Evidence of Orbital Ferromagnetism in Twisted Bilayer Graphene Aligned to Hexagonal Boron Nitride

Spin Polarization and Flat Bands in Eu-Doped Nanoporous and Twisted Bilayer Graphenes

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions' chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases.

Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Gate voltages applied to top and back gates of a tDBG device tune both the flatness and topology of the electronic bands, enabling an unusual level of experimental control. Metallic states with broken spin and valley symmetries have been observed in tDBG devices with twist angles in the range 1.2–1.3°, but the topologies and order parameters of these states have remained unclear. We report the observation of an anomalous Hall effect in the correlated metal state of tDBG, with hysteresis loops spanning hundreds of mT in out-of-plane magnetic field (B_⊥) that demonstrate spontaneously broken time-reversal symmetry. The B_⊥ hysteresis persists for in-plane fields up to several Tesla, suggesting valley (orbital) ferromagnetism. At the same time, the resistivity is strongly affected by even mT-scale values of in-plane magnetic field, pointing to spin-valley coupling or to a direct orbital coupling between in-plane field and the valley degree of freedom.

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Here, the authors report a strong anomalous Hall effect in the correlated-metal regime of tDBG, indicating time reversal symmetry breaking from orbital ferromagnetism, likely associated with valley polarization.

Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene

Strong electron correlation and spin-orbit coupling (SOC) can have a profound influence on the electronic properties of materials. We examined their combined influence on a two-dimensional electronic system at the atomic interface between magic-angle twisted bilayer graphene and a tungsten diselenide crystal. We found that strong electron correlation within the moiré flatband stabilizes correlated insulating states at both quarter and half filling, and that SOC transforms these Mott-like insulators into ferromagnets, as evidenced by a robust anomalous Hall effect with hysteretic switching behavior. The coupling between spin and valley degrees of freedom could be demonstrated through control of the magnetic order with an in-plane magnetic field or a perpendicular electric field. Our findings establish an experimental knob to engineer topological properties of moiré bands in twisted bilayer graphene and related systems.

Tunable Orbital Ferromagnetism at Noninteger Filling of a Moiré Superlattice

The flat bands resulting from moiré superlattices exhibit fascinating correlated electron phenomena such as correlated insulators, ( Nature 2018, 556 (7699), 80-84), ( Nature Physics 2019, 15 (3), 237) superconductivity, ( Nature 2018, 556 (7699), 43-50), ( Nature 2019, 572 (7768), 215-219) and orbital magnetism. ( Science 2019, 365 (6453), 605-608), ( Nature 2020, 579 (7797), 56-61), ( Science 2020, 367 (6480), 900-903) Such magnetism has been observed only at particular integer multiples of n₀, the density corresponding to one electron per moiré superlattice unit cell. Here, we report the experimental observation of ferromagnetism at noninteger filling (NIF) of a flat Chern band in a ABC-TLG/hBN moiré superlattice. This state exhibits prominent ferromagnetic hysteresis behavior with large anomalous Hall resistivity in a broad region of densities centered in the valence miniband at n = -2.3n₀. We observe that, not only the magnitude of the anomalous Hall signal, but also the sign of the hysteretic ferromagnetic response can be modulated by tuning the carrier density and displacement field. Rotating the sample in a fixed magnetic field demonstrates that the ferromagnetism is highly anisotropic and likely purely orbital in character.