We observe hysteretic switching of the resistivity as a function of applied current

The closest imaginable analog of the tBLG/hBN Chern magnet in this system is one in which interactions favor the formation of a valley-polarized ferromagnet, at which point the finite Chern number of the valley subbands would produce a Chern magnet. This was widely assumed to be the case at the time of the system’s discovery. There is now substantial evidence that this system instead forms a valley coherent state stabilized by its spin order, which would require a new mechanism for generating the Berry curvature necessary to produce a Chern magnet. In general I think it is fair to say that the details of the microscopic mechanism responsible for producing the Chern magnet in this system are not yet well understood. In light of the differences between these two systems, there was no particular reason to expect the same phenomena in MoTe2/WSe2 as in tBLG/hBN. As will shortly be explained, current-switching of the magnetic order was indeed found in MoTe2/WSe2. The fact that we find current-switching of magnetic order in both the tBLG/hBN Chern magnet and the AB-MoTe2/WSe2 Chern magnet is interesting. It may suggest that the phenomenon is a simple consequence of the presence of a finite Chern number; i.e., that it is a consequence of a local torque exerted by the spin/valley Hall effect, which is itself a simple consequence of the spin Hall effect and finite Berry curvature. These ideas will be discussed in the following sections. In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, hydroponic vertical garden these require a multi-layer geometry including both a free ferromagnetic layer and a second layer providing spin injection.

For example, spin may be injected by a nonmagnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin-orbit torque. Here, we demonstrate a spin-orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moir´e superlattice site. Magnetic imaging reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns with spin accumulation measured near the high Berry curvature Hubbard band edges. This suggests that intrinsic spin or valley Hall torques drive the observed current-driven magnetic switching in both MoTe2/WSe2 and other moir´e materials. The switching current density is significantly less than those reported in other platforms, suggesting moir´e heterostructures are a suitable platform for efficient control of magnetic order. To support a magnetic Chern insulator and thus exhibit a quantized anomalous Hall effect, a two dimensional electron system must host both spontaneously broken time-reversal symmetry and bands with finite Chern numbers. This makes Chern magnets ideal substrates upon which to engineer low-current magnetic switches, because the same Berry curvature responsible for the finite Chern number also produces spin or valley Hall effects that may be used to effect magnetic switching. Recently, moir´e heterostructures emerged as a versatile platform for realizing intrinsic Chern magnets. In these systems, two layers with mismatched lattices are combined, producing a long-wavelength moir´e pattern that reconstructs the single particle band structure within a reduced superlattice Brillouin zone. In certain cases, moir´e heterostructures host superlattice minibands with narrow bandwidth, placing them in a strongly interacting regime where Coulomb repulsion may lead to one or more broken symmetries.

In several such systems, the underlying bands have finite Chern numbers, setting the stage for the appearance of anomalous Hall effects when combined with time-reversal symmetry breaking. Notably, in twisted bilayer graphene low current magnetic switching has been observed, though consensus does not exist on the underlying mechanism. 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 lineoutlines 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, 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. 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, vertical vegetable tower 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.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 previously realized 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.