Simulation of Hot-Carrier Dynamics and Terahertz Emission in Laser-Excited Metallic Bilayers

We present a multiscale model that simulates optically induced spin currents in metallic bilayer structures that emit terahertz radiation after optical pulse excitation. We describe hot-electron transport in a metallic bilayer by a Boltzmann transport equation, which is solved numerically by a particle-in-cell approach. Optical excitation and propagation effects are taken into account by our determining the emitted terahertz waves from the excited-carrier dynamics. We apply this approach to an $\mathrm{Fe}$/$\mathrm{Pt}$ bilayer and show in detail how microscopic scattering effects and transport determine the emitted signal. The versatility of the approach presented here allows it to be readily adapted to a wide spectrum of spintronic-terahertz-emitter designs. As an example, we show how the terahertz generation efficiency, defined as the output-power-to-input-power ratio, can be increased and optimized with use of serially stacked layers in conjunction with terahertz antireflective coatings. We derive an analytical expression for the terahertz emission of a single layer that allows us to determine the relationship between the emitted field and the current profile that generates it.

Figure 1

A typical spintronic-terahertz-emitter structure. The red pulse represents the excitation by an optical field with magnetic field vector $H_x$, and the blue pulse shape represents the emitted terahertz field. The laser-induced spin current $j_s$ and the resulting charge current $j_c$ due to the inverse spin Hall effect are shown.

Figure 2

Absorption as a fraction of incident power for 800-nm $s$-polarized light in a $\mathrm{Fe}$(15 nm)$\mathrm{Pt}$(5 nm) layer as shown in Fig. 1: (a) for irradiation from the $\mathrm{Pt}$ side (solid line) and from the $\mathrm{Fe}$ side (dashed line); (b) optically induced spin current and (c) spectrum of the charge current after excitation with a 10-fs infrared laser pulse. FT, Fourier transform; ISHE, inverse spin Hall effect.

Figure 3

Ab initio input for the computation of the hot-electron dynamics: (a) carrier velocities and (b) electronic lifetimes. The energy is measured from the Fermi energy. The data are taken from Ref. [20] for $v_{\mathrm{Fe}}$, $v_{\mathrm{Pt}}$, and ${\tau }_{\mathrm{Pt}}$ and from Ref. [21] for ${\tau }_{\mathrm{Fe}}$.

Figure 4

(a) Emitted spectrum for different durations of the exciting laser pulse [10 fs (light blue) to 100 fs (dark blue) in steps of 10 fs] at a wavelength of 800 nm. (b) Position of the spectral maximum (dots) and its value (crosses) normalized to the strongest pulse. (c) Spectral width at 50% of the maximum value (dots) and comparison with the simple approximation of the inverse of the FWHM (solid line).

Figure 5

a) Composite structure with ARC and multiple SEs in series. The distance between ARC-SE-ARC structures is denoted by $\mathrm{\Delta }$. (b) Intensity normalized to the emission of a single structure for different distances and increasing number of layers.

Figure 6

Spintronic emitter structure with complex refractive index $\tilde{n}$, thickness $d$, and constant polarization density $j_c$. The surrounding semi-infinite layer is nonabsorbing with refraction index $n_b$. $R$ and $L$ denote the electric wave components on the right and left of the optical interfaces, respectively. The right-propagating waves are indicated by $+$ and the left-propagating waves are indicated by $-$.

Figure 7

Transmission amplitude (a) and attenuation factor (b) in iron (orange lines) and platinum (blue lines) layers of different thicknesses depending on frequency. The cases $d=1\mathrm{nm}$ (solid lines), $d=5\mathrm{nm}$ (dashed lines), and $d=10\mathrm{nm}$ (dotted lines) are shown. The parameters for the calculation of the complex refractive index in both materials are taken from Ref. [34].