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利用量子化学第一性原理计算, 对FeB20和Fe2B20团簇的几何构型、电子结构以及由激光诱导的超快自旋动力学进行了研究. 计算结果发现, FeB20团簇中Fe原子倾向吸附于B20管内, 而Fe2B20团簇的两个Fe原子分居管内外时更稳定. 后者由于磁原子个数的增多, 引入了更多的d电子态而表现出结构整体能级的下移; 同时, 由于该结构两磁原子吸附环境的不同, 使得其能态具有不同自旋局域的可能性. 基于体系所得多体电子基态和激发态, 在特定激光脉冲诱导下, 在两个团簇上均实现了亚皮秒时间尺度内的超快自旋翻转和自旋交叉两种动力学过程. 其中前者均可逆, 且保真度都高达89.7%及以上, 后者保真度略低, 均在78%及以下. 另外, 在Fe2B20团簇上, 实现了两个Fe原子之间的超快自旋转移动力学, 其所需激光能量由于初末态较大的能级差和较多的中间态参与而较之其他动力学最高. 本文工作为吸附磁原子的管状硼团簇体系上所实现的超快自旋动力学功能进行了预测, 可望对其未来的实验实现以及相关自旋逻辑功能器件的设计和应用提供理论指导.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 1 优化后的团簇结构 (侧视图和俯视图) (a) B20; (b) FeB20; (c) Fe2B20; 其中, 俯视图中的键长单位为 Å
Fig. 1. Side- and top-viewed optimized geometries of clusters: (a) B20; (b) FeB20; (c) Fe2B20. The bond lengths are in Å.
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
Fig. 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
Fig. 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 4 Fe2B20团簇上得到的超快自旋转移动力学, 其中初态、末态和中间态分别由黑色虚线、红色实线和点线表示
Fig. 4. Ultrafast spin-transfer scenario in Fe2B20. The initial, final, and intermediate states involved in the spin-transfer process 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
Fig. 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 
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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
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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
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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
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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