Presentación de resultados

First the heat capacity under magnetic field was investigated in order to establish the addenda contribution. Here two of the measurement methods described in chapter 3 were used - the relaxation time as well as the AC heating method.

Figure 4.17 (a) shows an example measurement for the relaxation time method at 410 mK and a magnetic field of 4 T. Here the temperature change of the sample relative to the temperature at time t0 = 0 is plotted as a function of time. At t0 an

AC current of 0.85µA and a frequency of 100 Hz is applied to the heater. With a resistance of 4.995 kΩ this results in a power dissipation of 3.6 nW. This causes the sample to heat up by 12 mK. The green line marks the range over which the average temperature before the heating step was measured. The red curve is an exponential fit to the data at time above t0. From this one extracts a time constant τ, typical for

all measurements presented, of τ = 6.3 s. As described earlier the temperature step ∆T in combination with the applied heat power ˙Q gives the thermal conductance k

between the sample platform and the thermal bath as k = ˙Q/∆T. One therefore can

20

This corresponds roughly to 1.11x10−4

0 1 2 3 4 5 6 7 T=410mK Time [s] D T [mK] Time [s] T emperature[mK] 420 410 400 0 20 40 0 40 80 0 4 8 12 Temperature [K] C/T [ J/K ] m 2 0 1 (a) (b) (c)

Figure 4.17: Figure (a) shows the temperature difference ∆T of the sample and addenda as a function of time for a typical relaxation time measurement. From time t= 0 continuous heating is applied to the setup. The green line shows the fit through the data in order to establish the initial temperature whereas the red curve is an exponential fit to the data to times abovet= 0. Figure (b) shows an analysis step for the AC measurement method. Here in blue the temperature of the setups is shown as a function of time while AC heating is applied and the temperature of the thermal bath is slowly lowered. The red curve shows a fit to the data as explained in the text. Figure c finally shows the result for the heat capacity divided by temperature as a function of temperature for both the relaxation time method (blue) and the AC method (red) (further details are given in the text). The black curve gives the expected heat capacity of the sample according to literature values [58].

calculate the total heat capacity of the setupC asC =kτ withτ. This has been done for a range of 11 temperatures between 200 mK and 1.2 K. At each temperature the procedure was carried out ten times and the results averaged. The heat capacity C

divided by temperatureT obtained this way is shown in blue in figure 4.17 (c). The second method used is the AC heating method. Figure 4.17 (b) shows in blue the temperature trace of the sample while a continuous 40 mHz AC current is applied. The AC measurement starts at a thermal bath temperature of 1.2 K with a current of 4.25µA. During the experiment both the temperature of the thermal bath and the current are lowered linearly at an approximate rate of 3.9 mK/min and 2.7 nA/min respectively until base temperature is reached. This causes sinusoidal temperature os- cillations as a function of time on the background of a linearly decreasing temperature, as shown in the data presented. The frequencyf of these oscillations is twice the exci- tation frequency orf = 80 mHz. The amplitude A of the oscillations is extracted from the data by fitting the temperature signal over time intervals of 45 s with a function of the form

T(t) =T0+at+Asin (2πf +φ0) , (4.6)

0 1 2 0 0.5 1.0 1.5 TemperatureT[K] CT / [ J/K ] m 2 TemperatureT[K] D m CT / [ J/K ] 2 0 0.5 1.0 0 0.2 0.4 0.6 -0.2 (a) (b) 4T 14T (A) (B) (C)

Figure 4.18: (a) The addenda contribution to the measured heat capacity as a function of temperature for two different magnetic fields as indicated. The expected features of a Schottky anomaly (A), the thermometer (B) and the contribution from amorphous materials (C) are clearly identifiable. (b) The difference in addenda contribution between 14 T and 4 T. This shows that only the Schottky anomaly is field dependent. The red curve is a fit through the data.

in red. As was discussed in the previous chapter the heat capacity C of the sample is then proportional to the inverse of the amplitude A−1

In figure 4.17 (c) the heat capacityCof the setup divided by temperatureT is shown as a function of temperature as obtained by the relaxation time (blue) and AC heating method (red)21_{. The black curve represents the heat capacity divided by temperature}

of the Sr2RuO4 sample as calculated from literature values. The difference between

these is the heat capacity of the addenda. It is plotted in figure 4.18 (a) together with the background contribution to the heat capacity at 14 T. Here one can identify three characteristic features labelled (A), (B) and (C). As discussed in section 4.2.5 these can be attributed to a Schottky anomaly (A), the thermometer(B) and a contribution from amorphous materials (C).

The high temperature addenda contribution Cadd/T for both 4 T and 14 T is quasi identical whereas at low temperatures they deviate. Figure 4.18 (b) shows the difference ∆C(T) = Cadd,4T/T −Cadd,14T/T between these two curves together with a fit of the

form ∆C(T) =a/(T2_{) which corresponds to the expected functional form of the change}

in a magnetic Schottky contribution to the heat capacity between different magnetic fields. Since the fit is a very good representation of the data, it is concluded that the heat capacity of the addenda is independent of magnetic field besides a Schottky

21

As described in 3 the AC heating method though having a better relative accuracy than the relaxation time method tends to systematically overestimate the heat capacity for several reason such as finite sample dimensions. Here a multiplicative correction factor of 0.95 has been applied in order to minimise the mean square deviation of the AC heating data from the more absolute accurate relaxation time measurement.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 TemperatureT[K] CT / [J/Ru-molK ] 2

Figure 4.19: Here the measured heat capac- ity of the sample in zero field (blue) is com- pared with the literature data (red) [57]. In green and black the specific heat at 4 T and 14 T is given for comparison.

contribution. This is a significant finding since it shows that the entropy of the addenda above the characteristic onset of the Schottky anomaly at 250 mK can be considered constant. Therefore, any measured entropy changes in the magnetocaloric experiments presented in chapter 5 have to come from the sample.

Compared to the absolute value estimated in section 4.2.5 the field independent contribution is a factor 1.5 to 2 larger. Taking into account the uncertainties in the theoretical estimate this can be considered as a good agreement, in particular since they agree qualitatively.