4. Results 69
4.2. Temperatures in the MTJs
During the laser irradiation a temperature difference is generated across the MgO barrier of the MTJs. Additionally, the base temperature rises.
COMSOL simulations are performed to estimate the size of both effects. An introduction to this method was given in Sec. 3.4. In this section the results of the simulations are presented. For the simulations the MTJ sizes, the laser spot size and the laser power are chosen according to the values used in the experiments. Furthermore, the influence of the size of the laser spot on the temperature profile in the MTJs is investigated.
4.2.1. Heusler compound MTJs
For the simulations of the temperature evolution upon heating in the Heusler compound based MTJs, a round MTJ of 3µm in diameter is assumed. The laser spot is modeled as a Gaussian beam with a beam waist of 5µm. This value equals the experimentally determined beam diameter of 10µm. For the laser with a power of 150 mW, a power of 120 mW is measured at the position of the sample. Hence, this value is used in the simulations.
Fig. 4.2 displays the results of the COMSOL simulations for the Co2FeAl and Co2FeSi based MTJs. In Fig. 4.2a it can be seen that a temperature gradient is generated across the barrier of the MTJ, pointing from the bottom Heusler electrode (lower temperature) to the top electrode. The gradient
MgO 352.0
351.6 351.2 350.8
Temperature (K)
-4 -2 0 2 4
Position (nm) Co2FeAl Co2FeSi
∆T=390mK
400 300 200 100 0
∆T (mK)
120 80 40 0
Laser power (mW)
353.0 MgO 352.0 351.0 350.0
Temperature (K)
-60 -40 -20 0 20 40 Position (nm) Co2FeAl
Co2FeSi 340
320 Temperature (K) 300
120 80 40 0
Laser power (mW) top
bottom a
b
c
d
Figure 4.2. Simulated temperature gradients in the Heusler based MTJs: a∆T across the 2 nm MgO barrier at 150 mW laser power.bTemperature evolution over the whole layer stacks. cDependence of∆T in the Co2FeAl based MTJs on the applied laser power.dIncrease of the base temperatureT with laser power for the Co2FeAl based MTJs.
across the insulating barrier is much steeper than the gradient generated in the metallic electrodes. This gradient over the barrier is the driving force for the Seebeck induced tunneling of electrons across the electrodes and enters the Landauer model in Eq. 2.9 as∆T. This gradient is also used to calcu-late the Seebeck coefficients from the experimentally determined Seebeck voltages. This is in accordance with other TMS experiments performed by Walteret al.[4]and Liebinget al.[5,20]. The obtained gradients amount to a
∆T of 390 mK for the laser set to a power of 150 mW for both Heusler based MTJ types.
However, if the temperature change at all interfaces, i.e., over all layers of the MTJ (Fig. 4.2b), is considered, a second much larger gradient is
observed in the Co2FeSi based MTJs. This gradient is attributed to the Mn-Ir pinning layer. Mn-Ir has a much lower heat conductivity than the surrounding layers (cf. Tab. 3.1), and hence, supports the generation of a temperature gradient. For the Co2FeAl based MTJs that do not contain an Mn-Ir layer, no second gradient, that is equally steep as the gradient over the MgO barrier, is observed. The large second gradient in the Co2FeSi based MTJs makes it necessary to check if the determined voltage indeed is mostly generated by the temperature gradient across the MgO barrier, and not by the second gradient in the samples. This is done by breaking the MgO barrier and determining the remaining Seebeck voltage, as discussed in detail in Sec. 4.4.
For the Co2FeAl based MTJs simulations with different laser powers are performed (Figs.4.2c,d). The generated temperature gradients rise linearly with the laser power and range between 30 mK for the laser set to 10 mW and nearly 400 mK for the laser set to 150 mW. Also, the base temperatures for different laser powers rise linearly from room temperature to approximately 350 K at 150 mW laser power. Since the temperature increases linearly with the applied laser power, a linear increase of the Seebeck voltage with laser power is expected. However, due to the simultaneous rise of the base temperature, it is possible to observe the temperature dependence of the Seebeck coefficients. This dependence might lead to a deviation of the Seebeck voltage from the expected ideal linear behavior.
4.2.2. Co-Fe-B based MTJs
The simulation of the temperature gradient in the Co-Fe-B based MTJs, in which the TMS effect under applied bias voltage is investigated, are performed with a spot diameter of 20µm and the laser power set to 150 mW.
The elliptical MTJ has a size of 6µm×4µm. The obtained results exhibit a rise of the base temperature from room temperature (293 K) to 306 K when the laser power is set to 150 mW. Simultaneously, a temperature gradient of 11 mK is generated across the 1.5 nm thick MgO barrier. The calculated value is much smaller than in the Heusler compound MTJs. This is owed to the larger beam diameter, the increased MTJ size and the decreased barrier thickness.
800 600 400
∆T (mK) 200
40 30 20 10
Beam diameter (µm)
380 360 340 320
Base temperature (K)
40 30 20 10
Beam diameter (µm)
a b
Figure 4.3. Dependence of the temperatures on the beam size in the Co2FeAl based MTJs: aThe temperature difference across the MgO barrier. bThe base temperature in the center of the MgO barrier. The simulations are performed for the laser set to a power of 150 mW.
4.2.3. Dependence on laser spot diameter
For the Co2FeAl based MTJs simulations of the temperatures with different sizes of the laser spot have been conducted (Fig. 4.3). The smallest diameter is chosen to be 4µm and the largest to be 40µm. Within this range, a significant drop of the temperature difference across the MgO barrier from
∆T =800 mK for the smallest beam size to 50 mK for the largest beam is obtained. Simultaneously, the base temperature decreases from 390 K to 310 K.
These results reveal how drastically the size of the laser spot influences the Seebeck effect measurements. Hence, the beam size has to be carefully checked before or after each measurement by the knife edge method as described in Sec. 3.1.1.