Laser-induced charge and spin photocurrents at the ${\mathrm{BiAg}}_2$ surface: A first-principles benchmark

Here, we report first-principles calculations of laser-induced photocurrents at the surface of a prototype Rashba system. By referring to Keldysh nonequilibrium formalism combined with the Wannier interpolation scheme, we perform first-principles electronic structure calculations of a prototype ${\mathrm{BiAg}}_2$ surface alloy, which is a well-known material realization of the Rashba model. In addition to the nonmagnetic ground state situation, we also study the case of in-plane magnetized ${\mathrm{BiAg}}_2$. We calculate the laser-induced charge photocurrents for the ferromagnetic case and the laser-induced spin photocurrents for both the nonmagnetic and the ferromagnetic cases. Our results confirm the emergence of very large in-plane photocurrents as predicted by the Rashba model and are in agreement with previous experimental measurements of THz emission generated at Bi/Ag interfaces. The resulting photocurrents satisfy all the symmetry restrictions with respect to the light helicity and the magnetization direction. We provide microscopic insights into the symmetry and magnitude of the computed currents based on the ab initio multiband electronic structure of the system, and scrutinize the importance of resonant two-band and three-band transitions for driven currents, thereby establishing a benchmark picture of photocurrents at Rashba-like surfaces and interfaces. Our work contributes to establishing the interfacial Rashba spin-orbit interaction as a major mechanism for the generation of in-plane photocurrents, which are of great interest in the field of ultrafast and terahertz spintronics.

Figure 1

(a) The crystal structure of the ${\mathrm{BiAg}}_2$ surface considered in this work shown from a top and side view. (b) The first Brillouin zone and the high-symmetry points. (c) The comparison between the first-principles (DFT, dotted blue line) and the interpolated (Wannier, solid red line) band structures. (d) The interpolated band structure of ${\mathrm{BiAg}}_2$ around the Fermi energy for the nonmagnetic (NM, solid red line) and the ferromagnetic (FM, dashed blue line) case. For the ferromagnetic case, an exchange field with a strength of 0.5 eV is applied in-plane along the $y$ axis.

Figure 2

Charge photocurrents in relation to (a) the lifetime broadening $\mathrm{\Gamma }$, (b) the Fermi energy level ${\mathcal{E}}_F$, and (c) the frequency of light $\hslash \omega$ for the ferromagnetic ${\mathrm{BiAg}}_2$ surface. The shown symmetry-allowed components are $J_x$ for circularly polarized light (shadowed dashed red line) and linearly polarized light along the $x$ (green line) or $y$ axis (black line), as well as $J_y$ for circularly polarized light (shadowed dotted blue line). The inset in (a) depicts only the three-band contributions to the ferromagnetic charge photocurrents, discussed in Sec. 5. (a), (b) $\hslash \omega =1.55$ eV; (b), (c) $\mathrm{\Gamma }=25$ meV. In (a), (c), the calculations are performed for true Fermi energy. For all calculations, the considered light intensity is $I=10$ GW/${\mathrm{cm}}^2$. With ${\epsilon }^{+}$, we denote circularly polarized light with $\lambda =+1$ helicity, while with $\epsilon \parallel {\widehat{\mathbf{e}}}_x\left({\widehat{\mathbf{e}}}_y\right)$, we denote linearly polarized light along $x\left(y\right)$.

Figure 3

Spin photocurrents in relation to (a) the lifetime broadening $\mathrm{\Gamma }$, (b) the Fermi energy level ${\mathcal{E}}_F$, and (c) the light frequency $\hslash \omega$ for the nonmagnetic ${\mathrm{BiAg}}_2$ surface. The symmetry-allowed components which are shown are the $J_x^x$ for circularly polarized light (shadowed dashed red line), as well as $J_y^x$ for circularly polarized light (shadowed dotted blue line) and linearly polarized light along the $x$ (green line) or $y$ (black line) axis. (a), (b) $\hslash \omega =1.55$ eV; (b), (c) $\mathrm{\Gamma }=25$ meV. In (a), (c), the calculations are performed for the true Fermi energy. For all calculations, the considered light intensity is $I=10$ GW/${\mathrm{cm}}^2$.

Figure 4

Spin photocurrents in relation to (a), (d), (g) the lifetime broadening $\mathrm{\Gamma }$, (b), (e), (h) the Fermi energy level ${\mathcal{E}}_F$, and (c), (f), (i) the light frequency $\hslash \omega$ for the ferromagnetic ${\mathrm{BiAg}}_2$ surface. In (a)–(c), $J_x^x$ and $J_y^x$ with circularly polarized light (shadowed dashed red and shadowed dotted blue lines, respectively) together with $J_y^x$ from linearly polarized along the $x$ (green line) or $y$ (black line) axis light are shown. In (d)–(f), $J_x^y$ and $J_y^y$ from circularly polarized light (shadowed dashed red and shadowed dotted blue lines, respectively) together with $J_x^y$ from linearly polarized along the $x$ (green line) or $y$ (black line) axis light are shown. In (g)–(i), $J_x^z$ and $J_y^z$ from circularly polarized light (shadowed dashed red and shadowed dotted blue lines, respectively) together with $J_y^z$ from linearly polarized along the $x$ (green line) or $y$ (black line) axis light are shown. In (a), (b), (d), (e), (g), (h), $\hslash \omega =1.55$ eV, and in (b), (c), (e), (f), (h), (i), $\mathrm{\Gamma }=25$ meV. In (a), (c), (d), (f), (g), (i), the calculations are performed at the true Fermi energy level. For all calculations, the considered light intensity is $I=10$ GW/${\mathrm{cm}}^2$.

Figure 5

Spin photocurrents in relation to the lifetime broadening $\mathrm{\Gamma }$ for the (a)–(c) nonmagnetic and the (d)–(f) ferromagnetic ${\mathrm{BiAg}}_2$ surface. $J_x^x$ and $J_y^x$ with circularly polarized light (shadowed dashed red and shadowed dotted blue lines, respectively) together with $J_y^x$ linearly polarized along the $x$ (green line) or $y$ (black line) axis are shown. In (a), (d), all the contributions to the spin photocurrents are presented, whereas in (b), (e), only the two-band and in (c), (f) only the three-band contributions are shown. For all cases, the calculations are performed at the true Fermi energy level with $\hslash \omega =1.55$ eV. For all calculations, the considered light intensity is $I=10$ GW/${\mathrm{cm}}^2$.

Figure 6

Band-resolved two-band contributions of the laser-induced (a) charge and (b) spin photocurrents for the ferromagnetic ${\mathrm{BiAg}}_2$ surface. Presented in (a) is the $J_x$ response and in (b) is the $J_y^x$ response, both for light linearly polarized along the $x$ axis. The horizontal dotted red lines at $\pm 1.55$ eV denote the energy of the laser pulse. The dashed red arrows depict two-band transitions between bands whose energy difference matches the laser pulse energy. In both cases, $\hslash \omega =1.55$ eV and $\mathrm{\Gamma }=25$ meV. Throughout the calculations, the considered light intensity is $I=10$ GW/${\mathrm{cm}}^2$.