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The giant magneto impedance, GMI, effect of Co-based metallic fibers prepared by melt-extracted technology is investigated under different bias direct electrical current I b. The GMI curves have single peaks which are symmetric about zero field at and below 1MHz. However, the bimodal GMI curves which have asymmetric peaks are observed when I b is over 2mA at 0.1MHz. And asymmetric GMI, AGMI, effect is also appeared at 1MHz when I b just is 1mA and the field sensitivity of GMI effect is increased 5.6 times. The GMI effect and magnetization process is affected by the bias magnetic field profoundly induced by I b , which is correlated with the outer shell domain structures with circumferentially magnetization easy axis existed in the outer shell of Co-rich magnetic wires with low and negative magnetostriction. Below 1 MHz, only if the bias current is over 1.5mA which induces a magnetic circumferential magnetic field is above the coercivity of 14.4A/m, the circumferential magnetization and GMI effect can experience the bias magnetic field effect. Above 1MHz, the skin effect gets stronger and significantly decreases the total participants of circular magnetization process in the fibers and consequently, the circular outer shell magnetization process gets much sensitive to circular bias magnetic field. AGMI effect with high field sensitivity is realized due to the bias current.

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