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Register a new userRevealing the Underlying Mechanisms of Stacking Order and Interlayer Magnetism in Bilayer CrBr$_3$
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Aiming to clarify the mechanisms governing the interlayer magnetic coupling, we have investigated the stacking energy and interlayer magnetism of bilayer CrBr$_3$ systemically. The magnetic ground states of bilayer CrBr$_3$ with different R-type and H-type stacking orders are established, which is found to be in good agreement with recent experiment (Science $mathbf{366}$,983(2019)).Further analyses indicate that the stacking energy is mainly determined by the Coulomb interaction between the interlayer nearest-neighbor Br-Br atoms. While interlayer magnetism can be understood by a competition between super-super-exchange interactions involving $t_{2g}$-$t_{2g}$ and $t_{2g}$-$e_g$ orbitals and semi-covalent exchange interactions of $e_g$-$e_g$ orbitals. Our studies give an insightful understanding for stacking order and interlayer magnetism of bilayer CrBr$_3$, which should be useful to understand quantum confinement effect of other layered magnets in two-dimensional limit.
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Diverse interlayer tunability of physical properties of two-dimensional layers mostly lies in the covalent-like quasi-bonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g. magnetism. Inspired by several recent experiments showing interlayer anti-ferromagnetically coupled CrI3 bilayers, we carried out first-principles calculations for CrI3 bilayers. We found that the anti-ferromagnetic coupling results from a new stacking order with the C2/m space group symmetry, rather than the graphene-like one with R3 as previously believed. Moreover, we demonstrated that the intra- and inter-layer couplings in CrI3 bilayer are governed by two different mechanisms, namely ferromagnetic super-exchange and direct-exchange interactions, which are largely decoupled because of their significant difference in strength at the strong- and weak-interaction limits. This allows the much weaker interlayer magnetic coupling to be more feasibly tuned by stacking orders solely. Given the fact that interlayer magnetic properties can be altered by changing crystal structure with different stacking orders, our work opens a new paradigm for tuning interlayer magnetic properties with the freedom of stacking order in two dimensional layered materials.
Recent transport experiments have demonstrated that the rhombohedral stacking trilayer graphene is an insulator with an intrinsic gap of 6meV and the Bernal stacking trilayer one is a metal. We propose a Hubbard model with a moderate $U$ for layered graphene sheets, and show that the model well explains the experiments of the stacking dependent energy gap. The on-site Coulomb repulsion drives the metallic phase of the non-interacting system to a weak surface antiferromagnetic insulator for the rhombohedral stacking layers, but does not alter the metallic phase for the Bernal stacking layers.
2D ferroelectrics with robust polarization down to atomic thicknesses provide novel building blocks for functional heterostructures. Experimental reports, however, remain scarce because of the requirement of a layered polar crystal. Here, we demonstrate a rational design approach to engineering 2D ferroelectrics from a non-ferroelectric parent compound via employing van der Waals assembly. Parallel-stacked bilayer boron nitride is shown to exhibit out-of-plane electric polarization that reverses depending on the stacking order. The polarization switching is probed via the resistance of an adjacently-stacked graphene sheet. Furthermore, twisting the boron nitride sheets by a small-angle changes the dynamics of switching due to the formation of moire ferroelectricity with staggered polarization. The ferroelectricity persists to room temperature while keeping the high mobility of graphene, paving the way for potential ultrathin nonvolatile memory applications.
Chromium trihalides, CrX$_3$ (with X = Cl, Br, I), are a family of layered magnetic materials that can be easily exfoliated to provide ferromagnetic monolayers. When two layers are stacked together to form a bilayer the interlayer exchange coupling can be either ferromagnetic or antiferromagnetic depending on the stacking sequence. Here we combine crystallographic arguments based on the close-packing condition with first-principles simulations to enumerate all possible stacking patterns in CrX$_3$ bilayers that preserve the spatial periodicity of each layer. We recover all configurations observed in bulk crystals and disclose stacking sequences with no bulk counterpart where the two layers have opposite chirality. Stacking sequences are ranked according to their relative stability and a preferential interlayer magnetic ordering is assigned to each of them. Simulations provide a consistent picture to frame all current experimental observations on bulk and exfoliated CrX$_3$ crystals, with interesting implications for future measurements, including synthetic bilayers with non-standard stacking patterns.
When two 2D electron gas layers, each at Landau level filling factor $ u=1/2$, are close together a condensate of interlayer excitons emerges at low temperature. Although the excitonic phase is qualitatively well understood, the incoherent phase just above the critical layer separation is not. Using a combination of interlayer tunneling spectroscopy and conventional transport, we explore the incoherent phase in samples both near the phase boundary and further from it. In the more closely spaced bilayers we find the electronic spectral functions narrower and the Fermi energy of the $ u = 1/2$ composite fermion metal smaller than in the more widely separated bilayers. We attribute these effects to a softening of the intralayer Coulomb interaction due to interlayer screening.
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