In certain cases, moir´e heterostructures host super lattice 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.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 , procona florida container 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. To investigate this hypothesis experimentally, we use local magnetic imaging to directly probe the current-driven accumulation of magnetic moments throughout the density- and displacement field tuned phase space. Figs. 6.6c-e show δBI maps measured at three different points, away from the regime where the ground state is ferromagnetic. These fillings correspond to the Hubbard band edges, where the Berry curvature is expected to be enhanced by the appearance of correlation driven gaps. Notably, large spin Hall effects are observed near ν = −1 even far from band inversion, with possible implications for the nature of the strong insulating state observed there. We have shown here that the combination of intrinsic spin Hall effect with intrinsic magnetism provides a mechanism for a current-actuated magnetic switch in a single two dimensional electron system. The physical properties we invoke to explain this phenomenon are generic to all intrinsicChern magnets.
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 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, 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 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. As presented and described in Fig. 6.7A-C, AFM imaging reveals topographic defects precisely aligned with the regions in the Chern magnet in which magnetism has been destroyed. There are two clearly distinct distributions of defects, with thicknesses that differ by about an order of magnitude. It is possible that these correspond to bubbles between two distinct pairs of layers of the stack. Another possibility is that partial oxidation or deliquescence of the MoTe2 crystal has occured. This crystal is indeed air and moisture sensitive, and degradation can happen even inside a glovebox, as illustrated for a CrI3 crystal in Fig. 6.7D-F. Whatever issue is generating this disorder, it will likely be necessary to resolve it in order to fabricate more sophisticated devices based on this Chern magnet.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 super lattice, 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 super lattice. 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, procona London container 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 grapheneallotropes 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 . 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 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 of continued 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.