  Large scale computer simulations are used to elucidate a longstanding
controversy regarding the existence, or otherwise, of spin waves in
paramagnetic BCC iron. Spin dynamics simulations of the dynamic structure
factor of a Heisenberg model of Fe with first principles interactions reveal
that well defined peaks persist far above Curie temperature T_c. At large wave
vectors these peaks can be ascribed to propagating spin waves, at small wave
vectors the peaks correspond to over-damped spin waves. Paradoxically, spin
wave excitations exist despite only limited magnetic short-range order at and
above T_c.
