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, plant pots with drainage 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.
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. Current switching may be correlated precisely with magnetic structure.
To examine the metastable magnetic domain structure of the system under applied current, we use tuning-fork based gradient magnetometry where a magnetic signal is produced by modulating the tip position. Figure 6.5c shows the change in magnetization relative to the zero current state for ISD = 670 nA, well above the threshold current. The images in Figs. 6.5c-d are acquired over the scan range depicted by the dashed box in Fig. 6.4f. Above the threshold, a magnetic do- main a few µm2 in size is inverted relative to the ground state on one side of the device. Reversing the current flips the side hosting the reversed domain . We conclude that the current switching corresponds to the reversal of magnetic domains, with the inverted domains appearing on opposite edges for opposing directions of applied DC current. This is confirmed by the fact that the required switching current increases dramatically as a function of the applied magnetic field, which increases the energy cost of an inverted magnetic domain. The correspondence between magnetic dynamics and resistivity may be probed in detail using current modulation magnetometry, which examines the magnetic response, δBI to a small AC current. Figs. 6.5e and f show δBI , measured near the right and left edges of the device, respectively, for the same range of VBG, VT G, and VSD as Fig. 6.5a-b. The local δBI signal shows a single sharp dip feature on the right side of the device for ISD > 0 and on the left side for ISD < 0, but no signal for the opposite signs. These features correlate precisely with the current switching features observed in transport, as evidenced by overlaying a fit to the local δBI dip on the transport data in Fig. 6.5a-b. The δBI dips may be understood as a consequence of current-driven domain wall motion. As established above, applied current drives nucleation of minority magnetization domains.
Once these domains are nucleated, increasing the current magnitude is expected to enlarge them through domain wall motion. Where domain walls are weakly pinned, a small increase in the current δI drives a correspondingly small motion δx of the domain wall, producing a change in the local magnetic field δBI characterized by a sharp negative peak at the domain wall position . We may then use this mechanism to map out the microscopic evolution of domains with current. Fig. 6.5h shows a spatial map of δBI , measured at three different values of ISD corresponding to distinct features in the transport data. Evidently, the domain wall moves from its nucleation site on the device boundary towards the device bulk. Local measurements of δBI as a function of ISD show that this motion is itself characterized by threshold behavior, corresponding to the domain wall rapidly moving between stable pinning sites. A full correspondence of transport features and local domain dynamics is presented in the associated publication. The symmetry of the observed magnetic switching is suggestive of a spin or valley Hall effect driven mechanism. 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 multi-layers. 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, plastic plants pots and as a result of these effects this spin Hall torque device has better current-switching efficiency than any known spin torque device. We started this discussion with a favorable comparison of the impact of disorder on the ABMoTe2/WSe2 Chern magnet to graphene-based Chern magnets. I’m sure the reader was just as disappointed as we were to see the dramatic disorder landscape on display in Fig. 6.4E, which presents a map of the magnetization in the AB-MoTe2/WSe2 Chern magnet. This is not a refutation of our original claims; it remains true that the repeatability of the fabrication protocol of the AB-MoTe2/WSe2 Chern magnet is unambiguously much better than that of tBLG/hBN, or even tMBG. It is also easy to lose track of the scale of these images- the tBLG/hBN Chern magnet was only a few square microns, whereas this sample supports a Chern magnet that is almost a hundred square microns in area.
The presence of these ‘holes’ in the magnetization of this Chern magnet is not a result of strong twist angle disorder. We have so far discussed a variety of phenomena realized in gate-tunable exfoliated heterostructures. In all cases, these phenomena were accessible experimentally because of the presence of a moir´e superlattice, which gave us access to electronic bands that could be completely filled or depleted at will using an electrostatic gate. We will next be discussing an atomic crystal without a moir´e superlattice. This material does not have flat bands, and we will have no hope of completely filling or depleting any of the bands in the system. Instead, it has features in its band structure that lend themselves to interaction-driven phenomena, specifically flat-bottomed bands satisfying the Stoner criterion. The material we will be studying is an allotrope of three-layer graphene called ABC trilayer graphene. In addition to a variety of other interesting phases, this material supports both spin and orbital magnetism. We will discuss why this is the case, and we will study the ABC trilayer magnets using the nanoSQUID microscope. As in three dimensional crystals, many two dimensional crystals have multiple allotropes that are stable under different conditions. Trilayer graphene is such a material. We label multilayer graphene allotropes using letters that refer to the relative positions of atoms of different layers, projected onto the two dimensional plane. We have already encountered ABA trilayer graphene in the introduction, and this material has atoms in the third layer aligned to atoms in the first layer. At room temperature and pressure the ABA stacking order is preferred, but trilayer graphene has a metastable allotrope, ABC trilayer graphene, that can either be prepared or found naturally occurring. In ABC trilayer graphene atoms in the third layer are aligned neither with the first nor with the second layer. ABC trilayer graphene has band structure that differs significantly from ABA trilayer graphene, and these differences have important consequences for its properties. The band structure of ABC trilayer graphene at two different displacement fields is illustrated in Fig. 7.1. In the absence of a displacement field, the system is metallic at all electron densities. When a large displacement field is applied to the system, it becomes a band insulator when the Fermi level is tuned between the two resulting bands. This is the regime of displacement field that we will be discussing. ABC trilayer graphene has extremely weak spin-orbit coupling, so the spin degree of freedom is present and more or less completely orthogonal to electronic degrees of freedom, contributing only a twofold degeneracy to the band structure. Just like most other allotropes of graphene, ABC trilayer graphene has valley degeneracy, and this produces an overall fourfold energetic degeneracy of its band structure. This is illustrated in Fig. 7.2. As is abundantly clear from these plots, the bandspresent in ABC trilayer graphene are not flat; they have extremely large bandwidths. However, the bands do satisfy the flat-bottomed band condition, and as a result we can expect these systems to be able to spin- and valley-polarize without paying significant kinetic energy costs. A schematic of the device we will discuss is presented in Fig. 7.3A. This device allows us to perform several different experiments: we can tune the electron density and displacement field in the ABC trilayer graphene layer, we can measure in-plane electronic transport , and we can measure the out-of-plane capacitive conductivity as a function of electron density and displacement field. Data extracted from this contrast mechanism is presented in Fig. 7.3B. This dataset is restricted to the hole band; i.e., the bottom band in all of the plots we have so far encountered. Sharp features in this dataset correspond to spontaneous symmetry breaking; these features are marked with the numbers and .