The right side of this plot, labelled with an electron density of zero, corresponds to charge neutrality in this system and lies in the gap of the band insulator. Therefore and both correspond to situations in which the hole band is very slightly filled. The valley and spin subbands of ABC trilayer graphene are presented in schematic form in Fig. 7.4A in the absence of electronic interactions. When we tune the Fermi level into these bands and activate interactions, we cannot produce a gap- the bandwidths of these bands are far too high- but we can produce full spin or valley polarization, as illustrated in Fig. 7.4B. The precise situations in which we find this system at and are presented in Fig. 7.4C and D; these situations correspond repsectively to full spin polarization but no valley polarization in and full spin and valley polarization in . Valley polarization couples strongly to transport, generating a large anomalous Hall effect and ferromagnetic hysteresis, as presented in Fig. 7.4E. Although these magnets occur in an atomic crystal, they are composed entirely of electrons we have forced into the system with an electrostatic gate, and as a result we can expect their magnetizations to be considerably smaller than fully spin-polarized atomic crystals. We will use the nanoSQUID microscope to image these magnetic phases. An optical image of the ABC trilayer graphene device used to produce data for the publications is presented in Fig. 7.5A. A black dashed line outlines the region we will be imaging using the nanoSQUID microscope. A nanoSQUID image of this region using AC bottom gate contrast is presented in Fig. 7.5B. This magnetic image was taken in the same phase in which we observe magnetic hysteresis, as presented in Fig. 7.4E. Clearly the system is quite magnetized; we also see evidence of internal disorder, blueberry pot likely corresponding to bubbles between layers of the heterostructure. We can park the SQUID over a corner of the device and extract a density- and displacement field-tuned phase diagram of the magnetic field generated by the magnetization of the device; this is presented in Fig. 7.5C.
Electronic transport data of the same region is presented in Fig. 7.5D. The spin magnet has only a weak impact on electronic transport, but the valley ferromagnet couples extremely strongly to electrical resistance. The system also supports a pair of superconductors, including a spin-polarized one; these phases are subjects ofcontinued study. Capacitance data over the same region of phase space is presented in Fig. 7.5E. ABC trilayer graphene is the first atomic crystal known to support purely orbital magnetism. Other related systems have since been discovered to host similar phenomena, including bilayer graphene. 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, 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.
Many of these technologies were in widespread use until quite recently . Since the heyday of these technologies, however, nursery pots 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 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, 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 switch ability. 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 tothink 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.