Gate voltages and DC currents are applied, and amplified voltages recorded, with a home built data acquisition system based on AD5760 and AD7734 chips.In crystalline solids, orbital magnetization arises from the Berry curvature of the bands and intrinsic angular momentum of the Bloch electron wave packet. Although the orbital magnetization often contributes—at times substantially—to the net magnetization of ferromagnets, all knownν = An corresponds to the number of electrons per unit cell area A with n the carrier density.In an intrinsic orbital magnet in which all moments arise from conduction electrons, the magnetization depends strongly on the density. Additional density dependence arises from the fact that contributions to the orbital magnetization from both wave-packet angular momentum and Berry curvature need not be uniformly distributed within the Brillouin zone[84]. Transport observations of aquantum anomalous Hall effect measure only the total Berry curvature of a completely filled band. At partial band filling, however, extrinsic contributions from scattering complicate the relationship between transport and band properties. In contrast, measuring m provides direct information about the density-dependent occupation of the Bloch states in momentum space.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, hydroponic nft as shown in prior spatially resolved studies. For example, the twist angle between the layers as 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 superlattice 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 superlattice 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 superlattice 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 superlattice wrinkles. It may thus be the case that these wrinkles serve a function in moir´e superlattice 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.There is another way to make a moir´e superlattice. Two different 2D crystals with different lattice constants will form a moir´e superlattice 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 superlattice 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 superlattice 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, 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 superlattices 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 superlattices. 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 superlattices. 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 superlattices. 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, hydroponic channel at which point the finite Chern number of the valley subbands would produce a Chern magnet. 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 multilayer 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. 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 superlattice Brillouin zone. In certain cases, moir´e heterostructures host superlattice minibands with narrow bandwidth, placing them in a strongly interacting regime whereCoulomb 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.We emphasize that in both twisted bilayer graphene and our current MoTe2/WSe2 heterostructure, magnetic switching arises in regimes for which doping, elevated temperature, or disorder ensure that electrical current flows in the sample bulk. Ultra-low current switching of magnetic order has also been observed in twisted bilayer graphene. In that system, where spin orbit coupling is negligible, nearly identical mechanisms may arise mediated by orbital, rather than spin, Hall effects. The bulk nature of the spin Hall torque mechanism means that similar phenomena should manifest not only in the growing class of intrinsic Chern magnets, but in all metals combining strong Berry curvature and broken time-reversal symmetry, including crystalline graphite multilayers. Research into charge-to-spin current transduction has identified a set of specific issues restricting the efficiency of spin torque switching of magnetic order. Spin current is not necessarily conserved, and as a result a wide variety of spin current sinks exist within typical spin torque devices. Extensive evidence indicates that in many spin torque systems a significant fraction of the spin current is destroyed or reflected at the spin-orbit material/magnet boundary. In addition, the transition metals used as magnetic bits in traditional spin-orbit torque devices are electrically quite conductive, and can thus shunt current around the spin-orbit material, preventing it from generating spin current. These issues are entirely circumvented here through the use of a material that combines a spin Hall effect with magnetism, and as a result of these effects this spin Hall torque device has better current-switching efficiency than any known spin torque device.We do not know the precise origin of these holes, but there are a few possibilities that we can discuss. Bubbles are some of the most common defects in stacks of two dimensional crystals, and they can form between any two layers of a stack.