Light-induced magnetic precession in (Ga,Mn)As slabs: Hybrid standing-wave Damon-Eshbach modes

Coherent oscillations associated with spin precessions were observed in ultrafast optical experiments on ferromagnetic (Ga,Mn)As films. Using a complete theoretical description of the processes by which light couples to the magnetization, values for the anisotropy constants and the spin stiffness were unambiguously determined from the data. Estimates for the hole-Mn exchange coupling are significantly larger than those previously reported. Results also reveal an important negative contribution to the energy due to surface anisotropy leading to excitations that are a mixture of bulk waves and surface modes.

Figure 1

(Color online) Precession eigenstates for the two lowest even modes of a $71\text{−}\mathrm{nm}$-thick (Ga, Mn)As film, centered at $z=0$, using the values of the parameters $D$, $K_2$, and $K_4$ listed in Table and $2K_S∕D{M}_0=-0.33$, 0, and $1{\mathrm{nm}}^{-1}$. The in-plane external field $H_0=0.1\mathrm{T}$ is along [100].

Figure 2

(Color online) Results at $T=4\mathrm{K}$ for the as-grown sample with $L=120\mathrm{nm}$. The top panel shows Voigt-geometry DMK data (open circles) at $H_0=0.17\mathrm{T}$. The applied field is parallel to [100]. The black curve is the linear prediction fit, which gives two modes of period of 99.7 and $83.9\mathrm{ps}$. Their contributions to the fitted signal are shown, respectively, by the blue and red curves. The bottom panel shows the Fourier transform of the fit and, in the inset, the calculated $m_z$ component for the three lowest eigenmodes, using the parameter values listed in Table .

Figure 3

(Color online) Measured magnetic-field dependence of the precession mode frequencies (top panel) and the ratio $A_2∕A_0$ (bottom panel). For clarity, results for the films with $L=120\mathrm{nm}$ are not shown. Solid curves are fits using the theoretical expressions discussed in the text. The FMR spectrum of the $71\text{−}\mathrm{nm}$-thick sample is shown in the inset.

Figure 4

(Color online) Calculated surface-anisotropy dependence of the frequency and the ratio between the amplitudes of the two lowest even modes for $L=71\mathrm{nm}$ at $H_0=0$. Values for other parameters are listed in Table .