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In this study, we use first-principles calculations to investigate the geometry, the electronic and the magnetic structure as well as to propose the laser-induced ultrafast spin dynamics on the tubular FeB20 and Fe2B20 clusters. Our results show that the FeB20 is a stable configuration when its Fe atom gets preferably adsorbed inside the B20 tube, while the Fe2B20 is more stable configuration when one of its two Fe atoms is located inside and the other outside the boron tube. In the latter cluster, due to the higher number of d states introduced by the additional magnetic atom, the density-of-states in the low-energy region becomes higher, thus leading to richer spin dynamics. The different local geometries of the two Fe atoms lead to a multitude of many-body states with high degree of spin-density localization. Based on the calculated ground state and excited states and by using suitably tailored laser pulses we achieve ultrafast spin-flip and spin crossover scenarios for both structures. Besides, the spin-flips reach a high fidelity (above 89.7%) and are reversible, while the crossovers have lower fidelity (below 78%) and are irreversible. We also propose an ultrafast spin-transfer process from Fe2 to Fe1 for Fe2B20. The present investigation, in which we predict various ultrafast spin dynamic taken by magnetic atoms absorbed inside and outside of tubular boron clusters, is expected to provide significant theoretical guidance for the future experimental implementation and the potential applications of the relevant spin logic functional devices.
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图 2 FeB20与Fe2B20的SAC-CI能级, 黑色虚线表示单重态, 红色实线表示三重态. 其中, 各自旋动力学所涉及的有关初、末态在未考虑自旋轨道耦合时的能级位置被明确标出
Figure 2. The SAC-CI energy levels of clusters FeB20 and Fe2B20. The singlet and triplet terms are denoted by the black dashed and red solid lines, respectively. The related terms from which the involved initial and final states in the spin dynamics to be discussed later originate before the inclusion of SOC are marked.
图 3 超快自旋翻转动力学 (a) FeB20团簇的自旋翻转过程; (b) Fe2B20团簇的自旋翻转过程. 其中各动力学中初态、末态和中间态分别由黑色虚线、红色实线和点线表示
Figure 3. Ultrafast spin flip scenarios: (a) Spin-flip process in FeB20; (b) spin-flip process in Fe2B20. The initial, final, and intermediate states involved in each of the spin-flip processes are represented by the black dashed, red solid, and dotted lines, respectively.
图 5 超快自旋交叉动力学 (a) FeB20团簇的自旋交叉过程; (b) Fe2B20团簇的自旋交叉过程; 其中各动力学中初态、末态和中间态分别由黑色虚线、红色实线和点线表示
Figure 5. Ultrafast spin crossover scenarios: (a) Spin-crossover process in FeB20; (b) spin-crossover process in Fe2B20. The initial, final, and intermediate states involved in each of the spin-crossover processes are represented by black dashed, red solid, and dotted lines, respectively.
表 1 Fe2B20中具有单磁中心自旋局域能态的能量、自旋期望值及自旋密度
Table 1. Energies, spin expectation values, and spin density of the states with spin localized on one single magnetic atom for cluster Fe2B20.
Structure State Energy/eV $ \left\langle { {S}_{x} } \right\rangle $ $ \left\langle { {S}_{y} } \right\rangle $ $ \left\langle { {S}_{z} } \right\rangle $ Spin density Fe1 Fe2 B20 $ \left| {1} \right\rangle $ 0 0.38 –0.87 0 0.001 1.919 0.015 $ \left| {2} \right\rangle $ 0.001 –0.59 0.73 0 0.001 1.911 0.015 $ \left| {5} \right\rangle $ 0.513 0.21 –0.42 0 0.002 0.946 0.023 $ \left| {6} \right\rangle $ 0.515 –0.12 0.46 0 0.002 0.962 0.023 $ \left| {17} \right\rangle $ 1.797 0.16 –0.72 0 0.022 1.473 0.224 $ \left| {18} \right\rangle $ 1.797 –0.42 0.05 0 0.013 0.839 0.13 Fe2B20 $ \left| {19} \right\rangle $ 1.797 0.26 0.67 0 0.021 1.432 0.22 (B: θ = 90°, φ = 90°) $ \left| {25} \right\rangle $ 2.002 0.41 –0.35 0 0.004 1.099 0.120 $ \left| {26} \right\rangle $ 2.003 –0.23 0.54 0 0.005 1.189 0.133 $ \left| {39} \right\rangle $ 2.658 –0.02 –0.63 0 1.114 0.084 0.261 $ \left| {41} \right\rangle $ 2.659 –0.01 0.63 0 1.114 0.084 0.261 $ \left| {56} \right\rangle $ 2.948 0.42 –0.63 0 0.026 1.412 0.305 $ \left| {57} \right\rangle $ 2.949 –0.52 0.55 0 0.026 1.411 0.303 表 2 各自旋动力学过程中初、末态的能量、自旋期望值与自旋密度
Table 2. Energies, spin expectation values, and spin densities of the initial and final states of each scenario.
Scenario Structure State Energy/eV $ \left\langle { {S}_{x} } \right\rangle $ $ \left\langle { {S}_{y} } \right\rangle $ $ \left\langle { {S}_{z} } \right\rangle $ Spin density Fe1 Fe2 Flip FeB20 $ \left| {4} \right\rangle $ 1.021 –0.94 0 0 1.291 — (B: θ = 90°, φ = 90°) $ \left| {6} \right\rangle $ 1.022 0.94 0 0 1.291 — Fe2B20 $ \left| {8} \right\rangle $ 0.856 0 0 0.89 0.006 1.785 (B: θ = 0°, φ = 90°) $ \left| {9} \right\rangle $ 0.857 0 0 –0.89 0.006 1.785 Transfer Fe2B20 $ \left| {1} \right\rangle $ 0 0.38 –0.87 0 0.001 1.919 (B: θ = 90°, φ = 90°) $ \left| {41} \right\rangle $ 2.659 0.01 0.63 0 1.114 0.084 Crossover FeB20 $ \left| {6} \right\rangle $ 1.022 0.94 0 0 1.291 — (B: θ = 90°, φ = 90°) $ \left| {7} \right\rangle $ 1.133 0 0 0 0 — Fe2B20 $ \left| {37} \right\rangle $ 2.371 0 0 0 0 0 (B: θ = 90°, φ = 90°) $ \left| {45} \right\rangle $ 2.784 0 –0.52 0 0.090 0.873 表 3 超快自旋动力学过程所需的激光参数, 其中 θ和φ为入射激光在球坐标系下的方位角, γ为入射激光振动方向和光平面的夹角, FWHM为激光脉冲的半高全宽
Table 3. Laser parameters for the achieved scenarios. Here, θ and φ denote the angles of the incidence in spherical coordinates, and γ is the angle between the polarization of the light and the optical plane. FWHM is the full width at half maximum of the laser pulse.
Scenario Structure Initial/Final
stateFidelity Laser parameters θ/(º) φ(º) γ/(º) FWHM
/fsAmplitude
/(atomic units)Energy
/eVFlip FeB20 $ \left| {4} \right\rangle \to \left| {6} \right\rangle $ 89.7% 112.9 6.1 338.9 337.3 0.00997 0.299 Fe2B20 $ \left| {8} \right\rangle \to \left| {9} \right\rangle $ 93.5% 156.4 122.4 77.7 466.2 0.00634 2.114 Transfer Fe2B20 $ \left| {1} \right\rangle \to \left| {41} \right\rangle $ 91.9% 244.7 91.4 225.3 92.3 0.00781 2.661 Crossover FeB20 $ \left| {6} \right\rangle \to \left| {7} \right\rangle $ 77.9% 61.0 321.4 82.9 318.5 0.00783 0.212 Fe2B20 $ \left| {37} \right\rangle \to \left| {45} \right\rangle $ 74.5% 297.2 356.1 301.5 352.0 0.00306 0.416 表 A1 FeB20 and Fe2B20团簇所计算能态在未考虑SOC和考虑SOC之后的能量值(单位: eV)
Table A1. Energy values of the calculated states of clusters FeB20 and Fe2B20 before and after the inclusion of SOC (in eV)
FeB20 Fe2B20 Before SOC After SOC Before SOC After SOC Singlet 1.131 (1 1A') 1.133 1.504 (1 1A') 1.489 1.133 (2 1A') 1.134 1.850 (1 1A'') 1.857 2.320 (1 1A'') 2.319 2.199 (2 1A') 2.203 2.545 (SAC) 2.554 2.361 (SAC) 2.371 2.676 (2 1A'') 2.677 2.587 (3 1A') 2.592 2.676 (3 1A') 2.677 2.801 (2 1A'') 2.806 3.130 (3 1A'') 3.132 2.843 (4 1A') 2.845 3.636 (4 1A'') 3.638 2.996 (3 1A'') 3.002 4.266 (5 1A'') 4.269 3.133 (5 1A') 3.136 4.272 (4 1A') 4.272 3.429 (4 1A'') 3.434 4.282 (5 1A') 4.285 3.632 (5 1A'') 3.637 Triplet 0.000 (1 3A') 0.000 0.0005 0.001 0.000 (1 3A') 0.000 0.0007 0.002 1.019 (2 3A') 1.021 1.021 1.022 0.508 (1 3A'') 0.511 0.513 0.515 1.291 (3 3A') 1.271 1.271 1.294 0.851 (2 3A') 0.854 0.857 0.857 1.293 (1 3A'') 1.295 1.313 1.317 1.545 (2 3A'') 1.548 1.551 1.570 1.476 (2 3A'') 1.475 1.478 1.478 1.668 (3 3A') 1.673 1.673 1.673 2.361 (3 3A'') 2.363 2.363 2.364 1.793 (4 3A') 1.797 1.797 1.797 2.945 (4 3A'') 2.947 2.947 2.948 1.984 (5 3A') 1.989 1.989 1.989 3.119 (5 3A'') 3.120 3.121 3.121 1.997 (3 3A'') 2.001 2.002 2.003 3.462 (4 3A') 3.464 3.465 3.466 2.089 (6 3A') 2.093 2.094 2.094 3.467 (6 3A'') 3.470 3.471 3.471 2.100 (4 3A'') 2.105 2.105 2.105 3.471 (7 3A'') 3.473 3.473 3.474 2.112 (7 3A') 2.113 2.116 2.116 3.743 (5 3A') 3.745 3.745 3.745 2.653 (8 3A') 2.658 2.658 2.659 3.753 (8 3A'') 3.755 3.755 3.756 2.707 (5 3A'') 2.711 2.713 2.714 3.990 (6 3A') 3.989 3.990 3.994 2.779 (9 3A') 2.784 2.784 2.784 4.000 (7 3A') 4.003 4.008 4.008 2.783 (6 3A'') 2.787 2.788 2.788 4.419 (8 3A') 4.421 4.421 4.421 2.934 (10 3A') 2.939 2.939 2.940 4.435 (9 3A'') 4.436 4.436 4.438 2.943 (7 3A'') 2.948 2.949 2.952 4.436 (9 3A') 4.438 4.440 4.440 3.144 (8 3A'') 3.150 3.151 3.152 4.536 (10 3A') 4.528 4.528 4.539 3.301 (9 3A'') 3.305 3.306 3.306 4.540 (10 3A'') 4.543 4.554 4.557 3.338 (10 3A'') 3.343 3.343 3.344 -
[1] Bogani L, Wernsdorfer W 2008 Nat. Mater. 7 179Google Scholar
[2] Khajetoorians A A, Heinrich A J 2016 Science 352 296Google Scholar
[3] Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, Von Molnar S, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488Google Scholar
[4] Prinz G A 1998 Science 282 1660Google Scholar
[5] Bader S D, Parkin S S P 2010 Annu. Rev. Condens. Matter Phys. 1 71Google Scholar
[6] Dietl T 2005 J. Magn. Magn. Mater. 290-291 14Google Scholar
[7] Baibich M N, Broto J M, Fert A, Nguyen Van Dau F, Petroff F 1988 Phys. Rev. Lett. 61 2472Google Scholar
[8] Beaurepaire E, Merle J C, Daunois A, Bigot J Y 1996 Phys. Rev. Lett. 76 4250Google Scholar
[9] Scholl A, Baumgarten L, Jacquemin R, Eberhardt W 1997 Phys. Rev. Lett. 79 5146Google Scholar
[10] Pfau B, Schaffert S, Müller L, Gutt C, Al-shemmary. A, Büttner F, Delaunay R, Düsterer S, Flewett S, Frömter R, Geilhufe J, Guehrs E, Günther C M, Hawaldar R, Hille M, Jaouen N, Kobs A, Li K, Mohanty J, Redlin H, Schlotter W F, Stickler D, Treusch R, Vodungbo B, Kläui M, Oepen H P, Lüning J, Grübel G, Eisebitt S 2012 Nat. Commun. 3 1100Google Scholar
[11] Koopmans B, Ruigrok J J M, Longa F D, de Jonge W J M 2005 Phys. Rev. Lett. 95 267207Google Scholar
[12] Steiauf D, Fähnle M 2009 Phys. Rev. B 79 140401Google Scholar
[13] Battiato M, Carva K, Oppeneer P M 2010 Phys. Rev. Lett. 105 027203Google Scholar
[14] Bigot J Y, Vomir M, Beaurepaire E 2009 Nat. Phys. 5 515Google Scholar
[15] Gómez-Abal R, Hübner W 2002 Phys. Rev. B 65 195114Google Scholar
[16] Zhang Z Z, Cui B, Wang G Z, Ma B, Jin Q Y, Liu Y W 2010 Appl. Phys. Lett. 97 172508Google Scholar
[17] Zhang W, Liu Q, Yuan Z, Xia K, He W, Zhan Q F, Zhang X Q, Cheng Z H 2019 Phys. Rev. B 100 104412Google Scholar
[18] Lefkidis G, Reyes S A 2016 Phys. Rev. B 94 144433Google Scholar
[19] 李春, 杨帆, Lefkidis G, Hübner W 2011 物理学报 60 017802Google Scholar
Li C, Yang F, Lefkidis G, Hübner W 2011 Acta Phys. Sin. 60 017802Google Scholar
[20] Chaudhuri D, Xiang H P, Lefkidis G, Hübner W 2014 Phys. Rev. B 90 245113Google Scholar
[21] Jin W, Li C, Lefkidis G, Hübner W 2014 Phys. Rev. B 89 024419Google Scholar
[22] Chaudhuri D, Lefkidis G, Hübner W 2017 Phys. Rev. B 96 184413Google Scholar
[23] Li C, Zhang S B, Jin W, Lefkidis G, Hübner W 2014 Phys. Rev. B 89 184404Google Scholar
[24] Lefkidis G, Hübner W 2007 Phys. Rev. B 76 014418Google Scholar
[25] Dong C D, Lefkidis G, Hübner W 2013 Phys. Rev. B 88 214421Google Scholar
[26] Hübner W, Lefkidis G 2014 Phys. Rev. B 90 024401Google Scholar
[27] Liu J, Li C, Jin W, Lefkidis G, Hübner W 2021 Phys. Rev. Lett. 126 037402Google Scholar
[28] Li J H, Sun F, Du H L, Hong H L, Wang K H, Bian J 2019 Univ. Chem. Educ. 34 117Google Scholar
[29] Kiran B, Bulusu S, Zhai H J, Yoo S, Zeng X C, Wang L S 2005 Proc. Natl. Acad. Sci. U. S. A. 102 961Google Scholar
[30] An W, Bulusu S, Gao Y, Zeng X C 2006 J. Chem. Phys. 124 154310Google Scholar
[31] Marques M A L, Botti S 2005 J. Chem. Phys. 123 014310Google Scholar
[32] Tian J F, Xu Z C, Shen C M, Liu F, Xu N S, Gao H J 2010 Nanoscale 2 1375Google Scholar
[33] 刘立仁, 雷雪玲, 陈杭, 祝恒江 2009 物理学报 58 5355Google Scholar
Liu L R, Lei X L, Chen H, Zhu H J 2009 Acta Phys. Sin. 58 5355Google Scholar
[34] Oger E, Crawford N R M, Kelting R, Weis P, Kappes M M, Ahlrichs R 2007 Angew. Chem. Int. Edit. 46 8503Google Scholar
[35] Li W L, Romanescu C, Jian T, Wang L S 2012 J. Am. Chem. Soc. 134 13228Google Scholar
[36] Liu C S, Wang X F, Ye X J, Yan X H, Zeng Z 2014 J. Chem. Phys. 141 194306Google Scholar
[37] Liang W Y, Das A, Dong X, Cui Z H 2018 Phys. Chem. Chem. Phys. 20 16202Google Scholar
[38] Xu C, Cheng L J, Yang J L 2014 J. Chem. Phys. 141 124301Google Scholar
[39] Tam N M, Pham H T, Duong L V, Pham-Ho, My P, Nguyen M T 2015 Phys. Chem. Chem. Phys. 17 3000Google Scholar
[40] Ruan W, Xie A D, Wu D L, Luo W L, Yu X G 2014 Chin. Phys. B 23 033101Google Scholar
[41] 阮文, 余晓光, 谢安东, 伍冬兰, 罗文浪 2014 物理学报 63 243101Google Scholar
Ruan W, Yu X G, Xie A D, Wu D L, Luo W L 2014 Acta Phys. Sin. 63 243101Google Scholar
[42] 雷雪玲, 祝恒江, 葛桂贤, 王先明, 罗有华 2008 物理学报 57 5491Google Scholar
Lei X L, Zhu H J, Ge G X, Wang X M, Luo Y H 2008 Acta Phys. Sin. 57 5491Google Scholar
[43] Popov I A, Jian T, Lopez G V, Boldyrev A I, Wang L S 2015 Nat. Commun. 6 8654Google Scholar
[44] Penev E S, Bhowmick S, Sadrzadeh A, Yakobson B I 2012 Nano Lett. 12 2441Google Scholar
[45] Li X Y, Li X X, Yang J L 2019 J. Phys. Chem. Lett. 10 4417Google Scholar
[46] Liu J, Zhang Y M, Li C, Jin W, Lefkidis G, Hübner W 2020 Phys. Rev. B 102 024416Google Scholar
[47] Hübner W, Kersten S, Lefkidis G 2009 Phys. Rev. B 79 184431Google Scholar
[48] Li C, Jin W, Xiang H P, Lefkidis G, Hübner W 2011 Phys. Rev. B 84 054415Google Scholar
[49] Frisch M J, Trucks G W, Schlegel H B, et al. 2016 Gaussian16 Revision B. 01 (Gaussian Inc., Wallingford, CT)
[50] Jin W, Rupp F, Chevalier K, Wolf M M N, Colindres Rojas M, Lefkidis G, Krüger H J, Diller R, Hübner W 2012 Phys. Rev. Lett. 109 267209Google Scholar
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