Evaluation of the Imaginary Part of the Magnetic Susceptibility, $\chi ^{\prime \prime }$ , and Application to the Estimation of the Low Frequency, 1/ $f$ , Excess Noise in GMI Sensors

Abstract

The equivalent magnetic noise spectral density of giant magnetoimpedance (GMI)-based sensors exhibits a low-frequency excess noise inversely proportional to the frequency (1/f noise). In order to enhance the performance and reach the ultimate and intrinsic limit of the magnetometer, it is necessary to investigate the origin of this excess noise. Cross correlation measurements have permitted the demonstration that the excess low-frequency noise arises from the sensor, under defined excitation conditions, particularly the amplitude of the excitation current and the dc bias current. Given that the GMI effect is based on an impedance variation governed by the magnetization direction under an applied external magnetic field, the low-frequency magnetization fluctuations within the GMI wire have been considered to be a possible noise source. The fluctuation-dissipation theorem permits evaluation of the spectral power density of these fluctuations, which is proportional to the imaginary part of the susceptibility, $\chi ^{\prime \prime }$ . The latter may be evaluated by two different methods, based on the measurement of the real part of the wire impedance and on the evaluation of the circumferential hysteresis loop area. The results obtained by both methods are compared and discussed. The values of $\chi ^{\prime \prime }$ thus obtained are then used in order to predict the equivalent magnetic noise level at 1 Hz, and are compared with that measured at 1 Hz. The comparison is conducted for different amplitudes of the dc bias current, and the results obtained indicate that the proposed methods have the potential of predicting the excess noise in GMI sensors.