Switchable Interlayer Magnetic Coupling of Bilayer CrI3

Abstract

Due to the weak van der Waals (vdW) interlayer interaction, interfacial geometry of two-dimensional (2D) magnetic vdW materials can be freely assembled, and the stacking order between layers can be readily controlled, such as laterally shifting or rotating, which may trigger the variation of magnetic order. We investigate the H-type bilayer CrI3 where the two layers are aligned in anti-parallel directions. Based on first-principles calculations, we propose two states with different interlayer magnetic couplings, i.e., ferromagnetic and antiferromagnetic, and analyze the superexchange mechanism inside. It is found that the two magnetic coupling states are stacking-dependent, and could be switched by applying out-of-plane axial strain and electron doping. Our findings show great application potential in the design of heterostructural and spintronic devices based on 2D magnetic vdW materials.

Strain Tunable Electronic Band Structure and Magnetic Anisotropy of CrI3 Bilayer

“…So, in the ground state of BL CrI 3 , the AFM interlayer exchange coupling may be largely due to the interaction through the t g 2 -t g 2 and e g -e g channels. Recently Jiang et al 48 explained switchable interlayer magnetic coupling in BL CrI 3 . According to their studies, in the phase where interlayer AFM coupling dominates, an I atom in the upper layer resides directly above another one in the lower layer.…”

Understanding External Pressure Effects and Interlayer Orbital Exchange Pathways in the Two-Dimensional Magnet─Chromium Triiodide

“…The second-layer iodide then interacts via a σ-type overlap with the e g orbital of Cr 3+ in the second layer. This state is a “virtual state”, as has been noted to occur in ref , which allows the interactions between the filled t 2g and e g orbitals. In the ferromagnetic case, this results in the Cr 3+ ions showing the e g character that can be noted in Figure B,C.…”

“…In this work, we focus primarily on the isotropic exchange coupling constant J ij to identify the important ferromagnetic and antiferromagnetic interlayer coupling. Other important factors (e.g., single-ion anisotropy or anisotropic exchange) have not been included because they do not affect the qualitative discussion of the orbital pathways. − Commonly, J is calculated using the four-state method − J i j = prefix− E false↑ false↑ − E false↑ false↓ − E false↓ false↑ + E false↓ false↓ 4 S 2 where all of the centers (beyond i and j ) are held at a constant spin configuration for each of the four calculations, and each energy value, E ij , corresponds to the center i or j having spins aligned either parallel (↑) or antiparallel (↓) to the magnetization axis. In order to avoid extraneous spin interactions in the periodic cells, a large supercell is required for the calculation.…”

“…The CrI 3 exchange coupling has been previously examined through the use of density functional theory (DFT), both at the collinear and noncollinear levels of theory (where the noncollinear approach includes spin–orbit coupling); however, these works suggest that the inclusion of spin–orbit coupling has little effect on the observed exchange coupling strength. − These exchange coupling strengths are obtained by comparing ferromagnetic and antiferromagnetic states with the two different crystal stacking orders. ,,, It was concluded that the rhombohedral stacking has a ferromagnetic ground state, while the monoclinic stacking exhibits antiferromagnetic coupling. Competing orbital pathways favoring ferro- or antiferromagnetic coupling have been determined, with the overall magnetism of the 2D material depending on the relative strengths of the two. , …”

Stacking-dependent topological magnons in bilayer CrI$_3$

“…Overall, this results in a weak AFM interlayer ordering, which is in agreement with earlier theoretical and experimental studies. 2,52,[54][55][56][57][58][59][60][61] Interestingly, the sublattice symmetry is broken in the AB-and AB' stackings, leading to a difference in out-ofplane exchange interactions ∆J zz = |J zz A − J zz B | between sublattices A and B of 0.92 meV for the AB-stacking and 0.04 meV for the AB'-stacking. Note that J zz A and J zz B are the sum of the out-of-plane exchange components of all interacting spin pairs in a unit cell.…”