Ultrafast surface strain dynamics in MnAs thin films observed with second harmonic generation

Optical second harmonic generation (SHG) is used to probe surface strain in 150 and 190-nm thin films of MnAs grown epitaxially on GaAs(001). The $p$-polarized SHG signal produced by $p$-polarized 775-nm, 200-fs pulses is theoretically and experimentally shown to be sensitive to the normal component of surface strain from $-20$ to 70 ${}^{\circ }$C, which includes the ferromagnetic/paramagnetic striped coexistence phase region that exists from $\sim$10 to 40 ${}^{\circ }$C. We use this dependence to time-resolve the surface strain dynamics in MnAs following pumping with 200-fs pulses of 1.0 or 2.0 mJ cm${}^{-2}$ that raise the surface temperature by tens of degrees. For a film at $-20{}^{\circ }$C the strain reaches a minimum value in $\sim$10 ps, indicative of electron-lattice thermalization, before recovering on a 500-ps time scale consistent with a one-dimensional heat diffusion model. For a film at 20 ${}^{\circ }$C the minimum strain is reached only after $\sim$200 ps and attains a value higher than predicted by the heat diffusion model; recovery, however, still occurs in $\sim$500 ps. The long strain fall time possibly reflects the influence of latent heat and stripe dynamics in the coexistence phase. The larger calculated drop in surface strain may be due to deficiencies in the one-dimensional heat diffusion model. The nonequilibrium surface strain also may not be determined by the local temperature alone but by the constraints throughout the film/substrate system, which are certainly known to govern the strain and stripe characteristics under equilibrium conditions.

Figure 1

Schematic structure of a MnAs thin film in the coexistence phase.

Figure 2

Temperature dependence of the ${\sigma }_{xx}$ stress component [(blue) squares] for thin-film MnAs and the derived normal component of the surface strain, ${\varepsilon }_s$ [(red) circles], based on Eq. (6). The curves are guides for the eye. Stress data are reproduced from an earlier work[16] with permission from the American Physical Society and the authors.

Figure 3

Experimental arrangement used to observe SHG from MnAs thin films. LP, linear polarizer; HWP, half-wave plate; PMT, photomultiplier tube.

Figure 4

Normalized (see text) SHG intensity from a 150-nm MnAs film on GaAs(001) as a function of azimuthal rotation angle for several values of the equilibrium temperature, $T_0$. The solids curves are fits based on Eq. (4).

Figure 5

The $f^{\left(0\right)}$, $f^{\left(2\right)}$, and $f^{\left(4\right)}$ coefficients of SHG intensity as a function of temperature (left) and surface strain (right) for the 150-nm MnAs film. Inset for $f^{\left(0\right)}$: details beyond 40 ${}^{\circ }$C. Curves are fits based on fits to Eq. (4). Error bars have the same magnitude for all coefficients but are discernible only for $f^{\left(2\right)}$ and $f^{\left(4\right)}$.

Figure 6

Time-delay-dependent $f^{\left(0\right)}$, $f^{\left(2\right)}$, and $f^{\left(4\right)}$ coefficients obtained from the SHG intensity for a 150-nm MnAs film initially at $T_0=-20{}^{\circ }$C and optically excited at high fluence. Error bars have the same magnitude for all three components and are only apparent for the $f^{\left(2\right)}$ and $f^{\left(4\right)}$ elements. Shaded (red) curves show that the three coefficients give a consistent value for surface strain or temperature, based on the data in Fig. 5.

Figure 7

Extracted ${\varepsilon }_s$ and corresponding surface temperature [(blue) circles] as a function of the time delay after optical excitation at high fluence of a sample initially at $-20{}^{\circ }$C. Also shown are the calculated corresponding surface temperature and temperature-dependent surface strain obtained from the heat diffusion model for $\delta =17$ nm (black curves) and $\delta =40$ nm [lighter (red) curves].

Figure 8

Extracted ${\varepsilon }_s$ and corresponding surface temperature [(blue) circles] as a function of the time delay after optical excitation at low fluence of a sample held at $T_0=-20{}^{\circ }$C. Also shown are the corresponding surface temperature and temperature-dependent surface strain values obtained from the heat diffusion model assuming $\delta =17$ nm (black curves) and $\delta =40$ nm [lighter (red curves)].

Figure 9

Extracted surface strain, ${\varepsilon }_s$, and corresponding surface temperature [(blue) circles] as a function of the time delay after optical excitation of a film at $T_0=20{}^{\circ }$C and pumped with a high fluence. Curves show the surface strain and temperature derived from the heat diffusion model using $\delta =40$ nm.