Dependence Of Coercivity Research Articles

Study of magnetization reversal and magnetic hardening in SmCo5 single crystal magnets

Large SmCo5 single-crystal spheres are used as simple model objects for both theoretical and practical studies of the coercivity mechanism in permanent magnets (PM). These samples exhibit coercivity values exceeding 1 T, achieved through the enhancement of surface smoothness. The morphology and magnetic results indicate that surface defects play a key role in the reversal mechanism and nucleation process. The reversal mechanism and coercivity are studied by means of different magnetization protocols, shedding light on the influence of two types of nucleus of reversal magnetic domains. We then utilize these objects to probe the angular dependence of coercivity. Our examination of samples with differing surface states reveals that enhanced surface smoothness corresponds to a behavior closer to the coherent rotation model. This study underscores the massive influence of surface defects on magnetization reversal. Thus, the reduction of imperfections in PM grain boundaries holds the potential to significantly increase the nucleation field and thus the coercivity. More generally, our study introduces a methodology for examining the magnetization reversal of permanent magnets using simple model objects.

The dependence of intrinsic coercivity on Tb concentration and core-shell structure of diffused Nd-Fe-B magnets

In this paper, the variations of composition, core-shell structure, and magnetic properties of diffused Nd-Fe-B magnet with the diffusion depth have been intensively investigated. It was confirmed that the Tb concentration, core-shell structure and intrinsic coercivity (Hci) along the diffusion depth of magnets indicated obvious gradient characteristics. The Hci of diffused magnet was increased by 824.4 kA/m and reached 1864.7 kA/m. The Hci of the residual sample gradually decreased with cutting and removal of surface. However, it was emphasized that the Hci of 1702.6 kA/m with the increment of 662.3 kA/m was obtained in the central sample, in which the concentration of Tb was 0.13 wt%. The electron probe microanalyzer (EPMA) analyses showed that Tb-rich shells were continuously visible in the depth of 100 μm, and became discontinuous in the depth of 500 μm, and were nearly invisible in the center of diffused magnet with the depth of 2500 μm. In order to further characterize the atomic-scale morphology and elements, a high-angle annular dark field (HAADF) detector and an energy dispersive X-ray spectroscopy (EDS) on the double aberration-corrected scanning transmission electron microscopy (STEM) were employed. The results indicated that the thick Tb-rich shells were clearly visible near the surface of the diffused magnet, and the lattice constant c of 2:14:1 phase was reduced by 0.05 Å due to the partial substitution of Tb element for Pr/Nd elements. However, Tb-rich shells in the central part of diffused magnet was discontinuous and inhomogeneous, in which the Tb-rich and Tb-poor regions were occurred. It was mainly attributed to the low Tb concentration at grain boundaries in the center of the magnet, which was difficult to form complete Tb-rich shells.

Tomography-based digital twin of Nd-Fe-B permanent magnets

Many functional materials have been designed at the multiscale level. To properly simulate their physical properties, large and sophisticated computer models that can replicate microstructural features with nanometer-scale accuracy are required. This is the case for permanent magnets, which exhibit a long-standing problem of a significant offset between the simulated and experimental coercivities. To overcome this problem and resolve the Brown paradox, we propose an approach to construct large-scale finite element models based on the tomographic data from scanning electron microscopy. Our approach reconstructs a polycrystalline microstructure with actual shape, size, and packing of the grains as well as the individual regions of thin intergranular phase separated by triple junctions. Such a micromagnetic model can reproduce the experimental coercivity of ultrafine-grained Nd-Fe-B magnets along with its mechanism according to the angular dependence of coercivity. Furthermore, a remarkable role of thin triple junctions as nucleation centers for magnetization reversal is revealed. The developed digital twins of Nd-Fe-B permanent magnets can assist their optimization toward the ultimate coercivity, while the proposed tomography-based approach can be applied to a wide range of polycrystalline materials.

Magnetism of metastable γ-Fe85Pd15 nanowire arrays across an unusually broad temperature range (5 K to 800 K).

Arrays of 50 nm diameter Fe85Pd15 cylindrical nanowires were electrochemically grown, crystallizing in a metastable γ-Fe(Pd) fcc A1 disordered solid solution. After performing a heating-cooling thermal cycle between 300 K and 1000 K, the γ-Fe(Pd) fcc metastable phase still predominates (97%), coexisting with a not-fully-identified minority phase. The thermal cycling induces a moderate increase in the crystallite size and a reduction of the lattice parameter although leading to a significant heating-cooling magnetic hysteresis. No further changes in temperature-dependent magnetization, M(T), are observed during subsequent cycling. The full-range (5 K to 800 K) saturation magnetization Ms(T) curve is quite accurately described by a phenomenological expression, which provides a Bloch-type contribution as T → 0 and undergoes the critical behavior near the Curie temperature TC. An upturn in Ms(T) is observed below 100 K which is described by a spin-glass-like second contribution, with freezing temperature Tf = (80 ± 2) K, and kBTf comparable to the exchange interactions in Fe-Pd systems. A Curie temperature of TC = 830 K, and a critical exponent value β = 0.42 ± 0.05 are estimated. These regimes (below and above 100 K) are also observed in the magnetization process. The temperature dependence of coercivity between 100 K and 800 K is consistent with a nucleation/propagation remagnetization mechanism, with activation energy of (320 ± 20) kJ mol-1 and critical field for magnetization reversal of (65 ± 1) mT, at 0 K. The analysis of the effective magnetic anisotropy as a function of temperature allows us to conclude that it essentially arises from the balance between different magnetostatic contributions.

Reliable Accessibility of Intermediate Polarization States in Textured Ferroelectric Al0.66Sc0.34N Thin Film

AbstractFerroelectric materials are promising candidates for neuromorphic computing synaptic devices due to the nonvolatile multiplicity of spontaneous polarization. To ensure a sufficient memory window, ferroelectric materials with a large coercivity are urgently required for practical applications in highly scaled multi‐bit memory devices. Herein, a remarkable reliability of intermediate ferroelectric polarization states is demonstrated in a textured Al0.66Sc0.34N thin film with a coercive field of 2.4 MV cm−1. Al0.66Sc0.34N thin films are prepared at 300 °C on Pt (111)/Ti/SiO2/Si substrates using a radio frequency reactive sputtering method. Al0.66Sc0.34N thin films exhibit viable ferroelectricity with a large remanent polarization value of >100 µC cm−2. Through the conventional current–voltage characteristics, polarization switching kinetics, and temperature dependence of coercivity, the reproducibility of multiple polarization states with apparent accuracy is attributed to a small critical volume (3.7 × 10−28 m3) and a large activation energy (3.3 × 1027 eV m−3) for nucleation of the ferroelectric domain. This study demonstrates the potential of ferroelectric Al1‐xScxN for synaptic weight elements in neural network hardware.

Magnetic and magnetocaloric properties of polycrystalline Pr[formula omitted]Ca[formula omitted]MnO[formula omitted] (x [formula omitted] 0.85, 0.90, 0.95) compounds: Emergence of large inverse and conventional magnetocaloric effects

Magnetic and magnetocaloric effect have been investigated for the electron doped polycrystalline Pr1−xCaxMnO3 (x ∼ 0.85, 0.90, 0.95) compounds. The experimental outcomes indicate that the nature of the ground state is very much sensitive with the doping concentration. Pr0.15Ca0.85MnO3 compound exhibits antiferromagnetic ground state. In contrast to that ferromagnetic nature was found for the Pr0.10Ca0.90MnO3 and Pr0.05Ca0.95MnO3 compounds. Although, for x∼0.90 ferromagnetic phase was stable. However for x∼ 0.95, the ferromagnetic state is quite unstable. Additionally for the doping concentration x∼ 0.95, the anomalous nature was found in temperature dependent coercivity. Magnetocaloric effect study indicate that antiferromagnetic Pr0.15Ca0.85MnO3 compound exhibits large inverse magnetocaloric effect (10.5 J/kg-K at H = 70 kOe magnetic field). On the other hand, ferromagnetic Pr0.10Ca0.90MnO3 and Pr0.05Ca0.95MnO3 compounds show conventional magnetocaloric effect. The magnetocaloric entropy change for x∼0.90 compound is significantly large (7.5 J/kg-K at H = 70 kOe magnetic field) and comparable with the other reported magnetic refrigerant materials. Universal master curve for magnetic entropy change have been constructed for all the materials having inverse and conventional magnetocaloric effect by proper scaling of temperature axis.

Unveiling the origin of the large coercivity in (Nd, Dy)-Fe-B sintered magnets

Nd-Fe-B-based permanent magnets are widely used for energy conversion applications. However, their usage at elevated temperatures is difficult due to the relatively low coercivity (Hc) with respect to the anisotropy field (HA) of the Nd2Fe14B compound, which is typically 0.2HA. In this work, we found that the coercivity of an (Nd0.8Dy0.2)-Fe-B sintered magnet could reach 0.4HA, which was twice as high as the Hc/HA of its Dy-free counterpart. Detailed microstructural characterizations, density functional theory and micromagnetic simulations showed that the large value of coercivity, Hc = 0.4HA, originated not only from the enhanced HA of the main phase (intrinsic factor) but also from the reduced magnetization of the thin intergranular phase (extrinsic factor). The latter was attributed to the dissolution of 4 at.% Dy in the intergranular phase that anti-ferromagnetically coupled with Fe. The reduction in the magnetization of the intergranular phase resulted in a change in the angular dependence of coercivity from the Kondorsky type for the Dy-free magnet to the Stoner–Wohlfarth-like shape for the Dy-containing magnet, indicating that the typical pinning-controlled coercivity mechanism began to show nucleation features as the magnetization of the intergranular phase was reduced by Dy substitution.

Dependence of coercivity, relative permeability and magnetic losses on oscillating magnetic field frequencies and maximum polarisation for NGO and HGO steels

This study investigated two types of electrical steels: high permeability grain oriented (HGO) 3.25 wt%Si and 0.25 mm thick and two non-grain oriented (NGO) grades 2 wt%Si and 0.50 mm and 0.54 mm thick The dependence of the frequency of the external magnetic field H and maximum polarisation Jmax on the different magnetic losses (hysteresis, classical and excess), coercivity, relative permeability were investigated over a wide frequency range of 3-2000 Hz (10 and 100 Hz increments for low and high frequencies, respectively), and Jmax range of 0.1–1.5 T (0.1 T increment). With this large data set it was observed that the relative permeability as a function of Jmax exhibited a maximum at approximately 1.1 T (HGO) and 0.8 T (NGOs), and the coercivity was dependent on the frequency up to 2000 Hz. Further, the remanence increased up to frequencies of 250 Hz and then became constant. All these distinct dependencies with f and Jmax show the key role of grain size, morphology and crystallographic and magnetic texture on magnetic properties. Furthermore, a scenario showing the component losses that dominated under certain frequency and Jmax ranges was established; we found that the hysteresis loss was dominant for the NGO at frequencies up to 100 Hz and Jmax up to 1 T, whereas the excess loss was the smallest of all in the entire range studied. Above this 1 T field, the classical loss was the most expressive. Regarding HGO, another scenario was observed; the excess loss was the highest of all up to 500 Hz with Jmax up to 0.4 T, and the classical loss dominated above 400 Hz. This clearly shows that different scales in the magnetisation process relate different physical mechanisms (the wall pinning domain and magnetic domain), which regulate the loss components. Thus, our contribution shows the processes and/or parameters that must be considered to tune a certain magnetisation scale to obtain the best material efficiency and thus the best possible performance of a device.

Hard Magnetic Properties and the Features of Nanostructure of High-Temperature Sm-Co-Fe-Cu-Zr Magnet with Abnormal Temperature Dependence of Coercivity

This paper presents methods and approaches that can be used for production of Sm-Co-Fe-Cu-Zr permanent magnets with working temperatures of up to 550 °C. It is shown that the content of Sm, Cu, and Fe significantly affects the coercivity (Hc) value at high operating temperatures. A decrease in the content of Fe, which replaces Co, and an increase in the content of Sm in Sm-Co-Fe-Cu-Zr alloys lead to a decrease in Hc value at room temperature, but significantly increase Hc at temperatures of about 500 °C. Increasing the Cu concentration enhances the Hc values at all operating temperatures. From analysis of the dependence of temperature coefficients of the coercivity on the concentrations of various constituent elements in this alloy, the optimum chemical composition that qualifies for high-temperature permanent magnet (HTPM) application were determined. 3D atom probe tomography analysis shows that the nanostructure of the HTPM is characterized by the formation of Sm2(Co,Fe)17 (2:17) cells relatively smaller in size along with the slightly thickened Sm(Co,Cu)5 (1:5) boundary phase compared to those of the high-energy permanent magnet compositions. An inhomogeneous distribution of Cu was also noticed in the 1:5 phase. At the boundary between 1:5 and 2:17 phases, an interface with lowered anisotropy constants has developed, which could be the reason for the observed high coercivity values.

Effect of spin-reorientation transition of cell boundary phases on the temperature dependence of magnetization and coercivity in Sm2Co17 magnets

Four Sm2Co17 magnets with spin-reorientation transition (SRT) of cell boundary phases (CBPs) are prepared by liquid-phase sintering. The temperature of the SRT of CBPs () is regulated from 125 K to 195 K by adding 0 wt.%, 3 wt.%, 6 wt.% and 9 wt.% Dy88Cu12 alloy powder. The effect of SRT of Sm2Co17 magnet CBPs on the temperature dependence of the magnetization (M–T) and coercivity (H–T) is systematically investigated. The temperature dependence of the magnetization is influenced by the SRT of CBPs. The M–T curves measured during the heating process are larger than those measured during the cooling process when . When there is a bifurcation point. When the M–T curves overlap and the M–T derivation curve shows that the magnetization of the magnet has low temperature dependence of magnetization above . With increasing , the initial temperature of the low temperature dependence of magnetization shifts towards a higher temperature. The coercivity temperature coefficient becomes positive as the SRT effect increases, and the temperature range of the positive coercivity temperature coefficient moves towards higher temperatures as increases. This reveals that SRT of CBPs has little effect on the temperature dependence of magnetization above , while the temperature dependence of coercivity is optimized. The temperature range of magnetization and coercivity with low temperature dependence tends towards higher temperatures, which is conducive to the preparation of magnets with a low temperature coefficient at higher temperatures.

Magnetic frustration driven by conduction carrier blocking in Nd2Co0.85Si2.88

The intermetallic compound ${\mathrm{Nd}}_{2}{\mathrm{Co}}_{0.85}{\mathrm{Si}}_{2.88}$ having a triangular lattice could be synthesized in single phase only with defect crystal structure. Investigation through different experimental techniques indicate the presence of two magnetic transitions in the system. As verified experimentally and theoretically, the high-temperature transition ${T}_{\mathrm{H}}\ensuremath{\sim}$ 140 K is associated with the development of ferromagnetic interaction between itinerant Co moments, whereas the low-temperature transition at ${T}_{\mathrm{L}}\ensuremath{\sim}$ 6.5 K is due to the coupling among $\text{Nd}\text{\ensuremath{-}}4f$ and $\mathrm{Co}\text{\ensuremath{-}}3d$ moments, which is antiferromagnetic in nature. Detailed studies of temperature-dependent dc magnetic susceptibility, field dependence of isothermal magnetization, nonequilibrium dynamical behavior, viz., magnetic relaxation, aging effect, magnetic-memory effect, and temperature dependence of heat capacity, along with density functional theory (DFT) calculations, suggest that the ground state is magnetically frustrated spin glass in nature, having competing magnetic interactions of equivalent energies. DFT results further reveal that the $3d/5d$-conduction carriers are blocked in the system and act as a barrier for the $4f\text{\ensuremath{-}}4f$ RKKY interactions, resulting in spin frustration. Presence of vacancy defects in the crystal are also conducive to the spin frustration. This is an unique mechanism of magnetic frustration, not emphasized so far in any of the ternary ${R}_{2}T{X}_{3}$ ($R$ = rare earth, $T$ = transition elements, and $X$ = Si, Ge, In) type compounds. Due to the competing character of the itinerant $3d$ and localized $4f$ moments, the compound exhibits anomalous field dependence of magnetic coercivity. The system also exhibits a considerable magnetic entropy change of $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{\mathrm{M}}\ensuremath{\sim}$ 13.3 J/kg K with a relative cooling power (RCP) of 220 J/kg and adiabatic temperature change $\mathrm{\ensuremath{\Delta}}{T}_{\mathrm{ad}}$ of 6 K for magnetic field change of 70 kOe.

Comparative Study of the Magnetic Behavior of FINEMET Thin Magnetic Wires: Glass-Coated, Glass-Removed, and Cold-Drawn

In this paper, a comparative investigation of the magnetic behavior and its stress dependence in the case of FINEMET glass-coated, glass-removed, and cold-drawn microwires at low and high frequencies, respectively, is presented. The experimental results show major differences between their magnetic properties depending on the preparation method and microwire diameter. The evolution of the magnetic permeability, coercivity, and magnetoimpedance responses with the applied tensile force was investigated and analyzed in correlation with the stresses induced during preparation, their relief following annealing, and the annealing-induced structural transformations. The coercivity dependence on applied force was found to show the highest sensitivity in the glass-removed microwires, while the magnetic permeability and magnetoimpedance sensitivity to force were found to be higher in the cold-drawn samples. The results of this comparative study will enable an enhanced material selection process for various applications in miniaturized magnetic and stress sensors with increased sensitivity.

Roadmap towards optimal magnetic properties in L10-MnAl permanent magnets

Twin boundaries impact negatively the magnetic properties in conventionally-fabricated L10-type and RETM12-type permanent magnets. Herein, we propose a strategy to suppress twins’ formation by decreasing the grain and/or particle sizes below a critical size of Dt∼300 nm in L10-MnAl permanent magnets, thereby relieving twinning-inducing stress by shifting the balance between volume and surface energy. Twin-free monocrystalline nanoparticles smaller than Dt were used for preparing field-aligned polymer-bonded magnets with high texture. Generalizing our research findings, we propose here a roadmap for selecting the best route for manufacturing high-performance MnAl magnets, depending on their grain / particle size. The dependence of coercivity on grain/particle sizes shows that optimal coercivity can be reached within the range of 50–200 nm, which also shows a pathway to achieve the twin-free microstructure allowing the achievement of high texture degree in polymer-bounded or sintered magnets textured in a magnetic field. The results reported here can be applied to other twin-containing permanent magnet compounds, offering opportunities to drastically increase their texture and maximal energy products.

Frequency dependence of coercivity in nickel and Co–Fe–B thin film for DC to 100 kHz region

To investigate the magnetization process in the intermediate frequency region, the frequency dependences of coercivities in Ni and Co–Fe–B thin films were determined by anisotropic magnetoresistance measurements up to ∼160 kHz. In the low-frequency region (<5 kHz) the coercivity of Co–Fe–B was lower than that of Ni. However, the increasing rate of the coercivity in Ni was lower than that in Co–Fe–B. Consequently, above 19 kHz, the coercivity of Ni was lower than one of Co–Fe–B. Considering the basic material properties, better soft magnetic properties of Ni compared with Co–Fe–B should arise from the higher Walker breakdown field. This difference was mainly due to the Gilbert damping constant.

Size-dependent magnetic and magnetoresistance properties of Co2 FeGa nanowires

Co2FeGa Heusler alloy nanowires with diameters of about 30, 60 and 110 nm were prepared using a template-assisted electrochemical deposition method. We observe the different angular dependences of coercivity and remanence ratio for these samples. Magneto-transport measurements show that the 30 nm diameter Co2FeGa nanowires has a large magnetoresistance up to −56%, which is much higher than 60 and 110 nm diameter Co2FeGa nanowires. This is the first time that the magnetoresistance properties of Co2FeGa nanowires were presented.

Performance of switch between exchange bias and coercivity: Influences of antiferromagnetic anisotropy and exchange coupling

• A T -induced 100% switchbetween H Eand H Cin FMCo/AFM multilayers is predicted. • It demonstrates the switchingtemperaturelinearly tuned by K AF. • Theswitching temperaturewidth may be large for big J AF. • The performance of switch depends on uncompensated AFM spin configurations. • A temperature controlledwriting/reading switchis developed. The study on temperature dependence of exchange bias field and coercivity is crucial to solving the writing/reading dilemma in magnetic recording. Motivated by recent experimental findings, a complete switch between exchange bias field and coercivity with temperature is proposed, and the performance, characterized by average switching temperature ( T S ) and switching temperature width (Δ T W ), controlled by antiferromagnetic anisotropy ( K AF ) and exchange coupling ( J AF ) constants is studied based on a Monte-Carlo simulation. The results show that a linear relationship between T S and K AF is established when K AF is above a critical value, while T S is weakly influenced by J AF . On the contrary, Δ T W is insensitive to K AF , while strongly depends on J AF . Besides overcoming thermal energy, the increase of K AF for a small J AF guarantees the completely frozen states in the antiferromagnetic layers during magnetizing at higher temperature, below which the exchange bias field exists with a negligible coercivity. Otherwise, for a large J AF , the uncompensated antiferromagnetic magnetization behavior during the ferromagnetic magnetization reversal becomes complicated, and the switching process in the low temperature range depends on the irreversibility of uncompensated antiferromagnetic magnetization reversal during magnetizing, while in the high temperature range mainly influenced by the field-cooling process, resulting in a large Δ T W . This work provides an opportunity to control/optimize the performance of the temperature-induced switch between unidirectional and uniaxial symmetries through precisely tuning K AF and/or J AF to meet different application demands in the next generation information technology.

Manipulated magnetic coercivity and spin reorientation transition in NiCo2O4 films

Half-metallic NiCo2O4 with high spin polarizability has great potential applications in spintronics. The manipulation of magnetic anisotropy is crucial for spintronics based on spin-transfer or spin–orbit torques, as it is directly related to the critical switching current density. Here, we report epitaxial growth of metallic NiCo2O4 film with perpendicular magnetic anisotropy on MgAl2O4 single crystal substrates. The modulation of the magnetic anisotropy was achieved by changing the growth conditions (deposition temperature and thickness) of NiCo2O4 films and by means of protonation. Strong dependence of magnetic coercivity on deposition temperature (350–500 °C) has been observed due to variable phase configuration. Furthermore, the magnetic coercive field can also be effectively controlled by the film thickness (3–78 nm) through strain relaxation. More importantly, spin reorientation transition has been achieved by proton and electron doping in the NiCo2O4 films, resulting in reconfigured valence states of Ni and Co cations and a magnetic easy axis rotation from out-of-plane to in-plane. The effective modulation of the magnetic anisotropy provides important insights into the functional design of NiCo2O4-based spintronics with ultralow energy dissipation.

Microscopic study on the angular dependence of coercivity at zero and finite temperatures

The angular dependence of coercivity in permanent magnets is an unsettled issue in magnetism. We investigate the angular dependences of threshold fields for magnetization reversal in a single-grain and hard-soft-hard magnet model at zero and finite temperatures. We study thermal fluctuation effects on magnetization reversal, which is a stochastic process for barrier crossing at finite temperatures. We show that the mechanism of magnetization reversal in the single grain is different between zero and finite temperatures, although the normalized threshold field at finite temperatures exhibits a similar angular dependence to that of the Stoner-Wohlfarth field. We examine the angular dependences of nucleation and pinning fields for different magnetic parameters in the soft and hard magnet phases. We find that the angular dependences of the nucleation and pinning fields differ from that of the single grain, in which an exchange field resistant to reversal plays an important role, and that the thermal fluctuation reduces the threshold fields, varies the angular dependences, and makes the difference between nucleation and pinning fields smaller. We also analyze the effect of the grain alignment distribution on the threshold fields and find that the distribution changes the angular dependences of the threshold fields in different ways. We discuss the detailed features of these phenomena and the mechanisms behind them.

Investigation of the structural, morphological, and magnetic properties of small crystalline Co–Cu ferrite nanoparticles in the single-domain regime

Single-domain Co0.5Cu0.5Fe2O4 ferrite nanoparticles with a crystallite size of 23 nm were hydrothermally prepared and characterized using x-ray diffraction, transmission electron microscopy, Fourier-transform infrared (FT-IR) spectroscopy, and vibrating sample magnetometry. According to the Rietveld refinement results, the prepared nanoparticles were single-phase with spinel type structures. The transmission electron microscope measurements demonstrated that the nanoparticles were spherical in shape. The FT-IR spectrum showed two principle absorption bands, confirming the characteristic features of cubic spinel ferrites. Magnetization data revealed that the prepared nanoparticles were ferrimagnetic from room temperature to 10 K, with well-defined saturation magnetization, coercivity, and remanence magnetization. The remanence magnetization and coercivity were found to increase with decreasing temperature. The value of room temperature squareness ratio (Mr/Ms) of 0.42 was found to be somewhat similar to that expected (0.5) for a system of noninteracting single-domain nanoparticles, suggesting that the prepared nanoparticles are in a single-domain regime. The temperature dependence of coercivity was found to have slight deviations from Kneller’s law, possibly due to interactions between nanoparticles. The zero field cooled–field cooled curves indicated that below 150 K, the nanoparticles were ferrimagnetic dressed with spin-glass behavior, resulting from interactions between the ferrimagnetic nanoparticles and/or random freezing of surface spins.

Identifying the mechanism of hard magnet coercivity by its angular dependence

We completed the analytical framework of determining the angular dependence of coercivity for exchange-coupled phases connected with sharp interfaces in one-dimensional micromagnetics. For various thicknesses of soft phase in a hard matrix, the two types of angular dependence of coercivity, with or without a local minimum, were demarcated and illustrated as a phase diagram. The appearance or absence of a local minimum was confirmed as a sign of whether the switching was dominated by the spin rotation or by the depinning of the domain wall. The mechanism could transform from the former to the latter if the coupling ratio between soft and hard phases, ${\ensuremath{\varepsilon}}_{AM}={A}_{s}{M}_{s}/{A}_{h}{M}_{h}$, was increased. The results explained the transformation of angular dependence curves reported in Nd-Fe-B-based permanent magnets.