Intergranular interaction in nanocrystalline Ce-Fe-B melt-spinning ribbons via first-order reversal curve analysis

Recent pressures on the availability and the cost of rare-earth (RE) metals, especially for Nd/Pr and Tb/Dy that are essential to high-performance Nd₂Fe₁₄B-type permanent magnets, have reinvigorated research on alternative, economically more attractive materials. A large amount of work has already been focused on improving phase structure and magnetic properties of Ce₂Fe₁₄B phase,^1–10 because the Ce element is the most abundant rare-earth. However, little attention has been devoted to intergranular interactions among the Ce₂Fe₁₄B grains, which strongly correlate with their magnetic performance. Many studies have shown that intergranular interactions play a dominant role during demagnetization processes and are sensitively influenced by microstructure, including grain size and intergranular phases.¹¹ For example, the smaller grain size corresponds to a stronger intergranular exchange coupling, which can increase the remanence ratio, especially in the isotropic magnets.^12–15 And in our recent work, we obtained a uniform and continuous intergranular phase results in a stronger magnetostatic coupling, hence strengthen the coercivity significantly.^16,17 A deeper understanding of the relationship between intergranular interactions, microstructural features, and magnetic properties is beneficial to a systematic improvement of hard magnetic properties for Ce-Fe-B based permanent magnets. In this point of view, a subtle characterization of intergranular interaction may provide us with more important information on the role of the magnetic interactions.

In this work, the detailed intergranular interaction in nanocrystalline Ce-Fe-B alloy fabricated by melt-spinning followed by electron beam exposure was investigated by employing First Order Reversal Curves (FORC), which were defined as an experimental method for the accurate characterization of intergranular interactions in ferromagnetic systems.^18,19 The FORC diagrams are more appropriate than other similar experimental methods because they do not require a demagnetized state for measuring, as is the case in the well-known Henkel plot (δ_M). To better understand intergranular exchange interactions and magnetization reversal properties, the FORC diagrams, Henkel plots, and the magnetic domain structure of Ce-Fe-B alloy with different grain sizes are studied here.

Alloy ingot with the nominal composition of Ce_12.2Fe_81.6B₆ was prepared by arc melting of 99.9% pure primary materials in a high-purity argon atmosphere. Rapidly quenched ribbons were obtained by melt spinning onto a copper wheel in an argon atmosphere with a surface speed of 50 m/s. The melt-spinning ribbon thickness was around 15 μm estimated by scanning electron microscope (SEM, MERLIN Compact, ZEISS), and the width was about 5-10 mm. The details of the method based on electron-beam exposure (EBE) was reported in Ref. 17. The annealed ribbons were characterized by X-ray powder diffraction (XRD, Cu-Kα radiation, λ = 1.54187 Å) with a single-crystal silicon substrate. Lorentz transmission electron microscope (LTEM, JEM-2010F) was used to examine the microstructure and magnetic domain configurations for the melt-spinning ribbons. LTEM samples were prepared by the ion milling technique (Gatan 691/695). Magnetic measurements were performed with a vibrating sample magnetometer (VSM, Lakeshore8600) at room temperature (RT). The FORC diagram here is plotted by the FORCinel program designed by Harrison et al. according to the repeated hysteresis curves under the different applied field, and the smoothing factor is chosen as 3 consistently to visualize the variation of magnetic interaction on a field plane clearly from FORC diagrams while keeping noise to an acceptable level.²⁰ 

The single-phase Ce₂Fe₁₄B was successfully prepared by EBE with a combination of melt-spinning. When the velocity of the melt-spinning is 50 m/s, the Ce₂Fe₁₄B ribbons exhibit a uniform amorphous structure, as shown in Fig. 1(a). The inset is the SAED pattern, showing a typical circular pattern for the amorphous state. Fig. 1(b) presents the XRD patterns of the free side of Ce_12.2Fe_81.6B_6.2 ribbons versus different electron beam currents (I_B) at RT. The melt-spinning ribbons keep amorphous when the I_B is less than 0.2 mA. Then the crystallized peaks of 2:14:1 phase (P42/mnm, PDF # 89-3484) appear and become sharper as the I_B increase. When I_B is over 0.5 mA, the CeFe₂ phase (Fd$3̄$m, PDF # 07-0135) forms because it is a thermostable phase and usually occurs in the sintering process when the temperature is high enough to activate the reaction.¹ As a result, the optimal electron beam condition should be controlled between 0.3 and 0.5 mA for Ce-Fe-B melt-spinning ribbons prepared under 50 m/s. In this case, the crystallization process is completed without forming other undesired phases.

The variation of coercivity with the increase of I_B is plotted in Fig. 2. It demonstrates that when the I_B is too small to provide enough thermal energy for activating the crystallization process, the ribbons would keep soft magnetic behavior, which is consistent with the XRD results (see Fig. 1(b)). When I_B = 0.3 mA, the optimal coercivity is obtained with H_cj(//) = 350.1 kA/m, H_cj(⊥) = 335.8 kA/m, and the corresponding remanence ratio: B_r/B_s(//) = 0.65, B_r/B_s (⊥) = 0.48. Then with the increase of the I_B from 0.3 to 0.5 mA, the coercivity and remanence ratio both decrease. The remanence ratio B_r/B_s(//) is larger than 0.5, suggesting a remanence enhancement effect in the Ce-Fe-B system. This demonstrates a strong exchange coupling interaction among the grains along the parallel direction. Then the B_r/B_s(//) is stable at around 0.5 when I_B is larger than 0.5 mA, corresponding to a non-interaction system. Meanwhile, the remanence ratio of the applied field perpendicular to the ribbon surface keeps less than 0.5 for all beam currents even if after the demagnetization correction (demagnetization factor: N = 1). This suggests the intergranular interaction exhibition is different along the different direction of the ribbon surface, resulting in different magnetic performance; hence a further characterization of intergranular interaction in different directions is necessary.

To further clarify the correlation between magnetic properties and the intergranular interaction along with different directions, the FORC diagrams were employed. Andrew P. Roberts proposed that the FORC diagrams could be used as a new tool for characterizing the interaction field and magnetostatic interaction of natural samples since superparamagnetic, single-domain, and multidomain grains, as well as magnetostatic interactions, all would produce characteristic and distinct manifestations on a FORC diagram.²¹ Afterwards, this has been applied to various magnetic materials, including Nd-Fe-B magnets.²² Especially, Rong et al. have taken the FORC diagrams to identify optimal conditions for exchange coupling between SmCo₅ and α-Fe grains. And they demonstrated that FORC analysis provides more information on the magnetostatic as well as the exchange interactions.²³ Hence, in this work, we also try to demonstrate the intergranular interactions in Ce-Fe-B grains by using FORC diagrams.

As illustrated in Fig. 3, the spread along the H_u axis of perpendicular direction is wider than that of parallel direction for I_B = 0.3 mA, indicating a stronger magnetostatic coupling interaction of the perpendicular direction. Besides, the spread along the H_c axis of the perpendicular direction is also wider than that of parallel direction with one peak along the H_c axis; these results mean the exchange coupling interaction exists in both directions. Combining with the Henkel plot in Fig. S9, it is concluded that the magnetostatic coupling interaction dominates in the perpendicular direction, while the exchange coupling interaction dominates in the parallel direction. With the I_B increase to 0.6 mA, the center of the peak along with the H_c axis shifts to the zero point, demonstrating that the intergranular interaction becomes weaker, and the switching field during the magnetization reversal process gets smaller with the increase of beam current. Correspondingly, the coercivity decreases: H_cj(//) = 86.7 kA/m, H_cj(⊥) = 99.5 kA/m.

Intergranular interactions are intimately related to the microstructure, which influences extrinsic magnetic properties significantly. The Ce₂Fe₁₄B grain grows up with the increase of I_B, from 96.4 nm of 0.3 mA to 194.8 nm of 0.6 mA, as shown in Fig. 4, which is smaller compared to the criticle size for single-domain particles (D_c ≈ 300 nm for Nd₂Fe₁₄B²⁴). It can be seen that under 0.3 and 0.4 mA, one domain includes several grains due to the strong exchange coupling interaction between neighboring grains, as shown in Figs. S6 and S7. When the grain size increase further in 0.6 mA, some magnetic domain wall appears inside the grain (red circles in Fig. 5). This magnetic domain configuration would decrease the nucleation field during the magnetization reversal process, therefore, resulting in the decrease of coercivity. This is consistent with the FORC results above, that the intergranular interaction becomes weaker under 0.6 mA, and the switching field gets smaller. More details of the magnetic domain configuration are shown in Figs. S6-S8. These results demonstrate that the intergranular interaction varies with the grain size, from a strong exchange coupling of the single-domain to a weaker coupling of multi-domains.

In summary, this study has shown the possibility of characterizing the intergranular interaction in nanocrystalline ternary Ce-Fe-B permanent magnet material through the FORC diagrams, which provide a visualization of the variation for magnetic intergranular interaction on a field surface. The FORC diagram exhibits that the intergranular interaction evolution in different directions. It was found that the intergranular interaction is dominated by the exchange coupling when the applied field is parallel to the ribbon surface while by the magnetostatic interaction when the applied field is perpendicular to the ribbon surface. Moreover, the magnetic domain configuration of nanocrystalline Ce-Fe-B melt-spinning ribbons observed by LTEM directly shows the intergranular interaction variation with grain size.

See supplementary material for the complete microstructure and FORC diagrams of the studied Ce-Fe-B nanocrystalline ribbons.

All authors contributed equally to this work.

This work was supported by the National Key Research and Development Program of China (No. 2016YFB0700901), National Natural Science Foundation of China (Grant Nos. 51731001, 11675006, 51371009). We appreciated the financial support from the China Scholarship Council (CSC) by a State Scholarship Fund (No. 201906010220).

The authors declare no conflict of interest.

The data that support the findings of this study are available from the corresponding author upon reasonable request.