1State Key Laboratory of Powder Metallurgy, and Powder Metallurgy Research Institute, Central South University, Changsha 410083, China 2School of Physics and Electronics, and Hunan Key Laboratory for Super-Microstructure and Ultrafast Process, Central South University, Changsha 410083, China 3School of Physics and Technology, Xinjiang University, Urumqi 830046, China
Abstract：Stacking-dependent magnetism in van der Waals materials has caught intense interests. Based on the first principle calculations, we investigate the coupling between stacking orders and interlayer magnetic orders in bilayer H-VSe$_{2}$. It is found that there are two stable stacking orders in bilayer H-VSe$_{2}$, named AB-stacking and A$^{\prime}$B-stacking. Under standard DFT framework, the A$^{\prime}$B-stacking prefers the interlayer AFM order and is semiconductive, whereas the AB-stacking prefers the FM order and is metallic. However, under the DFT+$U$ framework both the stacking orders prefer the interlayer AFM order and are semiconductive. By detailedly analyzing this difference, we find that the interlayer magnetism originates from the competition between antiferromagnetic interlayer super-superexchange and ferromagnetic interlayer double exchange, in which both the interlayer Se-4$p_{z}$ orbitals play a crucial role. In the DFT+$U$ calculations, the double exchange is suppressed due to the opened bandgap, such that the interlayer magnetic orders are decoupled with the stacking orders. Based on this competition mechanism, we propose that a moderate hole doping can significantly enhance the interlayer double exchange, and can be used to switch the interlayer magnetic orders in bilayer VSe$_{2}$. This method is also applicable to a wide range of semiconductive van der Waals magnets.
Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H, Yao W, Xiao D, Jarillo-Herrero P and Xu X D 2017 Nature546 270
Li T X, Jiang S W, Sivadas N, Wang Z F, Xu Y, Weber D, Goldberger J E, Watanabe K, Taniguchi T, Fennie C J, Mak K F and Shan J 2019 Nat. Mater.18 1303
[10]
Song T C, Fei Z Y, Yankowitz M, Lin Z, Jiang Q N, Hwangbo K, Zhang Q, Sun B S, Taniguchi T, Watanabe K, McGuire M A, Graf D, Cao T, Chu J H, Cobden D H, Dean C R, Xiao D and Xu X D 2019 Nat. Mater.18 1298
[11]
Gong C, Li L, Li Z L, Ji H W, Stern A, Xia Y, Cao T, Bao W, Wang C Z, Wang Y A, Qiu Z Q, Cava R J, Louie S G, Xia J and Zhang X 2017 Nature546 265
[12]
Deng Y J, Yu Y J, Song Y C, Zhang J Z, Wang N Z, Sun Z Y, Yi Y F, Wu Y Z, Wu S W, Zhu J Y, Wang J, Chen X H and Zhang Y B 2018 Nature563 94
[13]
Bonilla M, Kolekar S, Ma Y J, Diaz H C, Kalappattil V, Das R, Eggers T, Gutierrez H R, Phan M H and Batzill M 2018 Nat. Nanotechnol.13 289
[14]
O'Hara D J, Zhu T C, Trout A H, Ahmed A S, Luo Y K, Lee C H, Brenner M R, Rajan S, Gupta J A, McComb D W and Kawakami R K 2018 Nano Lett.18 3125
[15]
Hirahara T, Eremeev S V, Shirasawa T, Okuyama Y, Kubo T, Nakanishi R, Akiyama R, Takayama A, Hajiri T, Ideta S, Matsunami M, Sumida K, Miyamoto K, Takagi Y, Tanaka K, Okuda T, Yokoyama T, Kimura S, Hasegawa S and Chulkov E V 2017 Nano Lett.17 3493
2020, Vol. 37 
