Superexchange and spin-orbit coupling in monolayer and bilayer chromium trihalides

Abstract

We build a microscopic model to study the intra- and inter-layer superexchange due to electrons hopping in chromium trihalides (${\mathrm{CrX}}_3$, X= Cl, Br, and I). In evaluating the superexchange, we identify the relevant intermediate excitations in the hopping. In our study, we find that the intermediate hole-pairs excitations in the $p$-orbitals on X ion play a crucial role in mediating various types of exchange interactions. In particular, the inter-layer antiferromagnetic exchange may be realized by the hole-pair-mediated superexchange. Interestingly, we also find that these virtual hopping processes compete with each other leading to weak intra-layer ferromagnetic exchange. In addition, we also study the spin-orbit coupling effects on the superexchange and investigate the Dzyaloshinskii-Moriya interaction. Finally, we extract the microscopic model parameters from density functional theory for analyzing the exchange interactions in a monolayer ${\mathrm{CrI}}_3$.

18 pages, 4 figures, minor corrections with more references added

References in corpus (40)

• Advanced capabilities for materials modelling with Quantum ESPRESSO
• 2D materials and van der Waals heterostructures
• Magnetic 2D materials and heterostructures
• Ising-Type Magnetic Ordering in Atomically Thin FePS3
• Evolution of interlayer and intralayer magnetism in three atomically thin chromium trihalides
• Topological Magnons: A Review
• Strain-tunable magnetic and electronic properties of monolayer CrI3
• Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators
• Magnetic Two-Dimensional Chromium Trihalides: A Theoretical Perspective
• Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Gate-controllable magneto-optic Kerr effect in layered collinear antiferromagnets
• Twist engineering of the two-dimensional magnetism in double bilayer chromium triiodide homostructures
• Moiré skyrmions and chiral magnetic phases in twisted CrX${}_3$ (X $=$ I, Br, Cl) bilayers
• Electronic and optical properties of two-dimensional InSe from a DFT-parameterized tight-binding model
• Interaction-stabilized topological magnon insulator in ferromagnets
• Spin-correlated exciton-polaritons in a van der Waals magnet
• Relativistic exchange interactions in CrX${}_3$ (X=Cl, Br, I) monolayers
• Magnetic field effect on topological spin excitations in CrI${}_3$
• Microscopic origin of ferromagnetism in trihalides CrCl${}_3$ and CrI${}_3$
• Magnetic order induced polarization anomaly of Raman scattering in 2D magnet CrI${}_3$
• Magnetization textures in twisted bilayer 2D CrX${}_3$ (X=Br, I)
• Magnetic Anisotropy in Spin-3/2 with Heavy Ligand in Honeycomb Mott Insulators: Application to CrI${}_3$
• Topological magnon insulator spin excitations in the two-dimensional ferromagnet CrBr${}_3$
• Strength of effective Coulomb interaction in two-dimensional transition-metal Halides MX${}_2$ and MX${}_3$ (M=Ti, V, Cr, Mn, Fe, Co, Ni; X=Cl, Br, I)
• Moiré magnons in twisted bilayer magnets with collinear order
• Electronic Structure of Chromium Trihalides beyond Density Functional Theory
• Theory of magnetism in the van der Waals magnet CrI3
• Structural and magnetic response of CrI3 monolayer to electric field
• Structural Monoclinicity and Its Coupling to Layered Magnetism in Few-Layer $\mathrm{Cr}{\mathrm{I}}_3$
• Exotic Magnetic and Electronic Properties of Layered CrI3 Single Crystals Under High Pressure
• Trigonal Symmetry Breaking and its Electronic Effects in Two-Dimensional Dihalides and Trihalides
• Magnetism and stability of all primitive stacking patterns in bilayer chromium trihalides
• Tunable Strong Magnetic Anisotropy in Two-Dimensional van der Waals Antiferromagnets
• Uniaxial pressure effects in the two-dimensional van-der-Waals ferromagnet CrI${}_3$
• Insights on magnon topology and valley-polarization in 2D bilayer quantum magnets
• Interlayer magnetic interactions in $\pi /3$-twisted bilayer CrI${}_3$
• All optical resonant magnetization switching in ${\text{CrI}}_3$ monolayers
• Large cross-polarized Raman signal in CrI${}_3$: A first-principles study
• Intra-Atomic and Local Exchange Fields in the Van der Waals Magnet CrI3

Cited by in corpus (4)

• Moiré-driven multiferroic order in twisted CrCl${}_3$, CrBr${}_3$ and CrI${}_3$ bilayers
• Delving into the anisotropic interlayer exchange in bilayer CrI${}_3$
• Interlayer superexchange in bilayer chromium trihalides
• Orbital mixing and strong Hund's coupling stabilize spin order in van der Waals ferromagnet CrI3