  The phonon density of states (DOS) and magnetic excitation spectrum of
polycrystalline BiFeO$_3$ were measured for temperatures $200 \leq T \leq
750\,$K, using inelastic neutron scattering (INS). Our results indicate that
the magnetic spectrum of BiFeO$_3$ closely resembles that of similar Fe
perovskites, such as LaFeO$_3$, despite the cycloid modulation in BiFeO$_3$. We
do not find any evidence for a spin gap. A strong $T$-dependence of the phonon
DOS was found, with a marked broadening of the whole spectrum, providing
evidence of strong anharmonicity. This anharmonicity is corroborated by
large-amplitude motions of Bi and O ions observed with neutron diffraction.
These results highlight the importance of spin-phonon coupling in this
material.
