Orbital torques and orbital pumping in two-dimensional rare-earth dichalcogenides

The design of spin-orbit torque properties in two-dimensional (2D) materials presents one of the challenges of modern spintronics. In this context, 2D layers involving rare-earth ions − which give rise to robust magnetism, exhibit pronounced orbital polarization of the states, and carry strong spin-orbit interaction—hold particular promise. Here, we investigate ferromagnetic Janus H-phase monolayers of 4f-Eu rare-earth dichalcogenides EuSP, EuSSe, and EuSCl using first-principles calculations. We demonstrate that all compounds exhibit significant spin-orbit torques which originate predominantly in the colossal current-induced orbital response on the Eu f-electrons. Moreover, we demonstrate that the corresponding orbital torques can be used to drive strong in-plane currents of orbital angular momentum with non-trivial direction of orbital polarization, constituting the effect of in-plane orbital pumping. We provide an interpretation of this effect in terms of orbital-to-orbital-curent conversion, and draw a simple qualitative picture of orbital pumping by magnetization dynamics in two dimensional systems. Our findings promote f-orbital-based 2D materials as a promising platform for in-plane orbital pumping and spin-orbit torque applications, and motivate further research on educated design of orbital properties for orbitronics with 2D materials.