Our understanding of these magnetic phases is very far from complete, and we expect to encounter more surprises as our magnetic imaging campaign on this class of materials continues.The first systems with nonzero Chern numbers to be discovered were systems with quantum Hall effects. Quantum Hall insulators behave a lot like Chern magnets but are generally realized at much higher magnetic fields, and Berry curvature in these systems comes from the applied magnetic field, not from band structure. The fact that resistance in these materials is an intrinsic property and not an extrinsic one had implications for metrology that were immediately obvious to the earliest researchers that encountered the phenomenon. All of these devices have resistances that depend only on fundamental physical constants, so a resistance standard composed of these materials need not obey any particular geometric constraints, and can thus be easily replicated. The case for quantum Hall resistance standards was strong enough for the the National Institute for Standards and Technology to rapidly adopt them, and today the Ohm is defined by a graphene quantum Hall resistance standard at NIST.There are some downsides to the quantum Hall resistance standard. The modern voltage standard is a superconducting integrated circuit known as the Josephson voltage standard; it uses Shapiro steps to relate the absolute size of a set of voltage steps to a frequency standard.
Because the voltage standard and resistance standard are independently fixed to physical phenomena, cut flower transport bucket current standards are necessarily defined by the relationship between these two different standards. Unfortunately, the superconducting integrated circuits used as Josephson voltage standards must be operated in very low ambient magnetic field, because large magnetic fields destroy superconductivity. This makes them incompatible with the graphene quantum Hall resistance standard, which must operate in large magnetic fields, generally B > 5T. This is a surmountable problem- in practice it is handled by storing the two standards in different cryostats, or with significant magnetic shielding between them- but the significant distance separating the standards reduces the precision with which the current standard can be defined with respect to our current resistance and voltage standards. One possible way to resolve this conflict is to replace the quantum Hall resistance standard with a Chern magnet resistance standard. Chern magnets show quantized anomalous Hall effects at low or zero magnetic field, meaning they can be installed in very close proximity to Josephson voltage standards in calibration cryostats. Unfortunately, doped topological insulators have such small band gaps that even at the base temperatures of dilution fridges, there is enough thermal activation of electrons into the bulk to limit the precision of quantization of the quantized anomalous Hall effect in these systems. This made the class of Chern magnets discovered in 2013 unsuitable as replacements for the graphene quantum Hall resistance standard.
Since intrinsic Chern magnets have now been discovered, and are observed to have band gaps considerably exceeding those of doped topological insulators, it might make sense to replace the graphene quantum Hall resistance standard with an intrinsic Chern magnet resistance standard. The ease of replication of the fabrication process of MoTe2/WSe2 makes that material particularly intriguing as a candidate material for a new resistance standard, but over the past few years new intrinsic Chern magnets have been discovered almost every year, so we may soon be discussing much better materials for this application. In any case, it seems possible and perhaps even likely that Chern magnets will supplant quantum Hall systems as resistance standards in the near future.For decades, magnetic memories dominated information storage technology. Magnetic storage media are robust, do not require continuous access to power, survive high temperatures and extreme radiation environments, and are relatively cheap to manufacture. Hard drives, cassette tapes, floppy disks, and other legacy technologies leveraged the many advantages of magnetic information storage to fuel an explosion in affordable information storage, facilitating mass market access to movies, music, and personal computing. Since the heyday of these technologies, however, magnetic information storage has fallen out of favor, for one simple reason: magnetic bits cannot be easily written electronically.
Legacy mag-netic storage media address magnetic bits mechanically, which limits their maximum speed; modern flash memories can access data much faster precisely because each bit can be written and read electronically.Of course, that fact didn’t take away the many advantages of magnetic memories, and magnetic memories still persist in a variety of niche applications that depend particularly strongly on one of these advantages. Many computers destined to spend their lives in space still use hard drives, and sensors designed to operate over a wide range of temperatures and with intermittent access to power often use non-volatile magnetic memories as well. This has led researchers to search for phenomena and device architectures that allow magnetic order to be switched either with electrical currents or electrostatic gates. Until recently, the best technology available capable of electronic switching of magnetism used spin-orbit torques. In a spin-orbit torque device, current through a system with a strong spin Hall effect pumps spin into a separate magnet, which is eventually inverted by the torque exerted by those spins. This technology has matured considerably over the past few years, producing a cascade of new records for low current density magnetic switching and even a few consumer products in the memory market. The discovery of the first intrinsic Chern magnets produced a fascinating surprise for this field. The exotic orbital magnet in twisted bilayer graphene was found to be switchable with extremely small pulses of current, and the resulting current-switchable magnetic bits displaced previouslyrealized spin-orbit torque devices as the ultimate limit in low-current control of magnetism. A flurry of theoretical investigation of these systems followed, dedicated primarily to identifying and generalizing the mechanism underlying current control of magnetism in these systems. A few years later, AB-MoTe2/WSe2 joined twisted bilayer graphene, with a similarly small magnetic switching current. In the intervening time, a new phenomenon had been observed- switching of a Chern magnet with an electrostatic gate, in twisted monolayer/bilayer graphene. All of these phenomena represent newly discovered and now more or less well understood mechanisms for controlling magnetic bits electronically, procona flower transport containers and by the performance metrics used in the literature they reign supreme. Several electronic switching phenomena known in intrinsic Chern magnets are summarized in Fig. 8.3. Chern magnets differ from the magnetic materials used in more traditional magnetic memories in a wide variety of intriguing ways other than their electronic switchability. Chern magnets are not metals and thus don’t have the same limitations as metallic magnetic memories. For example, the resistance of a Chern magnet is independent of its size, depending only on fundamental physical constants. This makes the resistance of a Chern magnet completely insensitive to miniaturization. Dissipation does occur in Chern magnets, but it occurs only at the contacts to the Chern magnet, so once electrons enter the crystal they can undergo very long range transport completely free of dissipation. Chern magnets are atomically thin in the out-of-plane direction, and of course if they are separated by insulators they can easily be stacked to increase magnetic bit density. Chern magnets are two dimensional materials, and two dimensional materials already have small radiation cross-sections relative to three dimensional crystals like silicon, but the conduction path through a Chern magnet is both one dimensional and topologically protected, so it is overwhelmingly likely that Chern magnet memories would be even more radiation hard than the thin semiconducting films that form the current state of the art. All of these ideas make Chern magnets interesting candidates as substrates for magnetic memories of the distant future. Of course none of these ideas have been implemented in technologies yet, and that is because intrinsic Chern magnets have only been realized at fairly low temperatures .
All of the magnetic memory applications we’ve discussed depend critically on the discovery of intrinsic Chern magnets at considerably higher temperatures, and ideally room temperature.The Chern number is just a property of a band and does not come with an energy scale, so there is no reason to expect to encounter Chern bands only at low temperatures. Indeed, bands with finite Chern numbers have been shown to support quantized Hall effects in graphene quantum Hall devices at room temperature and high magnetic fields, as illustrated in Fig. 8.5A,B. The energy scale in a Chern magnet is set by the band gap produced by magnetic interactions. So if we’d like to know what the maximum temperature at which we can expect to find Chern magnets is, we need to think about the energy scales of known magnets. Magnetism is an interaction-driven electronic phase, and interaction-driven phases almost always melt at sufficiently high temperatures. However, among interaction-driven electronic phases ferromagnetism is particularly stable. Many common transition metals, including iron, cobalt, and nickel, support ferromagnetism into the range 600-1200 K, and all of these have found applications in a variety of electronic technologies as a result. These are of course all three dimensional crystals, and Chern magnets are two dimensional crystals. So the next question we can ask is: do two dimensional magnets exist with Curie temperatures as high as room temperature? The answer turns out to be yes, as illustrated in Fig. 8.5C,D. This magnetic system appears not to be a Chern magnet, unfortunately, but the point is that there is nothing in particular stopping a Chern magnet with a Curie temperature above 300 K from existing. 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 super lattice: MnBi2Te4. These other materials all also represent areas of active research.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 ABC trilayer orbital magnet imaging measurements were performed in this system. 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 circuitelement 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 .