Ultrafast magnetoelastic probing of surface acoustic transients

We generate in-plane magnetoelastic waves in nickel films using the all-optical transient grating technique. When performed on amorphous glass substrates, two dominant magnetoelastic excitations can be resonantly driven by the underlying elastic distortions, the Rayleigh surface acoustic wave and the surface skimming longitudinal wave. An applied field, oriented in the sample plane, selectively tunes the coupling between magnetic precession and one of the elastic waves, thus demonstrating selective excitation of coexisting, large-amplitude magnetoelastic waves. Analytical calculations based on the Green's function approach corroborate the generation of multiple surface acoustic transients with disparate decay dynamics.

Figure 1

Experimental geometry showing the thin nickel film with glass substrate. The transient grating is generated by two crossed femtosecond laser pump pulses, leading to a spatially periodic impulsive heating of a thin nickel film and the launching of acoustic waves along the surface of the semi-infinite glass substrate. Grating periodicities as small as $1 \mu \mathrm{m}$ can be achieved. A magnetic field can be rotated continuously in the sample plane. Faraday rotation of time-delayed optical probe pulses transmitted through the sample monitors the interaction between elastic and magnetic degrees of freedom.

Figure 2

(a) The time-resolved Faraday rotation measures the acoustically induced magnetization precession. As the period of the transient grating is increased, the precession decreases in frequency and amplitude. In the limit of a single pump beam excitation, the magnetic precession is completely suppressed. (c) The frequency of oscillation vs wave vector measures the velocity of acoustic propagation. Red and black data points represent frequencies extracted from (a), and blue data points are extracted from the nonmagnetic transient grating detection. Near-perfect linear dependence allows us to identify two types of excitations as the Rayleigh surface acoustic wave (lower branch) and the surface skimming longitudinal wave (upper branch) propagating at $3120\pm 20$ and $5590\pm 15$ m/s, respectively.

Figure 3

Under appropriate field conditions the time-periodic effective magnetic field of the elastic wave resonantly couples to the precessional motion in the film, driving large amplitude precessional motion. For $\mathrm{\Lambda }=1.1\mu \mathrm{m}$, the upper frequency at 5.1 GHz is that of the SSLW while the lower frequency at 2.8 GHz corresponds to the SAW. At the intersection of the elastic waves (white dashed lines) and ferromagnetic resonance (white solid line) an increase in oscillation amplitude is observed. In the upper panel, scaled line cuts along the white lines are shown.

Figure 4

Time-resolved Faraday traces at the resonances for (a) SAW and (b) SSLW, taken from Fig. 3 (main panel). Switching the polarity of the magnetic field yields nearly identical oscillation amplitudes and phases which can be understood by considering the applied torque induced by magnetoelastic coupling (see text). (c) Rotation of the applied magnetic field around the grating wave vector (geometry displayed in inset) results in an opposite sense of magnetization precession. The data shown in panel (c) is for $\mathrm{\Lambda }=1.1\mu \mathrm{m}$, and field tuned to the SSLW resonance.

Figure 5

Volumetric elastic strain are calculated for a bare substrate showing both in-plane and out-of-plane compressional components. The solutions to the Green's functions $G_{xx}$ and $G_{xz}$ are shown in the inset with the zero crossings indicating the velocities of respective SAW and SSLW modes. The convolution of Green's function with a periodic temperature variation (with period $\mathrm{\Lambda }=1.1\mu \mathrm{m}$) obtains the time dependence of ${\epsilon }_{xx}$ and ${\epsilon }_{zz}$ inside the glass near the surface. Calculated strains are subsequently incorporated into the magnetoelastic free energy and their effect on the magnetization drives precessional motion.

Figure 6

The Green's function $G_{xx}$ for nickel films of different thicknesses $h=0,20,40,60$ nm on glass substrate calculated for TG period $\mathrm{\Lambda }=1.1\mu \mathrm{m}$. As the film thickness increases, elastic velocities decrease while the SSLW mode also changes drastically in shape. (b, c) The time-domain signals for $h=0$ and $h=40$ nm thin nickel on glass exhibit a decaying SSLW mode and a SAW with constant amplitude. The SSLW temporal dynamics evolve from roughly $1/t$ dependence to exponential as the thickness increases.

Figure 7

The Green's function $G_{xx}$ calculated for different values $2\pi h/\mathrm{\Lambda }$ (upper panel). The structure of the Green's function for $\mathrm{\Lambda }\gg h$ [small abscissa, blue linecut in panel (b)] gets heavily modified for $\mathrm{\Lambda }\sim h$, where the appearance of additional bound and unbound elastic transients appear. Vertical cross sections of the Green's function in the lower panel for a 40-nm nickel film correspond to TG periods $\mathrm{\Lambda }=1100$, 110, and 50 nm, respectively. For $\mathrm{\Lambda }=1100$ nm, we show the dynamics associated with two modes, SAW and SSLW, closely align with our experimental configuration. For $\mathrm{\Lambda }=110$ nm several overdamped (leaky) pseudo-Sezawa modes are present, while for $\mathrm{\Lambda }=50$ nm an additional propagating Sezawa mode at $v\sim 3400$ m/s is observed.