Femtosecond Coherent Control of Spins in (Ga,Mn)As Ferromagnetic Semiconductors Using Light

Using density matrix equations of motion, we predict a femtosecond collective spin tilt triggered by nonlinear, near-ultraviolet ($\sim 3\mathrm{eV}$), coherent photoexcitation of (Ga,Mn)As ferromagnetic semiconductors with linearly polarized light. This dynamics results from carrier coherences and nonthermal populations excited in the $\{111\}$ equivalent directions of the Brillouin zone and triggers a subsequent uniform precession. We predict nonthermal magnetization control by tuning the laser frequency and polarization direction. Our mechanism explains recent ultrafast pump-probe experiments.

Figure 1

Femtosecond Mn spin dynamics for hole relaxation faster than the optical pulse. (a) and (b): $\Delta S_z/S\approx \Delta {\theta }_K/{\theta }_K$ of the two in-plane magnetic memory states $X^{-}$ (solid line) and $Y^{+}$ (dotted line) for two frequencies ${\omega }_p$ that excite different valence bands. Dashed-dotted curve in Fig. 1b: ${\omega }_p=1.6\mathrm{eV}$. Symbols: nonthermal dynamics (${\mathbf{H}}^{\mathrm{th}}=0$). Inset: Experiment [5] for $X^{-}$ and $Y^{+}$, ${\omega }_p=3.1\mathrm{eV}$. (c): Zero-$\mathbf{k}$ magnon oscillations following (a). (d): Populations and intervalence band coherences (inset) corresponding to (b). ${\Delta }_{\mathrm{pd}}=130\mathrm{meV}$, $T_2=33\mathrm{fs}$, $K_c=0.014\mathrm{meV}$, $K_u=K_c/3$, $K_{uz}=5K_c$, $\alpha =0.03$, $E=2\times {10}^5\mathrm{V}/\mathrm{cm}$ ($d\sim 0.6–2\mathrm{meV}$).

Figure 2

(a): Femtosecond Mn spin dynamics for different $T_1$. (b) Hole population relaxation corresponding to (a). (c) and (d): Control, via the optical field polarization, of femtosecond dynamics (c) and zero-momentum magnon oscillations (d). $d\sim 0.1\mathrm{meV}$. Other parameters as in Fig. 1a.

Figure 3

Photoexcited total hole spin components parallel and perpendicular to ${\mathbf{S}}_0$: (a) Full calculation for the parameters of Fig. 2 (b) $H_{\mathrm{SO}}=0$.