Tuning Layer Orbital Hall Effect via Spin Rotation in Ferromagnetic Transition Metal Dichalcogenides

TL;DR

The work addresses tunable orbital transport in bilayer quantum anomalous Hall insulators (QAHIs) by exploiting spin rotation to control valley-resolved orbital angular momentum (OAM) and Berry curvature. It combines first-principles insights with a two-band $k \cdot p$ model to analyze how time-reversal ($\mathcal{T}$) and inversion ($\mathcal{I}$) symmetries, along with AA and AB stacking, shape OAM transport across valleys. In the QAHI limit ($\Delta=0$), OHE is dominated by a single valley, and spin polarization can invert the sign of Berry curvature and reallocate OAM between layers, yielding four distinct orbital-transport configurations. The findings reveal a route to spatially separating orbital currents in bilayer systems, enabling tunable orbitaltronic and valleytronic functionalities through stacking and spin control.

Abstract

Orbitronics, which leverages the angular momentum of atomic orbitals for information transmission, provides a novel strategy to overcome the limitations of electronic devices. Unlike electron spin, orbital angular momentum (OAM) is strongly influenced by crystal field effects and band topology, making its orientation difficult to manipulate with external fields. In this work, by using first principle calculations, we investigate quantum anomalous Hall insulators (QAHIs) as a model system to study the layer orbital Hall effect (OHE). Due to band inversion, only one valley remains orbital polarization, and thus the OHE originates from a single valley. Based on stacking symmetry analysis, we investigated both AA and AB stacking configurations, which possess mirror and inversion symmetries, respectively. The excitation of OAM exhibits valley selectivity, determined jointly by valley polarization and orbital polarization. In AA stacking, the absence of inversion center gives rise to intrinsic orbital polarization, leading to OAM excitations from different valleys in the two layers. In contrast, AB stacking is protected by inversion symmetry, which enforces valley polarization and causes OAM in both layers to originate from the same valley. Furthermore, the direction of spin polarization tunes the sign of the Berry curvature, thereby dictating the transport of OAM. As a result, in bilayer antiferromagnetic QAHI systems, orbital currents display a distinct layer-contrasting behavior in both flow direction and OAM accumulation.

Figures (4)

• Figure 1: Illustration of OHE in QAHI (a) without operations, (b) with time-reversal operation $\mathcal{T}$, (c) with inversion symmetry operation $\mathcal{I}$ and (d) with the $\mathcal{T}$ and $\mathcal{I}$ operations. The blue and red balls represent the carrier with OAM $\langle \hat{L}_z \rangle > 0$ and $\langle \hat{L}_z \rangle <0$, respectively. $K_+$ and $K_-$ are the valley index in the momentum space.
• Figure 2: Illustration of OHE in monolayered RuCl$_2$ (a) without operations, (b) with time-reversal operation $\mathcal{T}$, (c) with inversion symmetry operation $\mathcal{I}$ and (d) with the $\mathcal{T}$ and $\mathcal{I}$ operations. The purple and green balls are Ru and Cl atoms, respectively. The red arrow represents the spin polarization.
• Figure 3: Atomic and electronic structures of RuCl$_2$ bilayer with (a) AA-stacking and (b) AB-stacking. The blue and orange triangles respectively represent the upper layer and the lower layer.
• Figure 4: Schematic of layered resolved orbital current in (a,b) AA-stacking and (c,d) AB-stacking. The blue and red balls represent the positive and negative of OAM, respectively, while the yellow arrows indicate the direction of OAM movement. In addition, the black arrows show the spin polarization of each layer.