As shown in Figs. 5.14 and 5.15, more subtle features of the transport curve can also be associated with the reversal of domains that do not bridge contacts. In the absence of significant magnetic disorder ferromagnetic domain walls minimize surface tension. In two dimensions, domain walls are pinned geometrically in devices of finite size with convex internal geometry. As discussed in Fig. 5.15, we observe pinning of domain walls at positions that do not correspond to minimal length internal chords of our device geometry–suggesting that magnetic order couples to structural disorder directly. This is corroborated by the fact that the observed domain reversals associated with the Barkhausen jumps are consistent over repeated thermal cycles between cryogenic and room temperature. Together, these findings suggest a close analogy topolycrystalline spin ferromagnets, which host ferromagnetic domain walls that are strongly pinned to crystalline grain boundaries ; indeed, these crystalline grains are responsible for Barkhausen noise as it was originally described. Although crystalline defects on the atomic scale are unlikely in tBLG thanks to the high quality of the constituent graphene and hBN layers, the thermodynamic instability of magic angle twisted bilayer graphene makes it highly susceptible to inhomogeneity at scales larger than the moir´e period, as shown in prior spatially resolved studies. For example, procona valencia buckets the twist angle between the layersas well as their registry to the underlying hBN substrate may all vary spatially, providing potential pinning sites.
Moir´e disorder may thus be analogous to crystalline disorder in conventional ferromagnets, which gives rise to Barkhausen noise as it was originally described. A subtler issue raised by our data is the density dependence of magnetic pinning; as shown in Fig. 5.3, Bc does not simply track 1/m across the entire density range, in particular failing to collapse with the rise in m in the Chern magnet gap. This suggests nontrivial dependence of either the pinning potential or the magnetocrystalline anisotropy energy on the realized many body state. Understanding the pinning dynamics is critical for stabilizing magnetism in tBLG and the growing class of related orbital magnets, which includes both moir´e systems as well as more traditional crystalline systems such as rhombohedral graphite. In order to understand the microscopic mechanism behind magnetic grain boundaries in the Chern magnet phase in tBLG/hBN, we used nanoSQUID magnetometry to map the local moir´e super lattice unit cell area, and thus the local twist angle, in this device, using techniques discussed in the literature. This technique involves applying a large magnetic field to the tBLG/hBN device and then using the chiral edge state magnetization of the Landau levels produced by the gap between the moir´e band and the dispersive bands to extract the electron density at which full filling of the moir´e super lattice band occurs . The strength of this Landau level’s magnetization can be mapped in real space , and the density at which maximum magnetization occurs can be processed into a local twist angle as a function of position . It was noted in that the moir´e super lattice twist angle distribution in tBLG is characterized by slow long length scale variations interspersed with thin wrinkles, across which the local twist angle changes rapidly. These are also present in the sample imaged here .
The magnetic grain boundaries we extracted by observing the domain dynamics of the Chern magnet appear to correspond to a subset of these moir´e super lattice wrinkles. It may thus be the case that these wrinkles serve a function in moir´e super lattice magnetism analogous to that of crystalline grain boundaries in more traditional transition metal magnets, pinning magnetic domain walls to structural disorder and producing Barkhausen noise in measurements of macroscopic properties.In tBLG, a set of moir´e subbands is created through rotational misalignment of a pair of identical graphene monolayers. In twisted monolayer-bilayer graphene a set of moir´e subbands is created through rotational misalignment of a graphene monolayer and a graphene bilayer. These systems both support Chern magnets. Both systems are also members of a class of moir´e super lattices known as homobilayers; in these systems, the 2D crystals forming the moir´e super lattice share the same lattice constant, and the moir´e super lattice appears as a result of rotational misalignment, as illustrated in Fig. 5.17A. Homobilayers have many desirable properties; the most important one is that the twist angle can easily be used as a variational parameter for minimizing the bandwidth of the moir´e subbands, producing the so-called ‘magic angle’ tBLG and tMBG systems. Homobilayers do, however, have some undesirable properties. Although local variations in electron density are negligible in these devices, the local filling factor of the moir´e super lattice varies with the moir´e unit cell area, and thus with the relative twist angle. The tBLG moir´e super lattice is shown for two different twist angles in 5. B-C across the magic angle regime; it is clear that the unit cell area couples strongly to twist angle in this regime, illustrating the sensitivity of these devices to twist angle disorder. The relative twist angle of the two crystals in moir´e super lattice devices is never uniform. Imaging studies have clearly shown that local twist angle variations provide the dominant source of disorder in tBLG .
Phenomena discovered in tBLG devices are notoriously difficult to replicate. Orbital magnetism at B = 0 has only been realized in a handful of tBLG devices, and quantization of the anomalous Hall resistance has only been demonstrated in a single tBLG device, in spite of years of sustained effort by several research groups. A mixture of careful device design limiting the active area of devices and the use of local probes has allowed researchers to make many important discoveries while sidestepping the twist angle disorder issue- indeed, some exotic phases are known in tBLG only from a single device, or even from individual scanning probe experiments- but if the field is ever to realize sophisticated devices incorporating these exotic electronic ground states the problem needs to be addressed.There is another way to make a moir´e super lattice. Two different 2D crystals with different lattice constants will form a moir´e super lattice without a relative twist angle; these systems are known as heterobilayers . These systems do not have ‘magic angles’ in the same sense that tBLG and tMBG do, and as a result there is no meaningful sense in which they are flat band systems, but interactions are so strong that they form interaction-driven phases at commensurate filling of the moir´e super lattice anyway. Indeed, many of the interaction-driven insulators these systems support survive to temperatures well above 100 K. The most important way in which heterobilayers differ from homobilayers, however, is in their insensitivity to twist angle disorder. In the small angle regime, the moir´e unit cell area of a heterobilayer is almost completely independent of twist angle, as illustrated in 5.17E-F. A new intrinsic Chern magnet was discovered in one of these systems, a heterobilayer moir´e super lattice formed through alignment of MoTe2 and WSe2 monolayers. The researchers who discovered this phase measured a well-quantized QAH effect in electronic transport in several devices, procona buckets demonstrating much better repeatability than was observed in tBLG. The unit cell area as a function of twist angle is plotted for three moir´e super lattices that support Chern insulators in 5.17G, with the magic angle regime highlighted for the homobilayers, demonstrating greatly diminished sensitivity of unit cell area to local twist angle in the heterobilayer AB-MoTe2/WSe2. MoTe2/WSe2 does have its own sources of disorder, but it is now clear that the insensitivity of this system to twist angle disorder has solved the replication issue for Chern magnets in moir´e super lattices. Dozens of MoTe2/WSe2 devices showing well-quantized QAH effects have now been fabricated, and these devices are all considerably larger and more uniform than the singular tBLG device that was shown to support a QAH effect, and was discussed in the previous chapters. The existence of reliable, high-yield fabrication processes for repeatably realizing uniform intrinsic Chern magnets is an important development, and this has opened the door to a wide variety of devices and measurements that would not have been feasible in tBLG/hBN.The basic physics of this electronic phase differs markedly from the systems we have so far discussed, and we will start our discussion of MoTe2/WSe2 by comparing and contrasting it with graphene moir´e super lattices. In tBLG/hBN and its cousins, valley and spin degeneracy and the absence of significant spin-orbit coupling combine to make the moir´e subbands fourfold degenerate. When inversion symmetry is broken the resulting valley subbands can have finite Chern numbers, so that when the system forms a valley ferromagnet a Chern magnet naturally appears.
Spin order may be present but is not necessary to realize the Chern magnet; it need not have any meaningful relationship with the valley order, since spin-orbit coupling is absent. MoTe2/WSe2 has strong spin-orbit coupling, and as a result, the spin order is locked to the valley degree of freedom. This manifests most obviously as a reduction of the degeneracy of the moir´e subbands; these are twofold degenerate in MoTe2/WSe2 and all other TMD-based moir´e super lattices. 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, 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 super lattice site. We observe hysteretic switching of the resistivity as a function of applied current. 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 super lattice Brillouin zone.