Electrical switching of magnetic order in an orbital Chern insulator

Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favors ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields---a longstanding technological goal in spintronics and multiferroics---can be achieved only indirectly. Here, we experimentally demonstrate direct electric field control of magnetic states in an orbital Chern insulator, a magnetic system in which non-trivial band topology favors long range order of orbital angular momentum but the spins are thought to remain disordered. We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically nontrivial valley-projected moir\'e minibands. At fillings of one and three electrons per moir\'e unit cell within these bands, we observe quantized anomalous Hall effects with transverse resistance approximately equal to $h/2e^2$, which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moir\'e unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate nonvolatile electric field induced reversal of the magnetic state. A theoretical analysis indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favored magnetic state. Voltage control of magnetic states can be used to electrically pattern nonvolatile magnetic domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow power magnetic memory.Comment: 21 pages, 17 figure

Magnetism and Topology in Twisted Graphene Heterostructures

Graphene, a crystalline atomic monolayer of carbon atoms, is a model system as the regularity and cleanliness of its lattice enables precise descriptions of its properties. Theoretical models predict that the behavior of electrons in a heterostructure consisting of two stacked graphene monolayers with a slight rotational misalignment in their lattices is dictated by interactions and topology. We investigate a twisted bilayer sample with both electrical resistivity measurements and nanoSQUID on tip microscopy. The latter, a novel magnetic imaging method developed as part of this dissertation, is uniquely well matched to studying the dilute magnetic signals expected in twisted graphene heterostructures. We observe the emergence of a quantized anomalous Hall effect in twisted bilayer graphene aligned to hexagonal boron nitride with Hall resistance is quantized to within 0.1\% of the von Klitzing constant h/e^2 at zero magnetic field. In contrast to magnetically doped (Bi,Sb)_2Te_3 quantum anomalous Hall variants, intrinsic strong correlations polarize the electrons into a single valley resolved miniband with Chern number C=1 arising from inversion symmetry breaking and the formation of a moir\'e: the system does not host band inversion or spin orbit coupling. The measured transport energy gap $\Delta/k_B\approx 27$ K, the largest observed to date, is almost four times the Curie temperature for magnetic ordering $T_C\approx 7.5$ K. We find that electrical currents as small as 1 nA can be used to controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory. Magnetic imaging reveals a magnetization primarily orbital in nature dominated by chiral edge state contributions from the topological gap of the quantum anomalous hall phase. Mapping the spatial evolution of field-driven magnetic reversal, we find a series of reproducible micron scale domains, pinned to structural disorder, whose boundaries host chiral edge states

Magnetism and Topology in Twisted Graphene Heterostructures

Graphene, a crystalline atomic monolayer of carbon atoms, is a model system as the regularity and cleanliness of its lattice enables precise descriptions of its properties. Theoretical models predict that the behavior of electrons in a heterostructure consisting of two stacked graphene monolayers with a slight rotational misalignment in their lattices is dictated by interactions and topology. We investigate a twisted bilayer sample with both electrical resistivity measurements and nanoSQUID on tip microscopy. The latter, a novel magnetic imaging method developed as part of this dissertation, is uniquely well matched to studying the dilute magnetic signals expected in twisted graphene heterostructures. We observe the emergence of a quantized anomalous Hall effect in twisted bilayer graphene aligned to hexagonal boron nitride with Hall resistance is quantized to within 0.1\% of the von Klitzing constant h/e^2 at zero magnetic field. In contrast to magnetically doped (Bi,Sb)_2Te_3 quantum anomalous Hall variants, intrinsic strong correlations polarize the electrons into a single valley resolved miniband with Chern number C=1 arising from inversion symmetry breaking and the formation of a moir\'e: the system does not host band inversion or spin orbit coupling. The measured transport energy gap $\Delta/k_B\approx 27$ K, the largest observed to date, is almost four times the Curie temperature for magnetic ordering $T_C\approx 7.5$ K. We find that electrical currents as small as 1 nA can be used to controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory. Magnetic imaging reveals a magnetization primarily orbital in nature dominated by chiral edge state contributions from the topological gap of the quantum anomalous hall phase. Mapping the spatial evolution of field-driven magnetic reversal, we find a series of reproducible micron scale domains, pinned to structural disorder, whose boundaries host chiral edge states

Electrical switching of magnetic order in an orbital Chern insulator

Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favors ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields---a longstanding technological goal in spintronics and multiferroics---can be achieved only indirectly. Here, we experimentally demonstrate direct electric field control of magnetic states in an orbital Chern insulator, a magnetic system in which non-trivial band topology favors long range order of orbital angular momentum but the spins are thought to remain disordered. We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically nontrivial valley-projected moiré minibands. At fillings of one and three electrons per moiré unit cell within these bands, we observe quantized anomalous Hall effects with transverse resistance approximately equal to h/2e2, which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moiré unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate nonvolatile electric field induced reversal of the magnetic state. A theoretical analysis indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favored magnetic state. Voltage control of magnetic states can be used to electrically pattern nonvolatile magnetic domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow power magnetic memory.Work at UCSB was primarily supported by the ARO under MURI W911NF- 16-1-0361. Measurements of twisted bilayer graphene (Extended Data Fig. E8) and measurements at elevated temperatures (Extended Data Fig. E3) were supported by a SEED grant and made use of shared facilities of the UCSB MRSEC (NSF DMR 1720256), a member of the Materials Research Facilities Network (www.mrfn.org). AFY acknowledges the support of the David and Lu- cille Packard Foundation under award 2016-65145. AHM and JZ were supported by the National Science Founda- tion through the Center for Dynamics and Control of 8 Materials, an NSF MRSEC under Cooperative Agree- ment No. DMR-1720595, and by the Welch Founda- tion under grant TBF1473. CLT acknowledges support from the Hertz Foundation and from the National Sci- ence Foundation Graduate Research Fellowship Program under grant 1650114. KW and TT acknowledge sup- port from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001, JSPS KAKENHI Grant Numbers JP20H00354 and the CREST(JPMJCR15F3), JST.Center for Dynamics and Control of Material