Coherent Magnetization Precession in Ferromagnetic (Ga,Mn)As Induced by Picosecond Acoustic Pulses

We show that the magnetization of a thin ferromagnetic (Ga,Mn)As layer can be modulated by picosecond acoustic pulses. In this approach a picosecond strain pulse injected into the structure induces a tilt of the magnetization vector $\mathbf{M}$, followed by the precession of $\mathbf{M}$ around its equilibrium orientation. This effect can be understood in terms of changes in magnetocrystalline anisotropy induced by the pulse. A model where only one anisotropy constant is affected by the strain pulse provides a good description of the observed time-dependent response.

Figure 1

(a) Schematic of sample and magnetic field orientations. The precession of $\mathbf{M}$ around its equilibrium direction results in a modulation of $M_z$. (b) Magnetic field dependence of the KR angle measured in the absence of strain pulses. (c) Schematic of pump-probe experiments with strain pulses. The laser characteristics are wavelength 800 nm, pulse duration 200-fs, repetition rate 100 kHz; pump and probe spot diameters are 300 and $150\mathrm{\text{−}}\mu \mathrm{m}$ respectively; the energy density per pulse are $2\mathrm{mJ}/{\mathrm{cm}}^2$ (pump) and $10\mu \mathrm{J}/{\mathrm{cm}}^2$ (probe). (d) Spatial shape of strain pulse ${\epsilon }_{zz}$ injected into the GaAs substrate. (e) Time evolution of relative thickness of the (Ga,Mn)As layer $\overline{\epsilon }(t)$.

Figure 2

Strain pulse-induced KR angle changes $\Delta \phi (t)$ measured at various magnetic fields (a) and at $B=0.8\mathrm{kOe}$ (b). The value $t=0$ corresponds to the time when the strain pulse enters the (Ga,Mn)As layer, and the vertical arrow shown in panel (a) indicates the time when the strain pulse leaves the (Ga,Mn)As layer. The thick solid curve in (b) is $\Delta M_z(t)/M$ calculated for $d\theta /d{\epsilon }_{zz}=60\mathrm{rad}$, $F=6.86\mathrm{GHz}$ and for a precession decay time of 400 ps. Inset in (b): $\Delta \phi (t)$ when the pump excitation is opposite to the probe spot (thin red line) and when they are displaced by $100\mu \mathrm{m}$ (thick blue line); the diameters of pump and probe spots are 100 and $50\mu \mathrm{m}$, respectively.

Figure 3

Magnetic field dependencies of the precession frequency $F$ (a) and the angle variation parameter $d\theta /d{\epsilon }_{zz}$ (b). Solid lines are the calculated dependences of $F$ and $d\theta /d{\epsilon }_{zz}$ obtained for $d{H}_{2\perp }/d{\epsilon }_{zz}=850\mathrm{kOe}$.