二維拓樸材料和自發磁化的結合具有實現量子反常霍爾效應（Quantum anomalous Hall effect, QAHE）的可能，而量子反常霍爾效應對於應用在低能耗的自旋電子元件上有極高的潛力。在這項研究中，我們利用自旋極化掃描穿隧顯微鏡（Spin-Polarized Scanning Tunneling Microscopy, SP-STM）來觀測具有磁性的錳（Mn）在 Bi/Ag(111) 表面原子尺度下的形貌及磁性結構。在高溫的條件下成長 Bi 在 Ag(111) 上時，Bi 在 Ag(111) 基板表面依照鍍量不同會形成兩種不同的態——$(\sqrt{3} \times \sqrt{3} )R30^\circ \ BiAg_2$的合金態以及$(p \times \sqrt{3} )\ Bi$的去合金態。形貌上來說，Mn 在 Bi/Ag(111) 上偏好在$(p \times \sqrt{3} )\ Bi$表面成長成平坦島嶼，並形成一個顯著的$(2 \times 2)$蜂巢狀網格結構，我們期待藉此能夠成長出具有磁性的二維拓墣絕緣體。

藉由改變磁場的 SP-STM 量測揭示了樣品表面表現出$(2 \times 2)$周期性的磁性訊號，其週期與表層的原子結構週期相同，不可能為蜂巢狀原子結構的磁性貢獻，因此我們提出這些磁信號來源於 Bi 蜂巢狀結構層下方最密堆積的 Mn。我們透過簡化的一維穿隧模型以及自旋穿隧理論進行對現有的自旋結構進行 SP-STM 模擬，我們的模擬顯示，磁性訊號所呈現的圖案與 Triple-q 反鐵磁自旋結構非常相似，我們可以通過調整掃描探針的自旋方向到特定角度在模擬中重現這個圖案。

The emergence of two-dimensional topological materials and spontaneous magnetization holds the potential for the realization of the quantum anomalous Hall effect, which holds great promise for applications in low-power electronic transmission devices. In this research, we employ spin-polarized scanning tunneling microscopy (SP-STM) to investigate the structural and magnetic characteristics of manganese (Mn) deposition on the Bi/Ag(111) surface. When growing Bi on Ag(111) under high-temperature condition, two different states of Bi form on the Ag(111) substrate depending on the deposition amount: an $(\sqrt{3} \times \sqrt{3} )R30^\circ \ BiAg_2$ alloying phase and a $(p \times \sqrt{3} )\ Bi$ dealloying phase. Morphologically, Mn on Bi/Ag(111) tends to grow into flat islands on the $(p \times \sqrt{3} )\ Bi$ surface. The deposition of Mn on Bi/Ag(111) gives rise to the formation of a remarkable $(2 \times 2)$ honeycomb lattice structure.

Field-dependent SP-STM measurements have unveiled magnetic signals exhibiting a $(2 \times 2)$ periodicity, matching the periodicity of the surface atomic structure. Since it is unlikely for the honeycomb atomic structure to contribute to magnetic properties, we propose that these magnetic signals originate from close-packed Mn beneath the Bi honeycomb layer. We simulate the existing spin structures using a simplified one-dimensional tunneling model and spin dependent tunneling theory in SP-STM. Our SP-STM simulations reveal that the magnetic contrast pattern closely resembles the triple-q spin state, and we can reproduce this pattern in simulation by adjusting the orientation of the tip to a specific angle.

[1] Gao, C. L., Wulfhekel, W. & Kirschner, J. Revealing the 120° antiferromagnetic néel structure in real space: One monolayer mn on ag(111). Phys. Rev. Lett. 101, 267205 (2008). URL https://link.aps.org/doi/10.1103/PhysRevLett.101.267205.
[2] Haze, M., Yoshida, Y. & Hasegawa, Y. Experimental verification of the rotational type of chiral spin spiral structures by spin-polarized scanning tunneling microscopy. Sci Rep 7, 13269 (2017). URL https://doi.org/10.1038/s41598-017-13329-9.
[3] Ferriani, P. et al. Atomic-scale spin spiral with a unique rotational sense: Mn monolayer on w(001). Phys. Rev. Lett. 101, 027201 (2008). URL https://link.aps.org/doi/10.1103/ PhysRevLett.101.027201.
[4] Yoshida, Y. et al. Conical spin-spiral state in an ultrathin film driven by higher-order spin interactions. Phys. Rev. Lett. 108, 087205 (2012). URL https://link.aps.org/doi/10. 1103/PhysRevLett.108.087205.
[5] Spethmann, J. et al. Discovery of magnetic single- and triple-q states in Mn/Re(0001). Phys. Rev. Lett. 124, 227203 (2020). URL https://link.aps.org/doi/10.1103/ PhysRevLett.124.227203.
[6] Zhang, K. H. L. et al. Observation of a surface alloying-to-dealloying transition during growth of bi on ag(111). Phys. Rev. B 83, 235418 (2011). URL https://link.aps.org/ doi/10.1103/PhysRevB.83.235418.
62
[7] Park, P., Cho, W. & Kim, C. e. a. Tetrahedral triple-q magnetic ordering and large sponta- neous hall conductivity in the metallic triangular antiferromagnet co1/3tas2. Nat Commun 14, 8346 (2023). URL https://doi.org/10.1038/s41467-023-43853-4.
[8] Kurz, P., Bihlmayer, G., Hirai, K. & Blügel, S. Three-dimensional spin structure on a two-dimensional lattice: Mn /cu(111). Phys. Rev. Lett. 86, 1106–1109 (2001). URL https://link.aps.org/doi/10.1103/PhysRevLett.86.1106.
[9] Hanke, J.-P. et al. Role of berry phase theory for describing orbital magnetism: From magnetic heterostructures to topological orbital ferromagnets. Phys. Rev. B 94, 121114 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.121114.
[10] Bedow, J. et al. Topological superconductivity induced by a triple-q magnetic structure. Phys. Rev. B 102, 180504 (2020). URL https://link.aps.org/doi/10.1103/PhysRevB. 102.180504.
[11] Heinze, S., Kurz, P. & Wortmann, D. e. a. Complex magnetism in ultra-thin films: atomic- scale spin structures and resolution by the spin-polarized scanning tunneling microscope. Appl Phys A 75, 25–36 (2002). URL https://doi.org/10.1007/s003390101052.
[12] Hoffmann, M. & Blügel, S. Systematic derivation of realistic spin models for beyond- heisenberg solids. Phys. Rev. B 101, 024418 (2020). URL https://link.aps.org/doi/10. 1103/PhysRevB.101.024418.
[13] Grytsiuk, S., Hanke, J. & Hoffmann, M. e. a. Topological–chiral magnetic interactions driven by emergent orbital magnetism. Nat Commun 11, 511 (2020). URL https://doi. org/10.1038/s41467-019-14030-3.
63

[14] Batista, C. D., Shifman, M., Wang, Z. & Zhang, S.-S. Principal chiral model in correlated electron systems. Phys. Rev. Lett. 121, 227201 (2018). URL https://link.aps.org/doi/ 10.1103/PhysRevLett.121.227201.
[15] Haldar, S., Meyer, S., Kubetzka, A. & Heinze, S. Distorted 3q state driven by topological- chiral magnetic interactions. Phys. Rev. B 104, L180404 (2021). URL https://link.aps. org/doi/10.1103/PhysRevB.104.L180404.
[16] Nickel,F.etal.Couplingofthetriple-qstatetotheatomiclatticebyanisotropicsymmetric exchange. Phys. Rev. B 108, L180411 (2023). URL https://link.aps.org/doi/10.1103/ PhysRevB.108.L180411.
[17] Ye,M.,Li,W.&Zhu,S.e.a.Carrier-mediatedferromagnetisminthemagnetictopological insulator cr-doped (sb, bi)2te3. Nat Commun 6, 8913 (2015). URL https://doi.org/10. 1038/ncomms9913.
[18] 黃勢棠. 單層錫烯成長於鐵磁性鈷奈米島 (2021).
[19] 莊益豪. 製備單層錫烯在鐵磁鈷奈米島嶼上 (2022).
[20] Malonda-Boungou, B., Meza-Aguilar, S., Debernardi, A. & Raji, A. Non-collinear mag- netism in mn monolayer on ag(111) fcc: Density functional calculations. Computational Condensed Matter 19, e00368 (2019). URL https://www.sciencedirect.com/science/ article/pii/S2352214318303149.
[21] Tian, S. et al. Internal flow and cavitation analysis of scroll oil pump by cfd method. Processes 9, 1975 (2021). URL https://doi.org/10.3390/pr9101705.
[22] Bishop, C. A. Vacuum deposition onto webs, films, and foils 63–80 (2007).
64

[23] Fedchak, J. A., Abbott, P. J., Hendricks, J. H., Arnold, P. C. & Peacock, N. T. Review Article: Recommended practice for calibrating vacuum gauges of the ionization type. Journal of Vacuum Science & Technology A 36, 030802 (2018). URL https://doi.org/ 10.1116/1.5025060.
[24] Cho, A. & Arthur, J. Molecular beam epitaxy. Progress in Solid State Chem- istry 10, 157–191 (1975). URL https://www.sciencedirect.com/science/article/pii/ 0079678675900059.
[25] Instruction manual for efm 2, efm 3, efm 3s, efm 4, efm 3t and efm 3i. Omicron Nano Technology (2008).
[26] Binnig,G.&Rohrer,H.Scanningtunnelingmicroscopy—frombirthtoadolescence.Rev. Mod. Phys. 59, 615–625 (1987). URL https://link.aps.org/doi/10.1103/RevModPhys. 59.615.
[27] Wiesendanger, R., Güntherodt, H.-J., Güntherodt, G., Gambino, R. J. & Ruf, R. Obser- vation of vacuum tunneling of spin-polarized electrons with the scanning tunneling mi- croscope. Phys. Rev. Lett. 65, 247–250 (1990). URL https://link.aps.org/doi/10.1103/ PhysRevLett.65.247.
[28] Tersoff, J. & Hamann, D. R. Theory and application for the scanning tunneling micro- scope. Phys. Rev. Lett. 50, 1998–2001 (1983). URL https://link.aps.org/doi/10.1103/ PhysRevLett.50.1998.
[29] Fischer, O., Kugler, M., Maggio-Aprile, I., Berthod, C. & Renner, C. Scanning tunneling spectroscopy of high-temperature superconductors. Rev. Mod. Phys. 79, 353–419 (2007). URL https://link.aps.org/doi/10.1103/RevModPhys.79.353.
65

[30] Bode,M.Spin-polarizedscanningtunnellingmicroscopy.ReportsonProgressinPhysics 66, 523 (2003). URL https://dx.doi.org/10.1088/0034-4885/66/4/203.
[31] 陳義斌. 自旋極化穿隧掃描顯微鏡研究錳於自旋阻挫系統與蜂巢狀結構 (2023).