It is well known that the annealing process plays a key role in tuning the properties of Fe-based amorphous soft magnetic alloys. However, the optimal annealing process for a particular amorphous alloy is often difficult to determine. Here, Fe_81.4B_13.2C_2.8Si_1.8P_0.8 and Fe_82.2B_12.4C_2.8Si_1.8P_0.8 amorphous alloys (denoted as Fe_81.4 and Fe_82.2) were prepared to systematically study the effects of the annealing temperature and time on the soft magnetic properties. The results show that the optimum annealing temperature ranges of the Fe_81.4 and Fe_82.2 amorphous alloys were 623 K to 653 K and 593 K to 623 K, and their coercivity (H_c) values were only 2.0–2.5 A/m and 1.3–2.7 A/m, respectively. Furthermore, a characteristic temperature T_ai was obtained to guide the choosing of the annealing temperature at which the dB_s/dT begins to decrease rapidly. Based on the theory of spontaneous magnetization, the relationship between T_ai and the optimum annealing temperature ranges was analyzed. When the annealing temperature was higher than T_ai, the effect of the internal magnetic field generated by spontaneous magnetization on the relaxation behavior was significantly reduced, and the alloys exhibited excellent soft magnetic properties. It is worth indicating that when annealed at 603 K (slightly higher than T_ai), the Fe_82.2 amorphous alloys exhibited excellent and stable soft magnetic properties even if annealed for a long time. The H_c of Fe_82.2B_12.4C_2.8Si_1.8P_0.8 amorphous alloys was only 1.9 A/m when annealed at 603 K for 330 min. This value of T_ai is expected to provide a suggestion for the proper annealing temperature of other amorphous soft magnetic alloys.

High-Cu-content (Cu-content > 1.3 at.%) nanocrystalline alloys exhibit wide heat-treatment windows and favorable soft magnetic properties due to the presence of pre-existing α-Fe nanocrystals. By fabricating ribbons with varying thicknesses to tailor cooling rates, distinct structural characteristics were achieved in Fe₈₂B_16.5Cu_1.5 alloy ribbons. Notably, the face-centered cubic (fcc) γ-Fe phase was identified in Fe-based nanocrystalline alloys. The precipitation of the fcc γ-Fe phase originates from a phase-selection mechanism under specific cooling conditions, while its retention in the as-quenched ribbon with a thickness of 27 μm is attributed to kinetic suppression during rapid cooling and the nanoscale stabilization effect. The formation of the fcc γ-Fe phase significantly reduced the saturation flux density (B_s) and increased coercivity (H_c), concurrently destabilizing the residual amorphous matrix. By suppressing the precipitation of the γ-Fe and Fe₃B phases through precise control of ribbon thickness and annealing parameters, the alloy ribbon with a thickness of 16 μm achieved an optimal combination of B_s (1.82 T) and H_c (8.3 A/m). These findings on anomalous fcc γ-Fe phase precipitation provide novel insights into metastable phase engineering and offer structural design guidelines for alloys containing pre-existing α-Fe nanocrystals.