The first intrinsic two dimensional ferromagnets were discovered in 2017, so I think it’s safe to say that our field hasn’t yet come particularly close to identifying all possible two dimensional magnets. It’s hard to do an accurate accounting of all of the so-far discovered two dimensional magnets, and it is certainly the case that many of these are are not Chern magnets. But of the two dimensional magnets we have found, a surprisingly large fraction are intrinsic Chern magnets. We know of eight intrinsic Chern magnets stable in the absence of an applied magnetic field in the published literature so far. These are presented, along with a few of their basic properties, in Table 8.1. We have discussed several of these materials in this thesis, but we have also skipped a few,including the only currently known intrinsic Chern magnet in an atomic crystal, i.e., not on a moir´e superlattice: MnBi2Te4. These other materials all also represent areas of active research. Of the Chern magnets we know about, 2/8 have C < 0 with B > 0, so that property might be quite common. Indeed, there’s no particular reason to expect the B > 0 ground state to have one sign of the Chern number over the other as far as I know. It’s worth mentioning that if we ever find one, a room temperature Chern magnet with C < 0 for B > 0 would also have extremely large ∆m, large pots plastic and will therefore likely be switchable, since ∆m increases linearly with EGap.
It is also the case that two of these materials have been observed to be switchable with pulses of electric current, although it is not yet clear if the tBLG/hBN and ABMoTe2/WSe2 Chern magnets share a common current-switching mechanism, or if their respective mechanisms would generalize well to large gap Chern magnets. I think it’s clear that we are in the early days of the study of this class of material systems, and without discovering more Chern magnets there is little we can say with much generality. All of this is to say that I don’t think it’s crazy to expect to discover Chern magnets at much higher energy scales than we have already encountered, and that should we ever find such a system, there are a variety of intriguing technological applications for which this class of material systems could be exploited. I have put some effort into making this thesis a self-contained explanation of the background, details, and impact of the instrumentation and research work I participated in during my PhD. More can always be said, of course, and there exist a few articles targeted at a general physics audience discussing these discoveries in the context of the field written by other authors. They are referenced at the end of the Curriculum Vitae at the beginning of this thesis, and they are worth reading if you are interested in more of the details of these experiments and their implications for the field. Chern magnets were predicted to exist in the 1980s and realized for the first time in the form of doped topological insulators in 2013.
The first intrinsic Chern magnets were discovered in 2018. I hope I’ve convinced the reader that there are reasons to study this class of materials beyond a simple desire to catalogue all possible phases of matter. The phenomenology of intrinsic Chern magnets turned out to be very rich and may one day add something to a wide variety of electronic technologies, including low dissipation, electronically switchable magnetic memories and electronic metrology. Over the course of my PhD, four nanoSQUID microscopes were proposed, and construction began in some form on all of them. By the time I left we had finished three of these microscopes. The first nanoSQUID microscope we completed was inserted into a bath of liquid helium and could operate at 4 K. The CrI3 magnetic imaging campaign was performed in this system. The second nanoSQUID microscope had a pumped He-4 evaporative cooling pot, and could reach temperatures of 1.5 K. The tBLG/hBN Chern magnet transport measurements, the tBLG/hBN Chern magnet imaging measurements, and the AB-MoTe2/WeSe2 Chern magnet imaging measurements were all performed in this system. The third nanoSQUID microscope had a closed cycle He-3 sorption pump cooling system, and could reach 300 mK. The fourth and final microscope remains under construction, and is designed to operate inside of a dilution refrigerator. Pictures of several of these microscopes are shown in Fig. 8.6. Acoustic isolation chambers and the 300 mK system are not shown. All nanoSQUIDs have liquid He-4 baths for primary stage cooling, and all are mounted on several thousand pound vibration isolation tables floating on air legs to protect the nanoSQUID sensors from mechanical and acoustic shocks close to the surface.
The nanoSQUID sensor circuit is fairly simple, with only one important non-standard circuit element in it, other than the nanoSQUID itself of course. This is the series SQUID array amplifier. Current is forced into the nanoSQUID sensor in parallel with a shunt resistor of comparable resistance to the nanoSQUID sensor in the voltage state, which is generally a few Ohms. Current through the nanoSQUID side of the circuit is inductively coupled to a series of identical SQUIDs. These SQUIDs in series generate a large voltage, which is detected at room temperature. Current is forced through a feedback coil to maintain constant flux through the SQUIDs in series. This allows the circuit to maintain sensitivity over a wide range of currents . 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, square planter pots 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, 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 thanscanning 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. This facilitates thermal transport between the nanoSQUID sensor and the sample. 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. The GDSII patterns for these QR codes were generated procedurally using the GDSPy python package, and all of the associated software is available on Github, including a few different QR code designs, here: https://github.com/afylab/QR-Code-Generator. 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 wirebonding. 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.