Parameter space for thermal spin transfer torque
5.1 Bias voltage dependence of the tunnel magneto-Seebeck effect
5.1.4 First results
Prior to the evaluation of the thermocurrent measurements, the bias dependent TMR measurements have to be analyzed. Fig. 5.4a shows two series of TMR mea-surements that were performed at a variety of bias voltages on a 6 µm ×4 µm
- 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0
468
1 0 1 2 1 4 1 6 1 8
R (kΩ)
B ( m T )
s e r i e s 1 s e r i e s 2
- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0
8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0
TMR (%) U b i a s ( m V )
s e r i e s 1 s e r i e s 2
a b
Figure 5.4: Dependence of TMR ratio on bias voltage. a, TMR measurements performed at different bias voltages. The resistance of parallel magnetization align-ment is found to be constant,RP ≈6 kΩ. b, TMR ratios calculated from the curves shown in a as function of bias voltage. No clear dependence on the bias voltage can be identified.
64
5.1 Bias voltage dependence of the tunnel magneto-Seebeck effect
- 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0
- 1 0 - 8 - 6 - 4 - 2
02468
1 0 1 2 1 4 1 6
Current (nA)
B ( m T )
V = + 5 0 m V V = + 1 0 m V V = 0 m V V = - 1 0 m V V = - 5 0 m V
Figure 5.5: Thermocurrent measurements at different bias voltages. Measure-ments at selected voltages between −50 mV and 50 mV are depicted. The current signal is detected by the lock-in amplifier at the laser heating modulation frequency of 1.5 kHz.
elliptical MTJ. The curves indicate several switching fields at which the magneti-zation alignment changes from antiparallel back to parallel. A possible reason for this behavior is the existence of several magnetic domains in the two ferromagnetic layers of the MTJ. All curves have a resistance RP≈ 6 kΩ for the parallel magne-tization state in common. The TMR ratios calculated from these curves are shown in Fig. 5.4b as a function of bias voltage. It can be seen that the TMR ratios are distributed randomly between 170 % and 90 % and that no clear dependence on the applied bias voltage can be identified. A possible reason for this broad distri-bution is the above mentioned multi-domain switching behavior of this MTJ. For this reason, an average TMR ratio of 145 % is used for further analysis. Given this TMR ratio and a resistance of 6 kW in the parallel state, the average resistance in antiparallel state becomes RAP≈14.7 kΩ.
A selection of thermocurrent measurements is shown in Fig. 5.5. The lock-in amplifier was triggered such that the thermocurrent signal appears at the X (in-phase) input of the lock-in amplifier. Thus, a positive current leads to a positive X signal and vice versa. Further, to obtain the curves plotted in Fig. 5.5, the voltages measured by the lock-in amplifier were converted to currents through division by the transimpedance gain of the preamplifier. A test without laser heating and a DC bias voltage of up to 300 mV revealed only a negligible current signal around 0.03 nA. This verifies that only currents caused by the laser heating are detected.
65
Chapter 5 Outlook
At 50 mV bias voltage, a positive thermocurrent is observed. The current is larger for antiparallel magnetization alignment of the electrodes. The same situation—
with a smaller difference between the voltages in parallel and antiparallel state—is observed at 10 mV, whereas the thermocurrent is larger in parallel state when the measurement is performed without bias voltage. At −10 mV, the thermocurrent for parallel alignment is almost shifted to zero and a negative current is observed in antiparallel state. Finally, at −50 mV bias voltage, negative thermocurrents are observed for both magnetization alignments, of which the magnitude is larger for the antiparallel configuration.
The Seebeck voltages generated during laser heating can be derived from the thermocurrent measurements presented in Fig. 5.5 and the TMR measurements depicted in Fig. 5.4. According to eq. (3.1) in section 3.4.1, the current I is given by
I =GV +GS∆T.
The Seebeck voltage (S∆T) thus becomes in general:
S∆T = 1
GI−V.
Due to the measurement technique, the DC bias voltage V is not detected in the thermocurrent measurements. In addition, substituting the conductance G with the resistance RP/AP of the two magnetization alignments, yields a relation that connects the thermocurrents and resistances found in parallel and antiparallel state to the respective Seebeck voltages:
(S∆T)P/AP =RP/APIP/AP. (5.5) The data in Fig. 5.6a are calculated from thermocurrent and TMR measurements using eq. (5.5). On the larger voltage scale up to ±200 mV, the Seebeck voltages depend linearly on the applied bias voltage. Both slopes, for parallel and antipar-allel magnetization configuration, are positive, whereupon the magnitude of the slope is larger for the latter configuration. For small bias voltages below 10 mV, the behavior of the Seebeck voltages exhibits more structure (inset of Fig. 5.6a): The voltages in parallel and antiparallel state are almost equal and nearly constant for bias voltages between 0 mV and 5 mV. Similarly, the voltages are also nearly con-stant between 0 mV and −5 mV, yet the difference between the Seebeck voltages observed in parallel and antiparallel state is large. At bias voltages higher than
±5 mV, the linear behavior starts to develop.
The different slopes of the Seebeck voltages lead to negative TMS ratios for positive bias voltages that decrease in magnitude when the bias voltage approaches zero. Between 0 mV and −10 mV the sign of the TMS ratio changes and due to the zero crossing of the parallel state Seebeck voltage at approximately −10 mV, a TMS ratio of 7000 % is obtained. With further increasing bias voltages, the TMS ratio drops again to a nearly constant value of 250 %.
66
5.1 Bias voltage dependence of the tunnel magneto-Seebeck effect
- 6 0 0 - 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0
0
1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0
S∆T (µV)
S∆T (µV)
P s t a t e A P s t a t e
- 1 0 0 1 0 - 6 0- 4 0- 2 002 04 06 0 V b i a s ( m V )
- 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 5 0 1 0 0 1 5 0 2 0 0
- 1 0 0 0 - 5 0 0
0
5 0 0 1 0 0 0 6 0 0 0 7 0 0 0
a b
TMS (%) V b i a s ( m V )Figure 5.6: Bias voltage dependence of the TMS effect. a, Seebeck voltages extracted from thermocurrent and TMR measurements at different bias voltages.
b, TMS ratio calculated from the Seebeck voltages shown above.
5.1.5 Discussion
The observations made in this experiment deviate from the theoretical predictions for different Co-Fe alloys introduced at the beginning of section 5.1. The ab initio calculations predict that the change of Fe content from x = 0 to x = 1 in a
67
Chapter 5 Outlook
FexCo1−xalloy leads to shifts of several hundred meV of features in the transmission function (Fig. 4 in ref. [52]). This energy range is also covered by the bias voltage measurements presented here. However, whereas the Seebeck voltages were found to be linearly dependent on the applied bias voltage, the calculations predict a rather oscillatory behavior of the Seebeck coefficients as a function of alloy composition.
On the other hand, the Co-Fe composition used in the experiment is close to x= 0.7 in Fig. 5.1. Close to this composition, the calculations also predict a linear behavior of the Seebeck coefficients. The slopes are positive, in the experiment as well as in the ab initio calculations.
Furthermore, the changes in Seebeck coefficients caused by modifications of the alloy composition cannot be compared directly to the bias voltage dependent mea-surements. Although both methods lead to shifts of the Fermi level in the fer-romagnetic electrodes of the MTJ, the application of a bias voltage changes only the Fermi level of one electrode, whereas a change of alloy composition in both electrodes also leads to a shift in Fermi level in the two.
As a consequence, further ab initiocalculations are currently underway that will allow a direct comparison between theory and experiment. On the experimental side, further measurement series have to be carried out to improve the experimen-tal statistics. These experiments should include power dependent measurements performed at each bias voltage to obtain a qualitative insight into the temperature dependence of the Seebeck coefficients (similar to Fig. 5.2).
The most interesting outcome of this measurement series is that a bias voltage can be used in the experiment to tailor the response of the Seebeck voltage, both in voltage sign and magnitude. Especially the measurement at −10 mV, in which the Seebeck voltage is close to zero for parallel alignment, presents the possibility of building a thermoelectric device that can be magnetically turned on and off.