This current amplification circuit has good current sensitivity and enormous dynamics range, easily able to accommodate the several hundred µA necessary to reach the critical current of the nanoSQUID sensor.There are a lot of things that make scanning probe microscopy tough relative to other techniques for performing microscopy. One particularly challenging issue is navigation of the sensor to the sample. Those experienced with optical imaging might be spoiled by a contrast mechanism that is sensitive to a ton of different phenomena- the nanoSQUID can only see local gradients in magnetic field and temperature, and those are rare unless you have intentionally built structures and devices that generate them for use in navigation. In particular, large thermal gradients and variations in local magnetic field aren’t general properties of surfaces, so it’s very easy to blunder a nanoSQUID sensor into a surface without ever seeing it coming! Experiments are thus much safer and more expedient if we can provide the nanoSQUID sensor with topographic feedback- i.e., some way of detecting surfaces without crashing into them and destroying the sensor. We did this using shear force microscopy, procona valencia which is a form of atomic force microscopy, or AFM.

There is nothing particularly atomic about this contrast mechanism in the nanoSQUID microscope- we don’t have nearly that much resolution- but it is incredibly useful for navigation because it allows us to safely and reliably detect surfaces without destroying the SQUID. Researchers and companies building scanning tunneling microscopes will often accomplish this by gluing their sensor, which is a microscopic metallic wire, onto a piezoelectric tuning fork and then exciting the tuning fork at its resonant frequency. This is a good strategy, but it must be modified for use with the nanoSQUID sensor, because the nanoSQUID sensor is considerably more massive than scanning tunneling microscope wires, so it cannot be glued onto the tuning fork without destroying its quality factor. We preserve the tuning fork’s quality factor by instead pressing a piezoelectric tuning fork against the side of the nanoSQUID sensor and performing shear force microscopy instead of tapping mode microscopy. The glass micropipettes serving as substrates for the nanoSQUID sensors are so thin that they bend easily when pressed agains the tuning fork, and this keeps them in mechanical contact with the fork. An optical microscope image of a nanoSQUID sensor pressed against a tuning fork is shown in Fig. 8.8A, and the resonant frequency of the piezoelectrically driven tuning fork is shown in Fig. 8.8B, with a fit to a Butterworth Van-Dyke model. A phase-locked loop and PID feedback system together allow us to approach the surface with the nanoSQUID sensor, detect it without crashing into it and destroying the tip, and maintain feedback while scanning. Schematics of this assembly are shown in Fig. 8.9.

A calibration of the scan range and height of the nanoSQUID AFM is shown in Fig. 8.10, with a comparison to a Bruker Icon AFM displayed as well. An image of these assemblies mounted on the microscope and ready to scan is provided in Fig. 8.11.By far the most common experimental campaign for the nanoSQUID microscope during my time in Andrea’s lab involved being handed a sample fabricated primarily for transport or capacitance measurements, with little consideration afforded to the viability or ease of a scanning probe microscopy campaign on the sample. I think this is fairly common in scanning probe microscopy, and it often means that we need to get sensors to samples without much in the way of navigation infrastructure. For this reason the vast majority of nanoSQUID microscopy campaigns start with thermal navigation. Before cooling down the nanoSQUID microscope, an attempt is made to align the nanoSQUID sensor with the heterostructure under an optical microscope, but the nanoSQUID sensor often still starts several hundred microns away from the sample. Once the system is cold, we generally proceed by injecting a few mBar of helium gas into the sample chamber. We then run an AC current through the sample, heating it and generating an AC temperature distribution. The nanoSQUID sensors are excellent thermometers as well as magnetometers, so we can use this thermal gradient to navigate to the sample.

An image of the resulting distribution of temperature over the device is shown in Fig. 8.13A. Some of the details are described in a later section, but in summary this technique works surprisingly well- we can usually find samples even several millimeters away from the nanoSQUID sensor using this technique. Once the nanoSQUID is reasonably close to the sample, it is usually necessary to pump out the heat exchange gas before attempting magnetic imaging, since thermal contrast can produce large backgrounds. After the heat exchange gas is removed, further navigation must proceed by imaging the magnetic fields produced by applied current through the Biot-Savart effect, as illustrated in Fig. 8.13B.Thermal navigation does not work for all systems. In the simplest case in which other techniques are necessary, current cannot be driven through magnetic insulators, so if you want to find them with the nanoSQUID you must arrange for some navigation technique other than flowing current through the sample. There are a variety of solutions to this problem, and perhaps the simplest is fabricating an additional device adjacent to the one you’d like to investigate and running current through that instead. There are reasons you might want to avoid this- some samples are so unstable in air and moisture that it makes sense to avoid photolithography on heterostructures entirely- and for these situations, I’m going to discuss ferromagnetic navigation. We start by generating a photolithography mask containing a large array of microscopic QR codes, as illustrated in Fig. 8.14A. These QR codes and the associated sample area with contact wires is shown in Fig. 8.14, and a chip with this pattern deposited onto it is shown in Fig. 8.14C, D. These patterns and wires are composed of 2 nm of Cr , 10-60 nm of permalloy, which is a nickel/iron alloy, and50 nm of Au, to prevent extensive oxidation of the permalloy and to facilitate electronic transport through the wires and easy wire bonding. NanoSQUID images of the magnetic field distributions above these patterns are shown in Fig. 8.14E, with line-by-line subtraction illustrating the visability of the QR code in Fig. 8.14F. Navigation of the nanoSQUID sensor to the chromium iodide flake was performed using these patterns, and an optical image of the scan region for that device is shown in Fig. 8.14G,H. The QR codes encode physical position in the plane in binary, as illustrated in Fig. 8.14I. They allow easy navigation to a sample without wires or thermal navigation, while simultaneously allowing the nanoSQUID sensor to stay a safe several microns away from the surface.The tuning fork is useful for safely approaching the surface of the sample, but it is also useful for performing high frequency measurements of distributions of magnetic field that are static in time. This is necessary for magnetic systems that aren’t gate- or current-tunable, but it is also necessary for systems that are metastable, and thus would decay into their ground states in response to density variations, flower bucket as in ferromagnetic hysteresis loops. This comes with some challenges, because it means that we must know the direction and magnitude of a in order to extract quantitative information from our datasets. This section will describe the method we use to determine a for a particular combination of tuning fork and nanoSQUID sensor. As illustrated in Fig. 8.15A, the nanoSQUID’s position is modulated at the resonant frequency of the tuning fork, which is generally between 30 and 36 kHz. A DC current is flowed through the sample in order to generate local variations in temperature around the device. The AC signal produced by the nanoSQUID at the modulation frequency of the tuning fork is measured. Both quadratures are shown in Fig. 8.15B,C. The signal is primarily in the Y quadrature because the tuning fork is driven at its resonant frequency.

A damped harmonic oscillator driven at its resonant frequency has its position precisely π 2 out of phase with its driving force, and the nanoSQUID signal is of course in phase with the position of the nanoSQUID, not the driving voltage. Small deviations from this relationship can be corrected, as shown in Fig. 8.15D. At the same time, the DC local thermal signal is collected using the nanoSQUID, as shown in Fig. 8.15E. Gradients of this data are extracted in each cardinal direction, as illustrated in Fig. 8.15F,G. A two parameter fit of the tuning fork data to these two gradients produces amplitudes of oscillation in the x and y directions . This gives us both the direction of tuning fork oscillation and the amplitude of its oscillation. We expect the amplitude to be linear in the driving force for a damped harmonic oscillator driven at its resonant frequency, and we can indeed see that this is the case by repeating this analysis for several different driving voltages .There are a few engineering challenges associated with fabricating nanoSQUID sensors. I will briefly describe a particularly challenging one in this section. Many of the best elemental superconductors are soft, heavy metals with low melting points like lead and indium. As any person who has spent some time in an experimental physics laboratory knows, solder doesn’t wet too many materials well, and it certainly doesn’t wet glass, so these metals tend to form droplets when deposited onto glass substrates. To form a uniform film, the superconducting metal must freeze instantly upon landing on the glass micropipette. To make sure this occurs, we must cryogencially cool the glass micropipettes while evaporating the superconducting metal onto them. This process involves specialized machinery that is covered in great depth in other documents and publications, so I won’t discuss it here. However, I do want to discuss the nature of the failure modes of this process. When liquids don’t wet surfaces well, they dewet into droplets, and these droplets tend to get more spherical and less film-like the worse they wet the surface. If this process is allowed to proceed to its conclusion before deposited metal solidifies, the resulting films won’t be connected at all, and your nanoSQUID circuit will be open. If the substrate is cold enough, the resulting film will at least be continuous, and it is likely that you will get a nanoSQUID. However, the formation of droplets is impossible to completely stop, especially near the edges of films and on the oblique surfaces of the nanoSQUID sensor . These droplets generally won’t short the sensor, but the nanoSQUID sensor is so small that electrons can reach these droplets through tunneling processes. Whenever droplets form between the two superconducting contacts on the nanoSQUID sensor electrons can tunnel between the contacts through the droplet, with the droplet functioning as a quantum dot. The resulting Coulomb blockade phenomenon gives nanoSQUID sensors a very slight electric field sensitivity. Gating exfoliated heterostructures tends to produce large electric fields, and these are detectable as variations in the current through the nanoSQUID as a result of Coulomb blockade in parallel with the SQUID on the tip. Droplets functioning as quantum dots and producing a parasitic Coulomb blockage are so common that we observe them on nearly every nanoSQUID sensor, and we almost always have finite electric field sensitivity . This can be useful for finding the edges of devices in the absence of magnetism, but it is important to remember that not all nanoSQUID signals can be understood as local magnetic fields. Other parasitic contrast mechanisms do exist, but they are rarely dominant over magnetic or electric field sensitivity. At high tuning fork amplitudes, interactions between the nanoSQUID tip and the surface can produce local variations in oscillation amplitude and appear as parasitic signals at the tuning fork frequency. Of course, the nanoSQUID is highly sensitive to local temperature, so systems with thermal gradients will generally have backgrounds associated with that. But by far the most important parasitic contrast mechanism in the nanoSQUID campaigns discussed here is electric field contrast through parasitic Coulomb blockade.The tip has been characterized and is a SQUID. Sensitivity is good enough that magnetic field noise is ≥25 nT/rtHz .