First-principles study of ultrafast spin dynamics in FemB20 (m = 1, 2) clusters

Lu Xin; Xie Meng-Lin; Liu Jing; Jin Wei; Li Chun; Georgios Lefkidis; Wolfgang Hübner

doi:10.7498/aps.70.20210056

Abstract

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.

Keywords:

Authors and contacts

1.
School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China
2.
School of Physics, Beihang University, Beijing 100191, China
3.
Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, Kaiserslautern 67653, Germany
4.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding author: Jin Wei, jinwei@snnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11504223, 11872309) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JM1033)

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References

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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

Figure 1. Side- and top-viewed optimized geometries of clusters: (a) B₂₀; (b) FeB₂₀; (c) Fe₂B₂₀. The bond lengths are in Å.

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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.

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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.

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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

Figure 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.

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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.

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图 A1 团簇FeB₂₀与Fe₂B₂₀的其他稳定构型

Figure A1. Other stable geometries of clusters FeB₂₀ and Fe₂B₂₀.

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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
Structure	State	Energy/eV	$ \left\langle { {S}_{x} } \right\rangle $	$ \left\langle { {S}_{y} } \right\rangle $	$ \left\langle { {S}_{z} } \right\rangle $	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
Scenario	Structure	State	Energy/eV	$ \left\langle { {S}_{x} } \right\rangle $	$ \left\langle { {S}_{y} } \right\rangle $	$ \left\langle { {S}_{z} } \right\rangle $	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
Transfer	(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 state	Fidelity	Laser parameters
Scenario	Structure	Initial/Final state	Fidelity	θ/(º)	φ(º)	γ/(º)	FWHM /fs	Amplitude /(atomic units)	Energy /eV
Flip	FeB₂₀	$ \left\| {4} \right\rangle \to \left\| {6} \right\rangle $	89.7%	112.9	6.1	338.9	337.3	0.00997	0.299
Flip	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
Crossover	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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First-principles study of ultrafast spin dynamics in Fe_mB₂₀ (m = 1, 2) clusters

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Corresponding author: Jin Wei, jinwei@snnu.edu.cn

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