Magneto Impedance Study for Pseudo Spin Valves
3.3 Magneto Impedance Behavior and Its Equivalent Circuit Analysis of a Co/Cu/Co/Py Pseudo Spin Valve with a Nano-Oxide Layer
3.3.1 Equivalent Circuit for Pseudo Spin Valve
Figure 3.1 shows the frequency dependence of |Z|, R, and X for the PSV at zero applied fields. The X curve was negative at low frequency. It turned positive at the frequency f ≥
476 kHz, indicative of the resonance frequency (fr) of the circuit. This is in agreement with the simulated equivalent circuit consisting of an equivalent resistance Rpsv (=103.71 Ω), inductance Lpsv (=79.85 nH), capacitance CPSV (= 20.83 pF) and a parasitic inductance Lp
(=627.8 nH), capacitance Cp (=225.04 nF) and resistance RP1 (=1.72 Ω), RP2 (=12.86 Ω), respectively, as shown in the inset panel in Fig. 3.1.
The impedance of the equivalent circuit of the PSV is
Z = 1 / [1 / (RPSV + i 2 π f LPSV)+ (i 2 π f CPSV)] + RP1 + i 2 π f LP + 1 / (1 / RP2 + i 2 π f CP), (3.3.1)
Fig. 3.1. The frequency dependences of |Z|, R and X for the PSV at zero field. The resonance frequency (fr) is found at 476 kHz, where X vanishes. The experimental data (open symbols) are very close to the theoretical result (solid curves) calculated from the equivalent circuit shown in the inserted panel.
The solid line in |Z| shown in Fig. 3.1 represents the best fit with the experiment data based on eq. (3.3.1). The solid line and the data points fall exactly on top of each other, indicating that the PSV is well represented by the equivalent circuit. Based on this observation, we elaborate on the impedance behavior of PSV under various conditions. The frequency behavior of the PSV, being metallic, is dominated by XL at high frequency, and XC is significant only at low frequency. Note that X changes from negative to positive as the frequency is swept from 100Hz to 40 MHz. X vanishes at fr= 476 kHz.
The real part and imaginary parts of the equivalent impedance of the PSV are
Reff = RPSV / [(1 - 4π2f 2CPSV LPSV)2 + 4π2f 2CPSV2
RPSV2
] + RP1 + RP2 / (1 + 4π2f 2CP2
RP22
)
Xeff = 2 π f {LP + (LPSV – 4π2f 2CPSV LPSV2
– CPSV RPSV2
) / [(1 – 4π2f 2 CPSV LPSV)2 + 4π2f
2CPSV2RPSV2] – CP RP22 / (1 + 4π2f 2CP2 RP22)} , (3.3.2)
Note that R decreased very slowly at low frequency, and then dropped at a relatively faster pace at higher frequency. This was confirmed by observation. Furthermore, the |Z| value would have shown a minimum at fr if the real part of the impedance R had remained constant.
In fact, this was not the case. Consequently, the minimum value of |Z| drifted to somewhere between 476 kHz and 5 MHz (smooth range), as indicated in Fig. 3.1. For the present case, the minimum value of |Z| took place at a frequency near 2.4 MHz, where the slope of the |Z|
curve is flat. Beyond this point, the impedance increased rapidly as XL became dominant. As noted, the capacitance contribution from the equivalent circuit was minimal. Most of the capacitance effect shown in the equivalent circuit had its origin from the parasitic effects of the wire itself.
With the above-mentioned Eq. (3.3.1) and (3.3.2), the simulation value of the LPSV is
79.85 nH. Let us make a rough order of magnitude estimate of the L value. By definition, L = BA / I, where B is the magnetic field; A (7.94×10-11 m2) is the cross section area of the magnetic multilayer through which B passes, and I (4.37 mA) is the current through the sample. The Ms of the PSV measured by VSM is 595.7 emu / cm3. By simple relation, L is roughly 13.6 nH. This is of the same order of magnitude as observed.
3.3.2 Magneto Impedance Behavior for Pseudo Spin Valve
Figures 3.2 (a) and (b) show the low frequency response of MI, MP, MR, and MX effects of the PSV at 100 Hz. The behavior of the PSV may be regarded as DC-like at this frequency, and both MX and MP may be treated as frequency independent. On closer inspection, however, the value of the MX at anti-parallel state at fr = 476 kHz is clearly non-zero.
Fig. 3.2. (a), and (b) magneto impedance at 100 Hz. At this low frequency, the magneto transport property can be regarded as DC. (c) at resonance frequency fr (476 kHz), MX shape of loop reverse to MR loop. (d) The value of MX is negative at f < fr, and switches to positive at f > f.
Fig. 3.3. (a) The frequency dependences of |Z|AP, △Z and MI ratios. (b) The frequency dependences of MR and |MX ratio|.
Interestingly, it shows an inverted negative MR-like loop behavior, as shown in Fig. 3.2 (c).
These results are agreement with a previous report [14]. An MX ratio of more than 1700%
was observed. This is due to the fact that the imaginary part of Z at parallel state crosses zero at fr. Figure 3.2 (d) shows that the MX values change from negative (at f < fr) to positive (at f
> fr) at 400~500kHz. The fr of the PSV is therefore bordering between 400 to 500 kHz in the present sample.
Figure 3.3 (a) shows the frequency dependence of △|Z| and |Z|AP and the MI ratio. The behavior of |Z|AP is nearly the same as that of |Z|, as shown in Fig. 3.1. As the frequency increases beyond the smooth range, |Z|AP increases steeply as the XL increases. It is remarkable that △|Z| decreases slowly but steadily before reaching the smooth range, and then decreases sharply upon passing that smooth range. Since the MI ratio was defined as △
|Z| divided by |Z|AP, it was predictable that the MI ratio would decrease steadily with increasing frequency, as observed.
Based on these observations, it is reasonable to argue that the variation of the impedance △|Z| of the PSV can be simplified as compounded by the parallel and anti-parallel states of the moments of the PSV. We have
△|Z| = ZAP - ZP = 1/ ((1/RPSV-AP)2+ (2 π f CPSV-AP)2) - 1/ ((1/RPSV-P)2+ (2 π f CPSV-P)2), (3.3.3)
Since the RPSV and CPSV depend upon the magnetization state, the behavior of the △ |Z| is sensitively influenced by the existence (or, effectively, the vacancy density) of the capacitance of the NOL in the PSV, and decreases as the frequency increases. The frequency dependences of the MR and the absolute value of the MX ratios are shown in Fig. 3.3 (b). The MR ratio changes only slightly as the frequency changes. In contrast, the |MX ratio| is sharply peaked at the fr. The value of |MX ratio| is very small at a frequency away from the fr but shows an
astounding peak when XAP is close to zero. A small change in XAP would bring about a great change in the |MX ratio| (~ 1793% in the present sample).
3.3.3 Annealing Effect
The DC MR ratio of the PSV decreased as the annealing temperature increased, which occurred because NOL formed in the interface between spacer and magnetic layer. For this reason, we used the impedance technique to analysis the capacitance effect, which is caused by oxidation. Figure 3.4 shows that the resistance of the PSV increased from 21.80 to 28.98 ohm and the DC MR ratio of the PSV decreased from 5.41 to 0.48 % as the annealing temperature increased from RT to 200oC, which indicates that oxidation occurred in the PSV.
Fig. 3.4. The DC MR ratio and resistance (R) of the PSV are functions of the annealing temperature.
Therefore, the effective capacitance was measured by imaginary part of impedance (Im (Z)) curves, as shown in Fig. 3.5. Im (Z) reached a minimum at roll-off frequency (froll). The plot of froll as a function of annealing temperature is shown in Fig. 3.6; froll increased linearly from 345 to 465 kHz between annealing temperatures RT to 200 oC. It is quite interesting to analyze the effective capacitance effects with changes in annealing temperature. According to the effective capacitance calculation, froll can be shown as:
froll = 1 / ( 2πReffCeff ), (3.3.4)
Fig. 3.5. Imaginary part of impedance curves for PSV with different AT temperatures ranging from RT to 200oC.
Fig. 3.7. The hysteresis loops of the PSV with AT temperatures RT, 140oC, 160oC, 180oC, 200oC, respectively. The inset panels show the equivalent capacitor modes.
Fig. 3.6. The roll-off frequency and effective capacitance of the PSV are functions of the annealing temperature.
The effective capacitance is in reverse proportion to the froll and estimated values, and it varies from 21.8 to11.8 nF as annealing temperatures increases from RT to 200 oC. One possible explanation is that the effective capacitance decreases as annealing temperature increases by hysteresis loops, as shown in Fig. 3.7. The coercivity (Hc) of Co is 20 Oe, and the HC of Co-Py coupled is 12 Oe in the PSV, which was deposited at RT. When the annealing temperature was increased to 140oC, the HC of Co was apparently incoherent in the PSV, indicating that the oxidation effect occurred in the Co layer. The oxidative thickness is in proportion to froll and in reverse proportion to Ceff [52]. The result of froll, which increased as annealing temperature increased to 140oC, indicated that the oxidative thickness of Co layer was increasing. This increase in thickness caused the resistance to increase and the DC MR ratio to decrease slightly. Above the annealing temperature of 140 oC, it is difficult to distinguish the Hc of Co or that of Co-Py, implying that the oxidation effect occurs in the Co/Cu or Co-Py/Cu interfaces. They could be regarded to two capacitors in series, thus causing a decrease in effective capacitance, as shown in the inset panel in Fig. 3.7. Therefore, the froll increases and effective capacitance decreases as the annealing temperature increases, indicating that the increase in annealing temperature causes the oxidative thickness to increase and oxidize more than one layer.
3.3.4 Conclusion
In conclusion, the AC behavior in the Pseudo spin valve led to interesting MR and MX loops, with the MR loop a reversal of the MX loop. The magneto impedance effect of PSV has been investigated at RT. It is found that the PSV can be regarded as a combination of resistances (RPSV, RP1, RP2 ), inductances (LPSV, LP), and capacitances (CPSV, Cp), and equivalent circuit theory can be used to analysis the AC behavior of this system. It is quite interesting that the |MX| ratio is more than 1700 % at fr = 476 kHz. This suggests strongly that PSV is potentially a very sensitive frequency sensor. The magneto impedance behavior in the
Co/Cu/Co/NiFe pseudo spin valve with a nano-oxide layer after annealing treatment has also been studied. Its roll-off frequency increases from 345 to 465 kHz, and the effective capacitance decreases from 21.8 to11.8 nF as the annealing temperature increases from RT to 200oC. We can utilize the equivalent capacitor circuit to explain the NOL behavior with annealing temperature. This study shows that impedance analysis is a useful technique, and its nondestructive measurement should be more widely appreciated.