Charge and spin photocurrents in the Rashba model

In metallic noncentrosymmetric crystals and at surfaces the response of spin currents and charge currents to applied electric fields contains contributions that are second order in the electric field, which are forbidden by symmetry in centrosymmetric systems. Thereby, photocurrents and spin photocurrents can be generated in inversion asymmetric metals by the application of femtosecond laser pulses. We study the laser-induced charge current in the ferromagnetic Rashba model with in-plane magnetization and find that this magnetic photogalvanic effect can be tuned to be comparable in size to the laser-induced photocurrents measured experimentally in magnetic bilayer systems such as Co/Pt. Additionally, we show that femtosecond laser pulses excite strong spin currents in the nonmagnetic Rashba model when the Rashba parameter is large.

Figure 1

Laser-induced charge-current density $J_{\alpha }$ vs Fermi energy ${\mathcal{E}}_{\mathrm{F}}$ for $\widehat{\mathit{n}}$ in the $y$ direction, ${\alpha }^{\mathrm{R}}=0.1\mathrm{eV}$ Å, $\mathrm{\Delta }V=1$ eV, and $\mathrm{\Gamma }=25\mathrm{meV}$. Some curves have been multiplied by the factor 10 for better visibility, as indicated in the legend.

Figure 2

Laser-induced charge-current density $J_{\alpha }$ vs broadening $\mathrm{\Gamma }$ for $\widehat{\mathit{n}}$ in the $y$ direction, ${\alpha }^{\mathrm{R}}=0.1\mathrm{eV}$ Å, $\mathrm{\Delta }V=1$ eV, and ${\mathcal{E}}_{\mathrm{F}}=1.36\mathrm{eV}$. Some curves have been multiplied by the factor 10 for better visibility, as indicated in the legend.

Figure 3

Laser-induced charge-current density $J_{\alpha }$ vs SOI strength ${\alpha }^{\mathrm{R}}$ for $\widehat{\mathit{n}}$ in the $y$ direction, $\mathrm{\Delta }V=1$ eV, ${\mathcal{E}}_{\mathrm{F}}=1.36\mathrm{eV}$, and $\mathrm{\Gamma }=25$ meV. Some curves have been multiplied by the factor 10 for better visibility, as indicated in the legend.

Figure 4

Laser-induced spin-current density $J_{\alpha }^s$ vs Fermi energy in the nonmagnetic Rashba model for the parameters ${\alpha }^{\mathrm{R}}=2\mathrm{eV}$ Å and $\mathrm{\Gamma }=136\mathrm{meV}$.

Figure 5

Laser-induced spin-current density $J_{\alpha }^s$ vs SOI strength ${\alpha }^{\mathrm{R}}$ in the nonmagnetic Rashba model for the parameters ${\mathcal{E}}_{\mathrm{F}}=1.36\mathrm{eV}$ and $\mathrm{\Gamma }=136\mathrm{meV}$.

Figure 6

Laser-induced spin-current density $J_{\alpha }^s$ vs SOI strength ${\alpha }^{\mathrm{R}}$ in the nonmagnetic Rashba model for the parameters ${\mathcal{E}}_{\mathrm{F}}=1.36\mathrm{eV}$ and $\mathrm{\Gamma }=25$ meV. Some curves have been multiplied by the factor 10 for better visibility, as indicated in the legend.