Giant Magnetoimpedance: A Relevant Application of Impedance Spectroscopy
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Mat. Res. Soc. Symp. Proc. Vol. 500 ©1998 Materials Research Society
30,
30 f= 10kHz 20 20
010
10
.. H, 6.4kA~m• 161
O-lO4
lop
2
10
Q(HZ)
H3
4
5
Hdc (k•m)
6(
Fig. 2. Behavior of the real part of inductance at 10 kHz, as a function of the DC field.
Fig. 1. Spectroscopic plot of the real inductance, L,, at zero-field and at 6.7 kA/m (data at f < I kHz showed some dispersion and are not shown).
L = (-j/o)Z
(1)
where L (= Lr + j Li)is the complex inductance, j the basis of imaginary numbers ((-1)1/2), o( the angular frequency and Z (= Zr + j Zi) the complex impedance. Note that due to j, there is a crossing of terms: real inductance, L4, depends on imaginary impedance, Zi, and imaginary inductance, Li, is determined by real impedance, Zr. The analysis of experimental results is therefore carried out in inductance formalisms, and by separating their real and imaginary contributions. Spectroscopic plots of the real part of inductance at 0 and 6.4 kA/m of DC field show the effects of the latter, Fig. 1. The zero-field experiment exhibits a larger value at low frequencies, followed by a dispersion. The high-field results are virtually independent of frequency, and show a small L, value very close to the zero-field results at high frequency (higher than the dispersion). From these results, a characteristic plot of GMI can be obtained at a constant frequency (at 10 kHz, for instance), by considering the variations in L, as a function of DC field, Fig. 2. This plot
clearly shows the sensitivity of GMI to small fields. 10' 0%
%0
HdC= 6.8 kAm
500
10'• 400
102
300
H,==0 .-T
10'
200 Hdc=0
100
Hdc = 6.4 kAlm
10o. 1in
025
50
,J
102
to,
t0'
10s
10t
107
10'
L, (gH)
t(Hz)
Fig. 4. Complex plane representation of inductance data, for zero- and maximum DC field.
Fig. 3. Spectroscopic plot of the imaginary part of inductance, for Hdc = 0 and 6.7 kA/m.
134
Imaginary inductance also shows the influence of the DC field, Fig. 3. Both experiments (at zero- and high-field) lead to a slope very close to -1 (in a log-log plot) up to frequencies of 10 kHz; the zero-field results then exhibit a lower slope. The largest changes therefore appear at higher frequencies. DISCUSSION The representation of data in the complex Li-Lr plane can be useful in the search for an equivalent circuit to model the sample behavior. At high DC fields, a "spike" is observed in this representation, while the zero-field results show a more complex behavior, Fig. 4. It can be shown [4] that the presence of a spike is associated with a RL series circuit. Figures 1 and 2 for the high-field results point also to a RL series circuit. On the other hand, the dispersion observed in the real part of inductance for the zero-field results (Fig. 1) seems to represent a relaxation behavior, related with an arrangement which should include a RL parallel circuit. We make therefore the assumption that the equivalent circuit is a R0L, series, in series with a RpL4 parallel for the zero-field condition. Also, that the equivalent circuit be
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