Anisotropic spin relaxation in exchange-coupled ferromagnet/topological-insulator $\mathrm{Fe}\text{/}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ heterojunctions (2024)

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  Figure 1

  (a) Schematic diagram of measurement configuration and defined coordinate system. (b) X-ray diffraction and low-energy electron diffraction pattern of 9-QL $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ on Si(111). The arrow points to the $\langle 110\rangle$ direction ($\mathrm{\Gamma }-K)$ of grown $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$, which is defined as the $x$ axis. (c) and (d) Real part of $S_{21}$ vs magnetic field at different frequencies for $\mathrm{Fe}\left(11\mathrm{nm}\right)/\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3\left(3\mathrm{QL}\right)/\mathrm{Si}\left(111\right)$ (FBS-3) and $\mathrm{Fe}\left(11\mathrm{nm}\right)/\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3\left(9\mathrm{QL}\right)/\mathrm{Si}\left(111\right)$ (FBS-9), respectively. (e) Resonance field $H_{\mathrm{res}}$@16 GHz at different azimuthal ${\phi }_H$ for FBS-3 and FBS-9 (f), respectively. The solid lines are fitting curves.

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  Figure 2

  Top panel: (a)–(c) Resonance linewidth $\mathrm{\Delta }H$ vs frequency $f$ along the separate azimuthal direction with ${\phi }_H=0^{\circ },{30}^{\circ },{60}^{\circ },{90}^{\circ }$ for FBS-9, FBS-3, and FCBS-9 samples. EA and HA represent the easy and hard axes of magnetic anisotropy. The green, yellow, purple, and pink solid lines are fitting curves. Bottom panel: (d)–(f) The obtained value of Gilbert damping factor $\alpha$ vs azimuthal ${\phi }_H$. The red solid lines are a guide for the eyes.

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  Figure 3

  (a) Typical spin-pumping voltage response $V_{\mathrm{sp}}$ as a function of the magnetic field. The colorful curves are experimental raw data at different ${\theta }_H$ from $0^{\circ }$ to ${85}^{\circ }$. The microwave is fixed at 10 GHz with a power of 50 mW. The inset shows the schematic image of the measurement configuration. (b) The experimental resonance field $H_{\mathrm{res}}$ vs ${\theta }_H$ at 10 GHz (top panel). The red solid line is the simulated curve. The calculated magnetization angle ${\theta }_M$ vs ${\theta }_H$ is shown in the bottom panel.

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  Figure 4

  The ${\theta }_H$ dependence of spin-to-charge conversion voltage $V_{\mathrm{IEE}}\left({\theta }_H\right)$ for FBS-9, FBS-3, and FCBS-9 along the EA direction (a)–(c) and along the HA direction (d)–(f), respectively. The solid lines are best-fitted curves. The dashed lines are plotted for comparison. (g) Comparison of Gilbert damping factor and spin relaxation time for FBS-9, FBS-3, and FCBS-9 along the EA and HA directions.

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  Figure 5

  Comparison of the band structure of $\mathrm{Fe}\left(6\mathrm{ML}\right)/\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3\left(9\mathrm{QL}\right)$ and spin polarization ${\sigma }_z$ component distribution along $\mathrm{\Gamma }\text{−}K$ and $\mathrm{\Gamma }\text{−}M$. (a) Overall energy band of Fe-${\mathrm{Bi}}_2{\mathrm{Se}}_3$ when magnetization is along $\mathrm{\Gamma }\text{−}M$ (red curve, $\langle 100\rangle$ direction) and $\mathrm{\Gamma }\text{−}K$ (black curve, $\langle 110\rangle$ direction). Spin polarization ${\sigma }_z$ component distribution near Fermi level when magnetization of Fe is along $\langle 100\rangle$ (b) and $\langle 110\rangle$ (c), respectively. The color of the right side ($\mathrm{\Gamma }\text{−}M$) in (c) is much darker than that in (b) ($\mathrm{\Gamma }\text{−}K$) near Fermi level, indicating the modulation of the ${\sigma }_z$ component when alternating the magnetization. The blue and red colors depict the relative magnitude of the ${\sigma }_z$ component.

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