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• Heat treatment interval of Fe 80 Zr 9 B 10 Cu 1 alloy is as high as 154.7 K. • Composition, microstructure and magnetic properties correlation is revealed and elaborated. • Composition impacts on crystallizations of FeZrB and FeZrBCu alloys are established. • Thermal stability of H c in FeZrBCu alloys is developed with composition and annealing engineering. Amorphous alloy ribbons of FeZrB and FeZrBCu (1 at.% Cu) are synthesized and annealed in vacuum. Synergistic effects of the addition of Cu, and different proportions of Fe, Zr and B, on both crystallization and magnetic property of FeZrB alloys, are systematically investigated. The addition of Cu results in a lower thermal stability of FeZrBCu alloys compared to FeZrB alloys, while the heat treatment interval of FeZrBCu alloys is wider. The crystallizations of FeZrB alloys differ from each other; in contrast, those of FeZrBCu alloys are similar. The coercivity (H c) is large for FeZrB alloys in general, but small for FeZrBCu alloys at the initial annealing stage due to the nanocrystalline structure in the two-phases and the fine α -Fe nanocrystals. All developed FeZrBCu alloys demonstrate low values of H c and excellent thermal stability of H c below 898 K. The correlated mechanisms linking crystallization and magnetic characteristics are discussed in detail. [ABSTRACT FROM AUTHOR]