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

Abstract: Strong electron correlation and spin-orbit coupling (SOC) provide two non-trivial threads to condensed matter physics. When these two strands of physics come together, a plethora of quantum phenomena with novel topological order have been predicted to emerge in the correlated SOC regime. In this work, we examine the combined influence of electron correlation and SOC on a 2-dimensional (2D) electronic system at the atomic interface between magic-angle twisted bilayer graphene (tBLG) and a tungsten diselenide (\WSe) crystal. In such a structure, strong electron correlation within the moir\'e flatband stabilizes correlated insulating states at both quarter and half-filling, whereas SOC transforms these Mott-like insulators into ferromagnets, evidenced by robust anomalous Hall effect with hysteretic switching behavior. The coupling between spin and valley degrees of freedom is unambiguously demonstrated as the magnetic order is shown to be tunable with an in-plane magnetic field, or a perpendicular electric field. In addition, we examine the influence of SOC on the isospin order and stability of superconductivity. Our findings establish an efficient experimental knob to engineer topological properties of moir\'e bands in twisted bilayer graphene and related systems.

Spin-Orbit Driven Ferromagnetism in Magic-Angle Twisted Bilayer Graphene

The paper at hand explores the intricate interplay between electron correlation and spin-orbit coupling (SOC) in magic-angle twisted bilayer graphene (tBLG) interfaced with tungsten diselenide (WSe₂). The study explores the emergence of ferromagnetism under conditions where both strong electron correlation and SOC are present, producing novel quantum phenomena and potentially leading to new topological states.

Highlights and Key Findings

1. Moiré Band Engineering and Correlated Insulating States: The research focuses on the moiré band structure of tBLG interfaced with WSe₂, which stabilizes correlated insulating states at fractional fillings (quarter and half) of the moiré bands. Notably, at half-filling, the strong correlation leads to robust Mott-like insulating states.
2. Induction of Ferromagnetism Through SOC: SOC is shown to alter the landscape of these insulating states. Specifically, the introduction of proximity-induced SOC via the WSe₂ layer leads to the transformation of these correlated insulators into ferromagnetic states. This is evidenced by the observation of an anomalous Hall effect (AHE) with hysteretic behavior, indicative of ferromagnetic order.
3. Impact of Ising and Rashba SOC: The SOC effects are modeled within a framework that incorporates both Ising and Rashba-type interactions. The interplay between these interactions breaks combined inversion and time reversal symmetries ($C_2T$), imparting non-zero Berry curvature and valley-dependent Chern numbers to the moiré bands, crucial for the observed AHE.
4. Control of Magnetic Order via External Fields: The study demonstrates the tunability of ferromagnetic order using external in-plane magnetic fields and perpendicular electric fields. This reveals the potential for novel device applications where magnetic properties can be dynamically controlled by applied fields.
5. Implications for Superconductivity and Isospin Dynamics: The paper investigates the influence of SOC on the stability of superconducting phases and the isospin order. While superconductivity in tBLG is known to be sensitive to $C_2T$ symmetry, the strong SOC disrupts this symmetry, affecting the superconducting transition.

Quantitative and Experimental Insights

• Robust Anomalous Hall Effect: The study provides clear experimental signatures of AHE at specific fillings, reinforced by the hysteretic nature of the Hall resistance, which serves as a robust indicator of ferromagnetic order.
• Proximity-Induced SOC Strength: The research quantitatively links the strength of the SOC to the physical proximity and rotational alignment between the graphene and WSe₂ layers, highlighting the importance of precise structural control in vdW heterostructures.

Theoretical and Practical Implications

This work advances the understanding of the topological and magnetic properties in graphene-based moiré systems. The introduction of SOC as an experimental knob to tune these properties opens pathways to engineer new quantum phases. The findings have implications for developing spintronic devices, wherein the magnetization can be controlled via external non-magnetic fields, enhancing the versatility of graphene's electronic applications.

Future Directions

• Enhancing SOC Effects: Future research could focus on achieving better control and understanding of SOC effects via different TMDs or other mechanisms to further tune the electronic properties of tBLG.
• Exploration of Superconductivity: Given the sensitivity of superconductivity in these systems to symmetry and SOC, additional studies exploring the boundary conditions for superconducting phases under varying SOC could provide deeper insights into the symmetry requirements of such phases.
• Device Applications: Translating these findings into practical device architectures could lead to breakthroughs in non-volatile memory and logic devices based on ferromagnetic and topological properties.

In conclusion, this study presents a comprehensive analysis of the emergent spin-orbit driven phenomena in tBLG that could redefine the material's use in next-generation electronic and spintronic applications. The insights gained pave the way for a deeper exploration of quantum materials and their multifaceted properties.