Spin fluctuations in the stacked-triangular antiferromagnet YMnO$_3$

The spectrum of spin fluctuations in the stacked-triangular antiferromagnet YMnO$_3$ was studied above the Néel temperature using both unpolarized and polarized inelastic neutron scattering. We find an in-plane and an out-of-plane excitation. The in-plane mode has two components just above T$_N$, a resolution-limited central peak and a Debye-like contribution. The quasi-elastic fluctuations have a line-width that increases with $q$ like $Dq^z$ and the dynamical exponent $z=2.3$. The out-of-plane fluctuations have a gap at the magnetic zone center and do not show any appreciable $q$-dependence at small wave-vectors.