Correlation between magnetic softness, sample surface and magnetoimpedance in Co$_{69}$Fe$_{4.5}$\textit{X}$_{1.5}$Si$_{10}$B$_{15}$ (\textit{X} = Ni, Al, Cr) amorphous ribbons

In this work we have studied the giant magnetoimpedance (GMI) effect and its field sensitivity ($\eta )$ in Co$_{69}$Fe$_{4.5}$X$_{1.5}$Si$_{10}$B$_{15}$ (X = Ni, Al, Cr) amorphous ribbons in the frequency (f) range of 0.1 to 10 MHz. We find that at f $<$ 5 MHz, the GMI effect and $\eta $ reach the largest values for the Al-containing sample and the smallest values for the Ni-containing sample, while an opposite trend is observed at f $>$ 5 MHz. Magnetization and atomic force microscopy (AFM) experiments reveal that the largest values of the low-frequency GMI effect and $\eta $ for the Al-containing sample result from the largest value of magnetic permeability, while the largest values of the high-frequency GMI effect and $\eta $ for the Ni-containing sample are attributed to the smallest surface roughness of this sample. These results point to the importance of the sample surface in determining high-frequency GMI behavior. A correlation between the sample surface and high-frequency GMI is established in the investigated ribbons.