Microscopic understanding of magnetic interactions in bilayer CrI3

Abstract

We performed a detailed microscopic analysis of the inter-layer magnetic couplings for bilayer CrI3. As the first step toward understanding the recent experimental observations and utilizing them for device applications, we estimated magnetic force response as well as total energy. Various van der Waals functionals unequivocally point to the ferromagnetic ground state for the low-temperature structured bilayer CrI3 which is further confirmed independently by magnetic force response calculations. The calculated orbital-dependent magnetic forces clearly show that eg-t2g interaction is the key to stabilize this ferromagnetic order. By suppressing this ferromagnetic interaction and enhancing antiferromagnetic orbital channels of eg-eg and t2g-t2g, one can realize the desirable antiferromagnetic order. We showed that high-temperature monoclinic stacking can be the case. Our results provide unique information and insight to understand the magnetism of multi-layer CrI3 paving the way to utilize it for applications.

Magnetism and magneto-optical effects in bulk and few-layer CrI3: a theoretical GGA + U study

“…explanation of this notable discrepancy between theory and experiment on BL CrI 3 is nontrivial. Indeed, very recently this problem has already been investigated theoretically by several groups [18][19][20][21]. These theoretical studies all showed that the interlayer magnetic coupling in BL CrI 3 is strongly stacking dependent and is also sensitive to the exchange-correlation functional used.…”

“…Although magnetic exchange coupling and magnetic anisotropy in ML CrI 3 have been theoretically investigated by several groups based on density functional calculations [14-17], they have not been studied in BL, TL and bulk CrI 3 . Furthermore, the interlayer exchange coupling in bulk and TL CrI 3 has not been addressed although that in the BL is presently under intensive investigations [18][19][20][21].MAE refers to the energy required to flip the magnetization from the easy to the hard axis, and is one of the principal specification parameters for a magnetic material. In fact, MAE is particularly important for 2D magnetic materials.…”

Valley polarization in monolayer CrX2 (X = S, Se) with magnetically doping and proximity coupling

“…The strongcorrelated correction is considered with GGA+U method to deal with the Cr's 3d electrons [49]. The effective onsite Coulomb interaction parameter (U) and exchange interaction parameter (J) are set to be 3.5 and 0.5 eV, respectively [20,[50][51][52]. The spin-orbit coupling (SOC) effect is taken into account in electronic structure calculations.…”

Van der Waals magnets: Wonder building blocks for two‐dimensional spintronics?

“…Besides the experimental effort in exploring the 2D magnetism, recent theoretical investigations have shown a strong dependence of the magnetic interlayer coupling in CrI 3 on stacking structure. In particular, a rhombohedral stacking structure is predicted to favor a ferromagnetic interlayer coupling, whereas a monoclinic stacking structure is coupled antiferromagnetically . For bulk CrI 3 crystal, a structural phase transition from a low‐temperature rhombohedral structure to a high‐temperature monoclinic structure is known to exist at ~200 K .…”

“…In particular, a rhombohedral stacking structure is predicted to favor a ferromagnetic interlayer coupling, whereas a monoclinic stacking structure is coupled antiferromagnetically. [70][71][72][73] For bulk CrI 3 crystal, a structural phase transition from a low-temperature rhombohedral structure to a high-temperature monoclinic structure is known to exist at~200 K. 57 Recently, the magnetic structure due to spin-lattice coupling in bilayer CrI 3 has been studied by second harmonic generation (SHG) at low temperatures. 74 The authors observed giant nonreciprocal SHG originating from layered antiferromagnetic order, which breaks both the spatial-inversion and time-reversal symmetries.…”