  The thermal conductivity of the antiferromagnet Nd$_2$CuO$_4$ was measured
down to 50 mK. Using the spin-flop transition to switch on and off the acoustic
Nd magnons, we can reliably separate the magnon and phonon contributions to
heat transport. We find that magnons travel ballistically below 0.5 K, with a
thermal conductivity growing as $T^3$, from which we extract their velocity. We
show that the rate of scattering of acoustic magnons by phonons grows as $T^3$,
and the scattering of phonons by magnons peaks at twice the average Nd magnon
frequency.
