  Clear anomalies in the lattice thermal expansion (deviation from linear
variation) and elastic properties (softening of the sound velocity) at the
antiferromagnetic-to-paramagnetic transition are observed in the prototypical
multiferroic BiFeO3 using a combination of picosecond acoustic pump-probe and
high-temperature X-ray diffraction experiments. Similar anomalies are also
evidenced using first-principles calculations supporting our experimental
findings. Those calculations in addition to a simple Landau-like model we also
developed allow to understand the elastic softening and lattice change at T_N
as a result of magnetostriction combined with electrostrictive and
magnetoelectric couplings which renormalize the elastic constants of the
high-temperature reference phase when the critical T_N temperature is reached.
