The giant magneto-impedance (GMI) effect associated with the variation of transverse permeability for the rib-bons Fe89Zr6Hf1B4 with different annealing temperatures TA = 793, 823, 893, 923, 993, and 1033 K was investigated. There is an optimum annealing temperature TA ≈ 993 K for obtaining the largest GMI effect for the ribbons Fe89Zr6Hf1B4. The magneto-impedance GMI (Z) = (Z(H) ? Z(0))/Z(0) for the ribbon with TA = 993 K can reach ?55.09% at a frequency f = 900 kHz under H = 7162 A/m. The relative changes of the real part of transverse permeability ?μ′/μ′0 = (μ′(H)? μ′(0))/μ′(0) under H = 7162 A?m?1 at f = 1 MHz are ?78.83%, ?89.98% and ?94.77 % for Fe89Zr6Hf1B4 ribbons with TA = 823, 893, and 993 K, respectively. The strong GMI effect is accompanied by the large change of transverse permeability. A large magnetoreactance GMI(X) = (X (H) ? X (0))/X (0) of ?81.09% can be obtained at f = 100 kHz under H = 7162 A/m for the ribbon with TA = 993 K. Meanwhile, this present result gave an experimental support to the previous concept / assumption that the positive peak in the field dependence of magneto-impedance is connected to the peak of transverse permeability with varying fields.
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