Propagating coherent acoustic phonon wave packets in ${\mathrm{In}}_x{\mathrm{Mn}}_{1-x}\mathrm{As}∕\mathrm{Ga}\mathrm{Sb}$

We observe pronounced oscillations in the differential reflectivity of a ferromagnetic $\mathrm{In}\mathrm{Mn}\mathrm{As}∕\mathrm{Ga}\mathrm{Sb}$ heterostructure using two-color pump-probe spectroscopy. Although originally thought to be associated with the ferromagnetism, our studies show that the oscillations instead result from changes in the position and frequency-dependent dielectric function due to the generation of coherent acoustic phonons in the ferromagnetic InMnAs layer and their subsequent propagation into the GaSb. Our theory accurately predicts the experimentally measured oscillation period and decay time as a function of probe wavelength.

Figure 1

(a) Schematic diagram of two-color pump-probe differential reflectivity experiment in an $\mathrm{In}\mathrm{Mn}\mathrm{As}∕\mathrm{Ga}\mathrm{Sb}$ heterostructure. The pump photoexcites carriers only in the InMnAs layer and the transient differential reflectivity is probed at higher energies. (b) Typical time-resolved differential reflectivity data, showing an initial drop followed by oscillations in reflectivity.

Figure 2

Two-color pump-probe differential reflectivity oscillations in an $\mathrm{In}\mathrm{Mn}\mathrm{As}∕\mathrm{Ga}\mathrm{Sb}$ heterostructure. The dependence of the oscillations on magnetic field is shown in (a) while the dependence on pump power is shown in (b). The oscillation period does not change as shown by the vertical dashed lines.

Figure 3

Experimental (a) and theoretical (b) coherent phonon differential reflectivity oscillations for probe wavelengths of 650, 775, and $850\mathrm{nm}$.

Figure 4

Experimental coherent phonon differential reflectivity oscillation period vs probe wavelength (open circles). The solid line shows the theoretical estimates.