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Aiming to clarify the mechanisms governing the interlayer magnetic coupling,we have investigated the stacking energy and interlayer magnetism of bilayerCrBr$_3$ systemically. The magnetic ground states of bilayer CrBr$_3$ withdifferent R-type and H-type stacking orders are established, which is found tobe in good agreement with recent experiment (Science$\mathbf{366}$,983(2019)).Further analyses indicate that the stacking energy ismainly determined by the Coulomb interaction between the interlayernearest-neighbor Br-Br atoms. While interlayer magnetism can be understood by acompetition between super-super-exchange interactions involving$t_{2g}$-$t_{2g}$ and $t_{2g}$-$e_g$ orbitals and semi-covalent exchangeinteractions of $e_g$-$e_g$ orbitals. Our studies give an insightfulunderstanding for stacking order and interlayer magnetism of bilayer CrBr$_3$,which should be useful to understand quantum confinement effect of otherlayered magnets in two-dimensional limit.

Revealing the Underlying Mechanisms of Stacking Order and Interlayer Magnetism in Bilayer CrBr$_3$