Incorporate feedback into sample CP2.

chapters/samples/CP2.6B/fabrication.tex

@@ -1,5 +1,5 @@
 % !TEX root = ../../../thesis.tex
-We followed the method outlined in Section~\ref{sec:method-sample-fabrication}. However, in addition to the \ce{Nb} and \ce{Au}, we first sputter a layer of \ce{Cu}. This allows us to make superconductor-normal-superconductor (SNS) junctions. Additionally we used a \ce{SiO} wafer. We again used the FIB to create the fine structures, see Figure~\ref{fig:CP2.6B-SEM-images}. Contrary to the first sample we decided to use a square geometry instead of a circular one. This improves the coupling between the junction loop and the dc-SQUID.
+We followed the method outlined in Section~\ref{sec:method-sample-fabrication}. However, in addition to the \ce{Nb} and \ce{Au}, we first sputter a layer of \ce{Cu}. This allows us to make superconductor-normal-superconductor (SNS) junctions. Additionally we used a \ce{Si} wafer with a \qty{300}{\nano\meter} thermal oxide layer. Figure~\ref{fig:CP2.6B-SEM-images} shows the fine structures created using the the FIB. Contrary to the first sample we decided to use a square geometry instead of a circular one. This improves the coupling between the junction loop and the dc-SQUID.
 
 \begin{figure}[ht!]
 	\begin{subfigure}[t]{0.3\textwidth}

chapters/samples/CP2.6B/main.tex

@@ -1,5 +1,5 @@
 % !TEX root = ../../../thesis.tex
-This sample's goal was to fix the shortcomings we noticed in our first sample. The first thing we want to improve is the dc-SQUID sensitivity. To do so we intend to use SNS junctions instead of constriction junctions. We have chosen for SNS junctions because they have been used before in our group and yielded good results\cite{rogSQUIDontipMagneticMicroscopy2022}. Furthermore, in order to decrease the chance of shorts we use a \ce{SiO} wafer instead of \ce{Si}. Additionally, to improve the coupling between the dc-SQUID and the junction loop we used a square geometry instead of a circular one. 
+This sample's goal was to fix the shortcomings we noticed in our first sample. The first thing we want to improve is the dc-SQUID sensitivity. To do so we intend to use SNS junctions instead of constriction junctions. We have chosen for SNS junctions because they have been used before in our group and yielded good results\cite{rogSQUIDontipMagneticMicroscopy2022}. Furthermore, in order to decrease the chance of shorts we use a \ce{Si} with a thermal oxide on top. Additionally, to improve the coupling between the dc-SQUID and the junction loop we used a square geometry instead of a circular one. 
 
 \subsection{Fabrication}
 \input{chapters/samples/CP2.6B/fabrication}

chapters/samples/CP2.6B/results.tex

@@ -1,5 +1,5 @@
 % !TEX root = ../../../thesis.tex
-We measured two RT-curves for the junction loop and dc-SQUID. See Figure~\ref{fig:CP2.6B_RT_curves}. We note that the critical temperature for the bulk of the sample is lower (\qty{7}{\kelvin}) compared to the first sample (\qty{8}{\kelvin}). This can be explained by the proximity effect due to the interface between the \ce{Cu} and \ce{Nb}\cite{cirilloSuperconductingProximityEffect2005}. The longer `tail' is characteristic for SNS junctions \textbf{sauce?}. The small increase in the resistance of the dc-SQUID before the transition is explained by \textbf{cause}.
+Figure~\ref{fig:CP2.6B_RT_curves} shows the RT-curves for the junction loop and dc-SQUID. We note that the critical temperature for the bulk of the sample is lower (\qty{7}{\kelvin}) compared to the first sample (\qty{8}{\kelvin}). This can be explained by the proximity effect due to the interface between the \ce{Cu} and \ce{Nb}\cite{cirilloSuperconductingProximityEffect2005}. The longer `tail' is characteristic for SNS junctions \textbf{sauce?}. The small increase in the resistance of the dc-SQUID before the transition is explained by \textbf{cause}.
 
 \begin{figure}[ht!]
 	\centering
@@ -8,7 +8,7 @@
 	\label{fig:CP2.6B_RT_curves}
 \end{figure}
 
-Additionally we measured the interference pattern of the dc-SQUID using constant bias currents. See Figure~\ref{fig:CP2.6B_SQUID_calibration_curves}. We note that the periodicity in the the data is roughly \qty{1}{\milli\tesla}. This matches the expected period. We furthermore note that the sensitivity in the linear regime increased by a factor 3 compared to the previous sample. The comparison is a bit unfair as this is at a bias current that is also 3 times larger. In the previous sample however, such a large bias current was simply not possible. We note two issues in these curves. First off, the period of the pattern does not seem to be constant. Secondly, the offset (in the field axis) varies a lot between curves whilst they should all be zero. The first issue might, partially, be explained by the dead band of \qty{0.05}{\milli\tesla} of the magnet\footnote{For these measurements we used the PPMS cryostat. The magnet in this cryostat does not support persistent mode but instead uses some feedback loop. This feedback loop only corrects the field however when it deviates roughly \qty{0.05}{\milli\tesla} from its set point.}. The offset changes can be explained by vortices getting trapped in either our sample or the magnet. This would cause small residual fields.
+Figure~\ref{fig:CP2.6B_SQUID_calibration_curves} shows the interference pattern of the dc-SQUID for several bias currents. We note that the periodicity in the the data is roughly \qty{1}{\milli\tesla}. This matches the expected period. We furthermore note that the sensitivity in the linear regime increased by a factor 3 compared to the previous sample. The comparison is a bit unfair as this is at a bias current that is also 3 times larger. In the previous sample however, such a large bias current was simply not possible. We note two issues in these curves. First off, the period of the pattern does not seem to be constant. Secondly, the offset (in the field axis) varies a lot between curves whilst they should all be zero. Both these issues can be explained by vortices getting trapped in the magnet or sample. 
 
 \begin{figure}[ht!]
 	\centering
@@ -17,9 +17,18 @@
 	\label{fig:CP2.6B_SQUID_calibration_curves}
 \end{figure}
 
-In an attempt to fix the `noise' caused by the feedback loop, we turned off the magnet. Unfortunately, it never turned back on as the magnet controller was apparently broken. A downside of this, is that we were also no longer able to read out the value of the field. Since we had no magnetic field any more, the most reasonable measurement to perform was measuring the CPR. We did so by using a constant bias of \qty{380}{\micro\ampere} for the dc-SQUID, sweeping a current through the junction loop and then measuring the voltage over the dc-SQUID. It should be mentioned that during these measurements there appeared to be a lot of drift causing measurement to differ widely. We suspect that an external magnetic field was responsible for this. 
+When we attempted to measure the CPR we noted weird spikes in the IV-curves. We initially attributed this to vortex trapping. However, upon closer inspection these jumps are highly correlated with the actual magnetic field produced by the magnet. Figure~\ref{fig:CP2.6B_PPMS_magnetic_field_drift} shows a clear correlation between the dc-SQUID voltage and the magnetic field as measured by the magnet. Even though we have a constant setpoint of \qty{0}{\milli\tesla} we see quite some drift. This is because the magnet does not have a persistent mode but instead uses a feedback loop. This feedback loop has a dead band of \qty{50}{\micro\tesla}. Changing the setpoint of the field or the rate of change did not affect the effect significantly.
 
-In Figure~\ref{fig:CP2.6B_SQUID_voltage_over_total_current} we see the raw data from one of the CPR measurements. We note a clear periodicity in the signal of around \qty{200}{\micro\ampere} and a somewhat linear trend on top of that. We present this specific measurement because it has no jumps in the dc-SQUID voltage, has a sufficiently small sample spacing, covers a wide enough range to see several periods and measured both positive and negative currents. Different sample spacings did not affect measured periodicity. For transparency we have included a few other data sets in Appendix~\ref{app:CP2.6B-data}.
+\begin{figure}[ht!]
+	\centering
+	\input{figures/samples/CP2/CP2.6B_PPMS_magnetic_field_drift_0mT_rate_200uT.pgf}
+	\caption{Correlation between the actual magnetic field of the cryostat and the voltage measured over the dc-SQUID. The setpoint of the magnetic field is \qty{0}{\milli\tesla} and a change rate of \qty{200}{\micro\tesla\per\second}. The standard deviation from the setpoint is \qty{30}{\micro\tesla}.}
+	\label{fig:CP2.6B_PPMS_magnetic_field_drift}
+\end{figure}
+
+In an attempt to fix the `noise' caused by the feedback loop, we turned off the magnet. Unfortunately, it never turned back on as the magnet controller was broken. A downside of this, is that we were also no longer able to read out the value of the field. We decided to perform a CPR measurement again by using a constant bias of \qty{380}{\micro\ampere} for the dc-SQUID, sweeping a current through the junction loop and then measuring the voltage over the dc-SQUID. It should be mentioned that during these measurements there appeared to be a lot of drift causing measurement to differ widely. We suspect that an external magnetic field was responsible for this. 
+
+Figure~\ref{fig:CP2.6B_SQUID_voltage_over_total_current} shows the raw data from one of the CPR measurements. We note a clear periodicity in the signal of around \qty{200}{\micro\ampere} and a somewhat linear trend on top of that. We present this specific measurement because it has no jumps in the dc-SQUID voltage, has a sufficiently small sample spacing, covers a wide enough range to see several periods and measured both positive and negative currents. Different sample spacings did not affect measured periodicity. For transparency we have included a few other data sets in Appendix~\ref{app:CP2.6B-data}.
 
 \begin{figure}[ht!]
 	\centering
@@ -28,7 +37,7 @@
 	\label{fig:CP2.6B_SQUID_voltage_over_total_current}
 \end{figure}
 
-Using the second calibration curve for \qty{380}{\micro\ampere} bias current we converted the dc-SQUID voltage to a flux. We have chosen to set the horizontal offset of this calibration to zero as there should be barely any background field. The difference in the two calibration curves also highlights that the horizontal offset was difficult to reproduce. The linear trend in the dc-SQUID's flux is the mutual inductance. By using a linear fit we can extract it and determine the current through the loop. Using this method we find the experimental mutual inductance to be \qty{-0.339\pm0.005}{\pico\henry}. This value is almost twice as large as the simulated value found in Table~\ref{tab:CP2.6B-geometries}. Similarly, we can determine the junction loop inductance by exploiting the fact that the periodicity must be $\Phi_0$ periodic. We find the inductance of the junction loop to be \qty{6\pm1}{\pico\henry}. This is twice the simulated value found in Table~\ref{tab:CP2.6B-geometries}.
+Using the second calibration curve for \qty{380}{\micro\ampere} bias current we converted the dc-SQUID voltage to a flux. We have chosen to set the horizontal offset of this calibration to zero as there should be barely any background field. The difference in the two calibration curves also highlights that the horizontal offset was difficult to reproduce. The linear trend in the dc-SQUID's flux is the mutual inductance. A linear fit determined the the mutual inductance to be \qty{-0.339\pm0.005}{\pico\henry}. This value is almost twice as large as the simulated value found in Table~\ref{tab:CP2.6B-geometries}. Similarly, we can determine the junction loop inductance by exploiting the fact that the periodicity must be $\Phi_0$ periodic. We find the inductance of the junction loop to be \qty{6\pm1}{\pico\henry}. This is twice the simulated value found in Table~\ref{tab:CP2.6B-geometries}.
 
 \begin{figure}[ht!]
 	\centering