of the solvent tanδ on the film’s magnetic property, especially the surface spin-canting layer and interparticular dipolar interaction. NZF films were deposited on Si(100) substrates using various ratios of ethanol (tanδ≈0.941), 1-decanol (tanδ≈0.1), and benzyl alcohol (tanδ≈0.667). The best characteristics were for ethanol:benzyl alcohol ratio (vol.) of 3:5. A smooth, densely packed NZF film (~ 200 nm) composed of highly crystalline nanoparticles (8.6 nm) resulted. Raman analysis of A1g mode shows a degree of inversion for Fe3+ ions x = 0.21 corresponding to 89% population of Fe3+ in octahedral site which led to a net magnetic moment enhancement (Ms of 79 emu/cc@300K), much higher than with 1-decanol [1]. The magnetic size deduced from the Langevin function (DL:9.4 nm) is consistent with that of Scherrer’s crystallite size with surface spin canting layer of 0.5 nm at 300 K. Temperature-dependent magnetization at different dc fields shows strong inter-particle dipolar interaction, estimated as EDipole≈ 1.9×10-17 J (300 K); 1.3×10-16 J (5 K). The blocking process shows individual 2-level energy system replaced by a multi-valley energy system. Thus, TB distribution and anisotropy energy barrier were ascertained from the derivative of thermoremnant magnetization with temperature. A close association between the anisotropy constants and strength of dipolar interaction is realized, driven by the influence of high microwave absorbing solvents.References: 1 R.R. Kahmei, R. Sai, S. Arackal, S.A. Shivashankar, and N. Bhat, IEEE Magn. Lett. 10, 1 (2019). 2 R. Sai, S.D. Kulkarni, M. Yamaguchi, N. Bhat, and S.A. Shivashankar, IEEE Magn. Lett. 8, 3 (2017). 3 I. Bilecka and M. Niederberger, Nanoscale 2, 1358 (2010).

The impact of the solvent tanδ on the magnetic characteristics of nanostructured NiZn-ferrite film deposited by microwave-assisted solvothermal technique

Recently, additive manufacturing (AM) of functional materials started integrating an additional physical property available besides the mechanical stability in printed parts. This additional property can be an increased electrical conductivity or as addressed here a specific magnetic stray field. AM allows near-net-shape manufacturing of complex magnet shapes, avoiding significant machining waste during conventional manufacture of the final shape from sintered magnet blocks. However, the development of the AM process in general requires a qualified starting material for each process such as powder bed fusion [1], binder jetting or material extrusion. Since the supply of metal powders for AM is limited in general, and there is no Nd-Fe-B based powder designed for use in AM, the development of a Nd-Fe-B-based starting material for commercial production is the goal of the EIT Raw Materials funded project 3DREMAG [2]. Commercial powders designed for injection molding are already used for different AM techniques in combination with different polymers and binders [3 and references therein]. E.g. self-produced Mn-Al powders were used in electron beam melting to produce polymer (and rare-earth element) free hard magnetic fully dense bodies [4]. The printing process was followed by a heat treatment to achieve 90% of the hard ferromagnetic tau-phase in the samples. It is very challenging to obtain fully dense Nd-Fe-B magnets by AM due to the specific microstructure of uniform micrometer sized Nd2Fe14B grains separated by a rare-earth rich grain boundary phase that has to be established to achieve high remanence and coercivity. To obtain sufficient amounts of powders that can be processed by powder bed fusion, Nd-Fe-B strip cast flakes are milled and further plasma spheroidized. First results of lab scale production of the powders and first AM tests will be presented and discussed.References: [1] Mateusz Skalon, Michael Görtler, Benjamin Meier, Siegfried Arneitz, Nikolaus Urban, Stefan Mitsche, Christian Huber, Joerg Franke and Christof Sommitsch, Influence of Melt-Pool Stability in 3D Printing of NdFeB Magnets on Density and Magnetic Properties, Materials 13 (2020), 139. [2] http://3dremag.eu [3] Christian Huber, Gerald Mitteralmskogler, Michael Goertler, Iulian Teliban, Martin Groenefeld, Dieter Suess, Additive manufactured isotropic NdFeB magnets by stereolithography, fused filament fabrication, and selective laser sintering, arXiv:1911.02881 [4] I. Radulov, V. Popov Jr, A. Koptyug, F. Maccari, A. Kovalevsky, S. Essel, J. Gassmann, K. Skokov, M. Bamberger, Production of net-shape Mn-Al permanent magnets by electron beam melting, Additive Manufacturing 30 (2019) 100787.

Nd-Fe-B based permanent magnetic materials design for additive manufacturing: 3DREMAG

The coercivity of RE2Fe14B-type permanent magnet is strongly influenced by the microstructural features such as grain boundary phases as well as grain size. Micromagnetic simulations are powerful tools for revealing the correlation between microstructure and the evolution of hard magnetic properties, including the effects of grain size and grain boundary phases. We have combined micromagnetic simulations and experiments to elucidate the role of excess RE (Nd/Pr) in determining the resulting hard magnetic properties of Nd-Pr-Fe-B melt-spun ribbons. Also, the effect of non-magnetic grain refining refractory carbide (TiC) on both the microstructure and magnetic hardening was studied. For the simulated polycrystalline microstructure of Nd-Pr-Fe-B magnets (Fig. 1(a)) with a mean grain size of 40 nm, the coercivity increases with decreasing inter-grain magnetic exchange interaction Fig. 1(b). The increasing trend in magnetic coercivity of measured melt-spun (Nd, Pr)–Fe–B alloys is ascribed to weak inter-grain exchange coupling due to non-magnetic RE-rich grain boundary phase (Fig. 1(c)) and/or TiC at grain boundary (Fig. 1(d)). This work provides useful information on the role of non-magnetic grain boundary phase to improve the coercivity in Nd-Pr-Fe-B magnets. Combined with experimental and modeling results, we will discuss the mechanism responsible for the enhancements in coercivity and the suitability of the alloys for high performance permanent magnet development. This research was supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office.

Understanding the Enhancement in Hard Magnetic Properties of Rapidly Solidified (Nd, Pr)-Fe-B Melt-spun Ribbons

Sintered R2Fe14B (R: rare earth element) magnets with 50 at substitution of Nd by Y and Ce were studied in order to reduce the amount of precious rare earth elements used and to make effective use of the surplus rare earth elements. Nd was substituted with Y for larger magnetization and Ce for higher coercivity. By substituting 50 at% of Nd by Y and Ce with an equiatomic composition, a maximum energy density of 355 kJ/m3 was achieved with the residual flux density of 1.38 T and the coercivity of 533 kA/m as shown in Fig. 1. In order to increase the coercivity, the introduction of R6Fe13Ga grain boundary phase to lead the magnetic separation between grains, which is commonly used for Nd2Fe14B, was studied, however the coercivity was not improved due to a large magnetization of R6Fe13Ga, 0.3 to 0.5 T. By introducing the RFe2 grain boundary phase, the coercivity of 1063 kA/m with the residual flux density of 1.22 T was achieved at the composition of Ce of 40% in the total rare earth elements in R2Fe14B sintered magnet. The magnetization of the RFe2 phase was estimated to be about 0.3 T and was not sufficiently low. Since the RFe2 boundary phase improved the covering of the grains, the magnetic separation was enhanced to increase the coercivity.

Magnetic Properties of R2Fe14B Sintered Magnets Substituted 50 at Substitution of Nd with Y and Ce

Pr2Fe14B-based thin films are the useful nano-material for the high-tech performance of the magnetic devices. With its studied outstanding magnetic property such as high uniaxial magnetocrystalline anisotropy (Ku), high coercivity (Hc), high saturation magnetization (Ms), large energy products (BHmax), excellent anisotropic behavior, and super low spin-reorientation at temperature about 4.2 K, Pr2Fe14B magnetic thin films become an alternative candidate for the Nd2Fe14B-based magnetic thin films. In this study, the perpendicular magnetic anisotropy (PMA) Pr-Fe-B films were deposited on corning glass substrate at 600 °C with Si3N4 cover layer and underlayer from Pr25Fe65B10 alloy target by RF magnetron sputtering technique. VSM, XRD, SEM, TEM, and EDS measurements were applied to investigate the relationship between thickness and the microscopic magnetization structures of the PrFeB layer which initiated and propagated crystallization of PMA Pr2Fe14B phase. The magnetic properties of sputtered Pr-Fe-B film was also investigated in terms of the micro-texture evolution. The structure with thickness 50 nm showed the initial point of crystalline characteristic. The initial appearance signal of c-axis orientation of Pr2Fe14B phase and the perpendicular coercive force in the film were comparable at 50 nm, and were alternatively evolved on glass substrates. SEM, TEM, and EDS results revealed that localized grains occurred at the initial stages of growth, and developed non-uniform grain networks across the substrate. The highly c-axis oriented films have a special microstructure which Pr2Fe14B phase showed blossom surface morphology. The exchange coupling was mainly explained for the two-phase nanostructure formed from hard magnetic phase and soft magnetic phase. The texture with the c-axis perpendicular to the film plane had finely signal of development after in-situ annealing at 600 °C. The magnetization irregularity of the thin film was strongly affected by the underlayer and the substrate. The magnetic analysis assuming that the value of film was composed of the correlation between microstructures and magnetic properties on underlayer and substrates.

Manifestation of initial crystallization and c-axis texture in Pr-Fe-B thin films grown on glass substrates

Nd–Fe–B permanent magnets are indispensable materials for high-technology commercial products such as motors, electronic devices, etc., because of their high coercive force. However, the mechanism of the coercive force has not been well understood [1]. For the understanding of the microscopic mechanisms, atomistic modeling, which is a new trend of permanent-magnet modeling, is important. We have studied dynamical and static properties of the Nd magnet, Nd2Fe14B, by applying the stochastic LLG equation [2] and Monte Carlo methods to an atomistic model, in which microscopic parameters were introduced by first-principles calculations [2-7]. We have shown the temperature dependencies of the magnetization, domain-wall profiles, dipolar-interaction effect, ferromagnetic resonance, inhomogeneity effect, surface Nd anisotropy effect, etc. [2-7] In this presentation, we mainly show dynamical aspects of the magnet, focusing on the effect of the interface between grains and grain boundaries. There exist difficulties to estimate long relaxation times of barrier-crossing magnetization reversal quantitatively due to the limitation of simulation time and the dependence on the damping factor. Here we propose a statistical method to estimate precisely long relaxation times in the stochastic region, by which one can identify an initial transient process and a long-time regularly relaxation process. We show an estimation of the coercive force of a single grain using this method [6]. Local environments around rare-earth ions at the interfaces of rare-earth magnets may be different from those in the bulk. First-principles studies have suggested that the magnetocrystalline anisotropies of the Nd atoms at the (001) surface of grains in the Nd magnet have in-plane (c-plane) anisotropy, while those in the bulk have out-of-plane anisotropy. Thus, we investigated the effect of the surface magnetic anisotropy of the Nd atoms on the coercivity in the Nd magnet (Fig. 1). We analyzed the coercive force in three cases, in which the Nd atoms in surface layers have (I) no anisotropy, (II) in-plane anisotropy, and (III) doubly reinforced anisotropy for not only the (001) surface but also (100) surface, with the layer-depth dependence [6]. We find that at zero temperature the modification of the anisotropy of the Nd atoms at the first-surface layer reduces the coercive force in cases I and II and enhances the force in case III, but at room temperature, this modification does not affect the coercive force, and the modification at several surface layers is necessary to reduce or enhance the coercivity at room temperature. We also present the nucleation and pinning fields of the Nd magnet as a function of the strength of the anisotropy energy of the soft magnet and also as a function of the thickness of the soft magnet (Fig. 2) [7]. In the Nd magnet, reflecting the lattice structure, the properties of domain walls (DWs) depend on their moving directions. Bloch and Néel DWs move along the a (or b) and c axes, respectively. We show the difference in the nucleation and pinning fields between the Bloch and Néel DWs. We find that the thermal fluctuation effect affects the threshold fields in the Nd magnet significantly. We also find that the strength of the anisotropy energies of the soft magnet phase is not so important for the pinning field, while it is essential for the nucleation field, etc.References: [1] S. Hirosawa et al., Adv. Nat. Sci.: Nanosci. Nanotechnol. 8, 013002 (2017). [2] M. Nishino and S. Miyashita, Phys. Rev. B 91, 134411 (2015); 100, 020403(R) (2019). [3] M. Nishino et al., Phys. Rev. B 95, 094429 (2017). [4] S. Miyashita et al., Scr. Mater. 154, 259 (2018). [5] T. Hinokihara et al., Phys. Rev. B. 97, 104427 (2018). [6] M. Nishino et al., submitted. [7] I. E. Uysal et al., Phys. Rev. B 101, 094421 (2020).

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