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

The study addresses why (Nd,Dy)-Fe-B sintered magnets can exhibit unusually large coercivity relative to the anisotropy field, quantified by k = Hc/HA. In conventional Nd-Fe-B magnets, only ~20% of HA is realized as coercivity, limiting high-temperature applications such as traction motors and wind turbines. While an ideal Stoner–Wohlfarth particle could reach k = 1, real polycrystalline magnets with intergranular phases and demagnetizing fields are limited to ~0.35HA in idealized simulations, and microstructural defects reduce k further. Microstructure engineering (e.g., RE-rich boundary phases, microalloying with Al, Cu, Ga, diffusion treatments, grain refinement) can raise k from ~0.1 to ~0.25–0.3 by weakening ferromagnetism in the intergranular phase. However, in (Nd,Dy)-Fe-B sintered magnets, k increases with Dy substitution and can reach 0.4, which cannot be explained solely by the intrinsic increase in HA due to Dy in the 2-14-1 phase. The research tests the hypothesis that, in addition to intrinsic HA enhancement, an extrinsic mechanism—reduction of intergranular phase magnetization via Dy incorporation—contributes to the large coercivity and changes the reversal mechanism from Kondorsky-type pinning to Stoner–Wohlfarth-like nucleation.

Prior works have shown k improvements through microstructure engineering in Nd-Fe-B, (Nd,Pr)-Fe-B, and Pr-Fe-B magnets, including increased RE content and microalloying with trace elements (Al, Cu, Ga), grain boundary diffusion to reduce IGP ferromagnetism, and grain-size refinement, typically raising k to ~0.25–0.3. Micromagnetic studies indicate that tuning reversal from pinning-controlled (Kondorsky) to nucleation-dominated (Stoner–Wohlfarth) can substantially improve k. Experimental observations for Nd/Pr-Fe-B magnets generally fit the pinning-type Kondorsky model: initial magnetization shows domain-wall pinning at IGP, and coercivity increases monotonically with field angle. Dy substitution in (Nd,Dy)-Fe-B is conventionally attributed to increased HA in the main phase; however, reported k rising with Dy content suggests additional extrinsic effects. Prior Nd-rich Ga-doped Nd-Fe-B magnets with weakly ferromagnetic IGP exhibited partial Stoner–Wohlfarth-like angular dependence but with lower k (~0.25), implying that further suppression of IGP magnetization could more strongly shift the mechanism.

Materials and processing: Dy-free and Dy-containing sintered magnets with at.% compositions Nd14.5Fe78.1Co1.0Cu0.2B6.2 and Nd10.8Dy3.7Fe78.1Co1.0Cu0.2B6.2 (9 wt% Dy) were prepared by conventional powder metallurgy. Sintering: 1010–1040 °C (Dy-free) and 1050–1080 °C (Dy-containing) for 2–4 h; higher temperature was required for Dy-containing densification. Post-sinter anneal: 500–650 °C for 1–2 h. Magnetic measurements: Room-temperature and high-temperature magnetic properties measured by pulse BH tracer; angular dependence of coercivity measured by tilting the easy axis. μ0H(0) defined as field at maximum susceptibility (dM/dH) on the demagnetization curve. Microstructure characterization: SEM (Carl Zeiss CrossBeam 1540 ESB) for general morphology; TEM (Titan G2 80–200, aberration-corrected) for detailed analysis. Atom probe tomography (APT): tips prepared by lift-out on a G4-UX dual-beam; measurements using CAMECA LEAP5000 XS in laser mode at 50 K, 30 pJ, 250 kHz; analysis by IVAS. XMCD: Soft X-ray XMCD at Fe L2,3-edges on BL25SU, SPring-8. Rod samples (~0.5×0.5×10 mm3) with easy axis along length; fractured in high vacuum to expose fresh surface; measurements under 1.9 T along easy axis; degree of circular polarization ~0.96 at 400 eV; beam–field angle 10°. TEY detection; temperature-dependent spectra during heating. A modified analysis separated contributions from intergranular phase (IGP) and Nd2Fe14B, accounting for intragrain fracture area fraction f, probing depth λ≈1.2 nm, IGP thickness tIGP, and Fe concentrations cIGP and cNFB from TEM-EDS; Fe 3d electron count 6.67 used in sum-rule analysis. XMCD microscopy: BL25SU TEY imaging at Fe L3 (707.9 eV); focal depth ±5 µm, spatial resolution ~100 nm; superconducting magnet up to ±8 T; 27 (Dy-free) and 35 (Dy-containing) images collected between remanence and 4 T. First-principles calculations: DFT (GGA) using OpenMX with open-core rare-earth pseudopotentials (Nd 4f as spin-polarized core); valence included Fe 3p and Nd 5s/5p. Convergence criteria: force 1.0×10−3 Hartree/Bohr; energy 1.0×10−5 Hartree. Amorphous IGP structures via melt-quench first-principles MD (1 fs timestep) with supercells (54 atoms) and compositions near NdFe92−xCo2Cu6 and Ndx−4Dy4Fe92−xCo2Cu6 (x=42, 50, 54). Structure optimization: 7×7×7 k-grid, 500 Ry cutoff; PAO basis s2p2d2 (Fe, Co, Cu), s3p2d2 (Nd, Dy). Initial spins on TM and RE antiparallel. Averages over five configurations per composition to capture amorphous variability. Micromagnetic simulations: Model with 125 polyhedral grains (average ~100 nm) separated by a 3 nm IGP. Nd2Fe14B intrinsic parameters at RT: K1 = 4.36 MJ m−3, A = 8 pJ m−1. For (Nd0.8Dy0.2)2Fe14B, parameters via Vegard’s law: K1 = 4.8 MJ m−3, A = 8.4 pJ m−1. Intergranular phase properties were varied systematically to study their effect on angular dependence of coercivity. One surface grain treated as a defect grain with reduced anisotropy K1def, consistent with experimental observations. Demagnetization simulated with code b4vex using field steps Δμ0H = −5 mT and conjugate-gradient free-energy minimization with modified line search.

• Dy-containing magnet exhibited a coercivity of 3.32 T (remanence 1.46 T for Dy-free; remanence for Dy-containing not specified here), compared to 1.28 T for the Dy-free sample.
• The coercivity ratio k = Hc/HA increased from ~0.19 (Dy-free) to ~0.40 (Dy-containing), achieving 0.4HA — roughly twice the Dy-free value and near the ideal micromagnetic limit for granular magnets.
• Angular dependence of coercivity changed markedly: Dy-free sample showed a monotonic increase with angle (Kondorsky-like pinning behavior), while the Dy-containing sample showed an initial decrease and a minimum near ~30°, followed by an increase, closely resembling a Stoner–Wohlfarth-like angular dependence, indicative of nucleation-dominated reversal.
• Temperature dependence of Hc changed from concave (Dy-free) to approximately linear (Dy-containing), consistent with reduced intergranular phase magnetization.
• Microstructure: Strong [001] texture in both; average grain size increased from 3.75 µm (Dy-free) to 5.88 µm (Dy-containing) due to higher sintering temperature, reducing grain-boundary area fraction from 12.3% to 8.1%.
• Secondary phases identified: metallic fcc-RE at triple junctions (beneficial precursor for forming thin IGP after annealing), and RE oxides (hcp-RE2O3 and fcc-REO).
• APT/TEM-EDS: IGP enriched in Nd and Cu and depleted in B for both; Dy-containing magnet showed slight Dy enrichment in IGP (~3.87 at.%) versus main phase (~2.67 at.%). Matrix compositions close to Nd2Fe14B (Dy-free) and (Nd0.78Dy0.22)2Fe14B (Dy-containing).
• XMCD and DFT: Demonstrated reduced Fe magnetic moment in the IGP of the Dy-containing magnet, attributed to ~4 at.% Dy dissolving in the IGP and antiferromagnetically coupling with Fe, thereby suppressing IGP magnetization.
• Micromagnetic simulations supported that lowering IGP magnetization shifts reversal from pinning to nucleation behavior and reproduces the observed Stoner–Wohlfarth-like angular dependence, explaining the high k (0.4).

The work shows that the exceptional coercivity (k ≈ 0.4) in (Nd,Dy)-Fe-B sintered magnets cannot be explained solely by intrinsic enhancement of HA from Dy substitution in the 2-14-1 phase. Instead, a crucial extrinsic contribution arises from reduced magnetization in the thin intergranular phase caused by Dy incorporation (~4 at.%), which antiferromagnetically couples with Fe. This weakening of IGP magnetism reduces exchange coupling across grain boundaries, suppresses domain-wall pinning, and shifts the magnetization reversal mechanism toward nucleation-dominated behavior, as evidenced by the Stoner–Wohlfarth-like angular dependence with a local minimum and by the linearized Hc–T trend. Microstructural analyses (EBSD/SEM/TEM) confirm the formation of thin Nd(Cu)-rich IGPs and the presence of metallic RE-rich phases that feed boundary formation upon annealing. APT validates slight Dy enrichment in the IGP, while XMCD directly detects reduced Fe magnetic moments at the surface-sensitive regions consistent with diminished IGP magnetization. First-principles calculations corroborate that Dy in amorphous Nd–Fe–Co–Cu boundary-like compositions reduces magnetization via antiferromagnetic coupling. Micromagnetic simulations, parametrized with experimentally inferred properties, demonstrate that lowering IGP magnetization reproduces the observed angular dependence and elevated k, establishing a coherent intrinsic–extrinsic picture of the coercivity origin.

This study unveils that the large coercivity in (Nd,Dy)-Fe-B sintered magnets (k ≈ 0.4) originates from a synergy of intrinsic and extrinsic effects: Dy increases HA in the main 2-14-1 phase and, critically, reduces the magnetization of the thin intergranular phase through Dy dissolution (~4 at.%) and antiferromagnetic coupling to Fe. This reduction in IGP magnetism transforms the reversal mechanism from pinning-dominated Kondorsky behavior to a Stoner–Wohlfarth-like nucleation regime, enabling a coercivity approaching micro-magnetic limits for granular magnets. The findings provide a pathway to approach the physical coercivity limit in hard magnets by engineering boundary magnetism via controlled alloying and microstructure processing.

• APT measurements noted an artifact at the interfaces due to different evaporation fields between the IGP and the 2-14-1 matrix, causing slight apparent depletion near boundaries; compositions were interpreted with this consideration.
• The Dy-containing samples required higher sintering temperatures, which increased grain size and reduced grain-boundary area fraction; this concurrent microstructural change may influence coercivity and complicate isolation of individual contributions.
• XMCD analysis relies on TEY probing with limited depth (~1.2 nm) and a model-based separation of IGP and matrix contributions, including estimation of intragrain fracture area fraction.
• Some intrinsic parameters for Dy-containing 2-14-1 (e.g., K1, HA) were estimated using Vegard’s law and literature values, introducing assumptions into simulations and comparisons.