  Local structural measurements have been performed on hexagonal HoMnO3 in
order to ascertain the specific changes in bond distances which accompany
magnetic ordering transitions. The transition from paramagnetic to the
antiferromagetic (noncollinear) phase near ~70 K is dominated by changes in the
a-b plane Mn-Mn bond distances. The spin rotation transition near ~40 K
involves both Mn-Mn and nearest neighbor Ho-Mn interactions while the low
temperature transition below 10 K involves all interactions, Mn-Mn, Ho-Mn
(nearest and next nearest) and Ho-Ho correlations. These changes in bond
distances reveal strong spin-lattice coupling. The similarity in magnitude of
the change in J(Mn-Mn) and J(Ho-Mn) enhances the system frustration. The
structural changes are interpreted in terms of a model of competing spin order
and local structural distortions. Density functional calculations are used to
estimate the energies associated with ionic displacements. The calculations
also reveal asymmetric polarization of the charge density of Ho, O3 and O4
sites along the z-axis in the ferroelectric phase. This polarization
facilitates coupling between Ho atoms on neighboring planes normal to the
z-axis.
