Magnetization precession induced by picosecond acoustic pulses in a freestanding film acting as an acoustic cavity

We report the magnetization dynamics excited by picosecond acoustic pulses confined in the acoustic cavity of freestanding nickel films. By detecting both sides of the sample we show that acoustic pulses moving back and forth inside the cavity efficiently control the magnetization precession. The multiple round trips of acoustic pulses, which survive for 12 bounces, enhance the amplitude of the magnetization precession by a factor of 4.5. Even though the conditions of total reflection are met in the freestanding film, the acoustic pulses have a large attenuation as compared to similar Ni films on $\mathrm{Si}{\mathrm{O}}_2$ substrate, for which we speculate that it is related to a stress induced by the substrate. Our results constitute a guideline for simple designs of acoustic cavities and for achieving a very large amplification of the magnetization precession angle. It is potentially useful for high-frequency magneto-optical modulators.

Figure 1

Experimental setup and characterization of the Ni freestanding film. (a) Sketch of the freestanding film cavity experiment. (b) Magnetization curve of the freestanding Ni film. (c) Magneto-optical polar Kerr angle ${\theta }_s\left(\phi \right)$ obtained from experimental data (solid circles) on the left axis and equilibrium angle $\mathrm{\Psi }\left(\phi \right)$ of the effective field on the right axis.

Figure 2

Magnetization dynamics on the back side of the Ni film. (a) Magnetization precession angle dynamics $\mathrm{\Delta }\mathrm{\Psi }\left(t\right)$ (left axis) for several angles φ and transient reflectivity $\mathrm{\Delta }R\left(t\right)/R$ (right axis) measured at the back side of the freestanding film. (b) Fourier transform of reflectivity (b1) and Kerr rotation (b2) obtained from Fig. 2. (c) Long delay scan for $\phi =15.5^{\circ }$ (solid circles) and model fit curves (green, orange, and blue curves: the magnetization precession associated with the Gilbert intrinsic damping ${\alpha }_G$, extrinsic damping ${\alpha }_{\mathrm{ext}}$, and effective damping ${\alpha }_{eff}$, respectively). (d) Gilbert effective damping ${\alpha }_{eff}$ with a function of the order of acoustic echoes, extracted from the model fit.

Figure 3

Magnetization dynamics on the front side compared to the back side. (a) Magnetization precession dynamics $\mathrm{\Delta }\theta \left(t\right)/{\theta }_s$ (left axis) for several angles φ and transient reflectivity $\mathrm{\Delta }R\left(t\right)/R$ (right axis) measured at the front side of the freestanding film. (b) Comparison between the front- and back-sides' temporal responses of the magnetization precession for $\phi =15.5^{\circ }$. The open and solid circles represent the front-side data on the left axis and back-side data on the right axis, which is forward shifted by $T_{ac}/2$. The inset on the top left shows a magnified view of the precession and the definition of the phase shift $\mathrm{\Delta }T$. The inset on the top right shows the evolution of the temporal different $\mathrm{\Delta }T$ between two precession curves as a function of the echo order $m$. (c) Fourier transforms of the front- and back-side precession for the same conditions as Fig. 3. Note the log scale.

Figure 4

Strain profiles in Ni and Ni/$\mathrm{Si}{\mathrm{O}}_2$. (a) and (c) Reconstructed strain profiles of echoes in the time domain ${\eta }_m\left(t\right)$ for the freestanding Ni and Ni/$\mathrm{Si}{\mathrm{O}}_2$, respectively. (b) and (d) Strain profiles of echoes in the frequency domain ${\tilde{\eta }}_m\left(\omega \right)$ for each film.