Orbital-Ordering Switch for Tunable Magnetic Anisotropy in Two-Dimensional CrCl₂

Spin-orbit coupling (SOC) intricately links an electron's spin and orbital motions, underpinning a myriad of physical phenomena from magnetocrystalline anisotropy to topological spin texture. While the prevailing focus centers on asymmetry-induced spin splitting like Rashba/Dresselhaus SOC, an unexplored avenue lies in orbital ordering, shaping crystal field symmetry crucial for centrosymmetric or low-dimensional magnetism. Our study presents a novel approach to manipulate magnetic anisotropy in two-dimensional (2D) magnets by toggling orbital orders in monolayer and bilayer CrCl₂. We demonstrate through first-principles calculations that the two distinct orbital-ordered phases, stabilized by in-plane epitaxial strains, exhibit markedly different magnetic ground states and anisotropy energies. Orbital-resolved analysis reveals that the occupation of specific Cr d orbitals governs the magnetic easy axis/plane behavior via orbital-selective spin-orbit interactions. We further extend this paradigm to engineered bilayers, showing that interlayer stacking and twist angles in bilayers can coherently reorient orbital arrangements, enabling the continuous in situ tuning of magnetic anisotropy. This study pioneers "orbital engineering", enabling intricate magnetic functionalities through van der Waals stacking and twisting beyond traditional Rashba field manipulation.