  Transient grating spectroscopy has become a mainstay among metal and
semiconductor characterization techniques. Here we extend the technique towards
the shortest achievable timescales by using tabletop high-harmonic generation
of attosecond extreme ultraviolet (XUV) pulses that diffract from transient
gratings generated with 500-1000 nm sub-5 fs near-infrared (NIR) pulses. We
demonstrate the power of attosecond transient grating spectroscopy (ATGS) by
investigating the ultrafast photoexcited dynamics in an Sb semimetal thin film.
ATGS provides an element-specific, background-free signal, unfettered by
spectral congestion, in contrast to transient absorption spectroscopy. With the
ATGS measurements in Sb polycrystalline thin films, we observe the generation
of coherent phonons and investigate the lattice and carrier dynamics. Among the
latter processes, we extract carrier thermalization, hot carrier cooling, and
electron-hole recombination, which are on the order of 20 fs, 50 fs, and 2 ps,
timescales, respectively. Furthermore, simultaneous collection of transient
absorption and transient grating data allows us to extract the total complex
dielectric constant in the sample dynamics, including the real-valued
refractive index, from which we are also able to investigate carrier-phonon
interactions and longer-lived phonon dynamics. The outlined experimental
technique expands the capabilities of transient grating spectroscopy and
attosecond spectroscopies by providing a wealth of information concerning
carrier and lattice dynamics with an element-selective technique, at the
shortest achievable timescales.
