Hot-deformed anisotropic Nd-Fe-B magnets may potentially attain high coercivity due to their fine and highly orientated crystal grain microstructure as a result of the unique production process that creates these magnets. However, despite their fine grain size of 100–500 nm, coercivity was only around 25% of the full potential of the anisotropy field. This grain size was close to the critical diameter of the single domain grain size of the Nd-Fe-B magnet. This study investigated the effects of chemical composition and deformation conditions on the magnetic properties of Nd-Fe-B magnets, observing their microstructure to obtain guidance on the ideal microstructure. We also improved the hot-deformation technique in parallel to optimize microstructure by controlling the compositions and hot-deformation conditions based on the results of basic studies. Lastly, we fabricated heavy rare-earth-free magnets with a coercivity exceeding 1600 kA/m (20 kOe), which is 20% higher than that of conventional magnets.

Permanent magnets, and particularly rare earth magnets such as Nd-Fe-B, have attracted much attention because of their magnetic properties. There are two well-established techniques for obtaining sintered magnets and bonded Nd-Fe-B magnets. Powder metallurgy is used to obtain high-performance anisotropic sintered magnets. To produce bonded magnets, either melt-spinning or the hydrogenation, disproportionation, desorption, and recombination process is used to produce magnet powders, which are then mixed with binders. Since the development of Nd-Fe-B magnets, several kinds of intermetallic compounds have been reported, such as Sm₂Fe₁₇N_x and Sm(Fe,M)₁₂ (M: Ti, V, etc.). However, it is difficult to apply a liquid-phase sintering process similar to the one used for Nd-Fe-B sintered magnets in order to produce high-performance Sm-Fe–based sintered magnets because of the low decomposition temperature of the compound and the lack of a liquid grain boundary phase like that in the Nd-Fe-B system. Therefore, bonded magnets are useful in the production of bulk magnets using these Sm-Fe based compounds. This article reviews recent progress in our work on the development of high-performance bonded magnets using Nd₂Fe₁₄B and Sm₂Fe₁₇N_x compounds.

Post-neodymium magnets that possess high heat resistance, coercivity, and (BH)_max are desired for future-generation motors. However, the candidate materials for post-neodymium magnets such as Sm₂Fe₁₇N₃ and metastable magnetic alloys have certain process-related problems: low sinterability due to thermal decomposition at elevated temperatures, deterioration of coercivity during sintering, and the poor coercivity of the raw powder. Various developments in powder processing are underway with the aim of overcoming these problems. So far, the development of advanced powder metallurgy techniques has achieved Sm₂Fe₁₇N₃ anisotropic sintered magnets without coercivity deterioration, and advances in chemical powder synthesis techniques have been successful in producing Sm₂Fe₁₇N₃ fine powders with huge coercivity. The challenge of a new powder process is expected to open the way to realizing post-neodymium magnets.

Physically, the coercivity of permanent magnets should scale with the anisotropy field of ferromagnetic compounds, H_A; however, the typical coercivity values of commercial polycrystalline sintered magnets are only ~0.2 H_A, which is known as Brown’s paradox. Recent advances in multi-scale microstructure characterizations using focused ion beam scanning electron microscope (FIB/SEM), aberration corrected scanning transmission electron microscopy (C_s-corrected STEM), and atom probe tomography (APT) revealed detailed microstructural features of commercial and experimental Nd-Fe-B magnets. These investigations suggest the magnetism of a thin layer formed along grain boundaries (intergranular phase) is a critical factor that influence the coercivity of polycrystalline magnets. To determine the magnetism of the thin intergranular phase, soft X-ray magnetic circular dichroism (XMCD) and electron holography played critical role. Large scale micromagnetic simulations using the models that are close to real microstructure incorporating the recent microstructure characterization results gave insights on how the coercivity and its thermal stability is influenced by the microstructures. Based on these new findings, coercivity of Nd-Fe-B magnets are being improved to its limit. This review replies to most frequently asked questions about the coercivity of Nd-Fe-B permanent magnets based on our recent studies.

For the Nd-Fe-B permanent magnets, a prototype thermodynamic database of the 8-element system (Nd, Fe, B, Al, Co, Cu, Dy, Ga) was constructed based on literature data and assessed parameters in the present work. The magnetic excess Gibbs energy of the Nd₂Fe₁₄B compound was reassessed using thoroughly measured heat capacity data. The Dy-Nd binary system was reassessed based on formation energies estimated from ab initio calculations. The constructed database was applied successfully for estimations of phase equilibria during the grain boundary diffusion processes (GBDP) and the reactions in the hydrogenation decomposition desorption recombination (HDDR) processes.

To control the coercivity of Nd hard magnets efficiently, the thermal stability of constituent phases and the microstructure changes observed in hard magnets during thermal processes should be understood. Recently, the CALPHAD method and phase-field method have been recognized as promising approaches to realize phase stability and microstructure developments in engineering materials. Thus, we applied these methods to understand the thermodynamic feature of grain boundary phase and the microstructural developments in Nd-Fe-B hard magnets. The results are as follows. 1) The liquid phase is a promising phase for covering the Nd₂Fe₁₄B grains uniformly. 2) The metastable phase diagram of the Fe-Nd-B ternary system suggests that the tie line end of the liquid phase changes drastically depending on the average composition of Nd. 3) The Nd concentration in the grain boundary phase can reach 100 at% if the volume fraction of the grain boundary phase is constrained. 4) The effect of Cu addition to the Nd-Fe-B system on the microstructural morphology is reasonably modeled based on the phase-field method. 5) The morphology of the liquid phase can be controlled using phase separation in the liquid phase and the grain size of Nd₂Fe₁₄B phase.

To realize a sustainable society, “green technology” with low (or even zero) CO₂ emissions, is required. A key material in such technology is a permanent magnet because it is utilized for electric-power conversion in several applications including electric vehicles (EVs), hybrid EVs (HEVs), and turbines for wind power generation. To realize highly efficient electric-power conversion, a stronger permanent magnet than Nd–Fe–B is necessary. One potential candidate is a Fe-rich SmFe₁₂-based compound with a ThMn₁₂ structure. In this paper, the phase stability, structure, and intrinsic and extrinsic magnetic properties in both film and bulk forms are reviewed. Based on these results, a possible way to realize a strong SmFe₁₂-based permanent magnet in bulk form is discussed.

Multielement rare earth (R)–transition metal (T) intermetallics are arguably the next generation of high-performance permanent magnetic materials for future applications in energy-saving and renewable energy technologies. Pseudobinary Sm₂Fe₁₇N₃ and (R,Zr)(Fe,Co,Ti)₁₂ (R = Nd, Sm) compounds have the highest potential to meet current demands for rare-earth-element-lean permanent magnets (PMs) with ultra-large energy product and operating temperatures up to 200°C. However, the synthesis of these materials, especially in the mesoscopic scale for maximizing the maximum energy product ((BH)_max), remains a great challenge. Nonequilibrium processes are apparently used to overcome the phase-stabilization challenge in preparing the R–T intermetallics but have limited control of the material’s microstructure. More radical bottom-up nanoparticle approaches based on chemical synthesis have also been explored, owing to their potential to achieve the desired composition, structure, size, and shape. While a great achievement has been made for the Sm₂Fe₁₇N₃, progress in the synthesis of (R,Zr)(Fe,Co,Ti)₁₂ magnetic mesoscopic particles (MMPs) and R–T/T exchange-coupled nanocomposites (NCMs) with substantial coercivity (H_c) and remanence (M_r), respectively, remains marginal.

First-principles calculation based on density functional theory is a powerful tool for understanding and designing magnetic materials. It enables us to quantitatively describe magnetic properties and structural stability, although further methodological developments for the treatment of strongly-correlated 4f electrons and finite-temperature magnetism are needed. Here, we review recent developments of computational schemes for rare-earth magnet compounds, and summarize our theoretical studies on Nd₂Fe₁₄B and RFe₁₂-type compounds. Effects of chemical substitution and interstitial dopants are clarified. We also discuss how data-driven approaches are used for studying multinary systems. Chemical composition can be optimized with fewer trials by the Bayesian optimization. We also present a data-assimilation method for predicting finite-temperature magnetization in wide composition space by integrating computational and experimental data.

Development of high-performance permanent magnets relies on both the main-phase compound with superior intrinsic magnetic properties and the microstructure effect for the prevention of magnetization reversal. In this article, the microstructure effect is discussed by focusing on the interface between the main phase and an intergranular phase and on the intergranular phase itself. First, surfaces of main-phase grains are considered, where a general trend in the surface termination and its origin are discussed. Next, microstructure interfaces in SmFe₁₂-based magnets are discussed, where magnetic decoupling between SmFe₁₂ grains is found for the SmCu subphase. Finally, general insights into finite-temperature magnetism are discussed with emphasis on the feedback effect from magnetism-dependent phonons on magnetism, which is followed by explanations on atomic arrangements and magnetism of intergranular phases in Nd-Fe-B magnets. Both amorphous and candidate crystalline structures of Nd-Fe alloys are considered. The addition of Cu and Ga to Nd-Fe alloys is demonstrated to be effective in decreasing the Curie temperature of the intergranular phase.

It has been empirically known that the coercivity of rare-earth permanent magnets depend on the size and shape of fine particles of the main phase in the system. Also, recent experimental observations have suggested that the atomic scale structures around the grain-boundaries of the fine particles play a crucial role to determine their switching fields. In this article, we review a theoretical attempt to describe the finite temperature magnetic properties and to evaluate the reduction of the switching fields of fine particles of several rare-earth permanent magnet materials based on an atomistic spin model that is constructed using first-principles calculations. It is shown that, over a wide temperature range, the spin model gives a good description of the magnetization curves of rare-earth intermetallic compounds such as R₂Fe₁₄B (R = Dy, Ho, Pr, Nd, Sm) and SmFe₁₂. The atomistic spin model approach is also used to describe the local magnetic anisotropy around the surfaces of the fine particles, and predicts that the rare-earth ions may exhibit planar magnetic anisotropy when they are on the crystalline-structure surfaces of the particles. The dynamical simulation of the atomistic spin model and the corresponding micromagnetic simulation show that the planar surface magnetic anisotropy causes a reduction in the switching field of fine particles by approximately 20-30%, which may be relevant to the atomic scale surface effects found in the experimental studies.

For the practical use of magnets, particularly at high temperatures, the temperature dependence of magnetic properties is an important ingredient. To study the temperature dependence, methods of treating the thermal fluctuation causing the so-called activation phenomena must be established. To study finite-temperature properties quantitatively, we need atomistic energy information to calculate the canonical distribution. In the present review, we report our recent studies on the thermal properties of the Nd₂Fe₁₄B magnet and the methods of studying them. We first propose an atomistic Hamiltonian and show various thermodynamic properties, e.g., the temperature dependences of the magnetization showing a spin reorientation transition, the magnetic anisotropy energy, the domain wall profiles, the anisotropy of the exchange stiffness constant, and the spectrum of ferromagnetic resonance. The effects of the dipole-dipole interaction (DDI) in large grains are also presented. In addition to these equilibrium properties, we also study coercivity, which is the most important issue for magnets. The temperature dependence of the coercivity of a single grain was studied using the stochastic Landau-Lifshitz-Gilbert equation and also by the analysis of the free energy landscape, which was obtained by Monte Carlo simulation. It was found that the upper limit of coercivity at room temperature is about 3 T, which is significantly lower than the so-called theoretical coercivity given by a simple coherent rotation model. The coercivity of a polycrystalline magnet, i.e., an ensemble of grains, is expected to be reduced further by the effects of the grain boundary phase, which is also studied. Surface nucleation is a key ingredient in the domain wall depinning process. Finally, we study the effect of DDI among grains and also discuss the distribution of properties of grains from the viewpoint of first order reversal curve.

Although coercivity is one of the fundamental properties of permanent magnets, it has not been well understood. In this paper, micromagnetics and thermal activation magnetization reversal theories are briefly reviewed, and then our recent macroscopic and microscopic experimental approaches for thermally activated magnetization reversal in advanced Nd-Fe-B hot-deformed magnets are explained. Our experimental results are well supported by the recent atomistic spin model calculations. Moreover, the systematic micromagnetics simulation study makes much clearer the physical picture of the thermally activated magnetization reversal process in permanent magnets.