  We have investigated the temperature evolution of the magnetic structures of
HoFeO$_3$ by single crystal neutron diffraction. The three different magnetic
structures found as a function of temperature for \hfo\ are described by the
magnetic groups Pb$'$n$'2_1$, Pbn$2_1$ and Pbn$'2_1'$ and are stable in the
temperature ranges $\approx$ 600-55~K, 55-37~K and 35$>T>2$~K respectively. In
all three the fundamental coupling between the Fe sub-lattices remains the same
and only their orientation and the degree of canting away from the ideal axial
direction varies. The magnetic polarisation of the Ho sub-lattices in these two
higher temperature regions, in which the major components of the Fe moment lie
along $x$ and $y$, is very small. The canting of the moments from the axial
directions is attributed to the antisymmetric interactions allowed by the
crystal symmetry. They include contributions from single ion anisotropy as well
as the Dzyaloshinski antisymmetric exchange. In the low temperature phase two
further structural transitions are apparent in which the spontaneous
magnetisation changes sign with respect to the underlying antiferromagnetic
configuration. In this temperature range the antisymmetric exchange energy
varies rapidly as the the Ho sub-lattices begin to order. So long as the
ordered Ho moments are small the antisymmetric exchange is due only to Fe-Fe
interactions, but as the degree of Ho order increases the Fe-Ho interactions
take over whilst at the lowest temperatures, when the Ho moments approach
saturation the Ho-Ho interactions dominate. The reversals of the spontaneous
magnetisation found in this study suggest that in \hfo\ the sums of the Fe-Fe
and Ho-Ho antisymmetric interactions have the same sign as one another, but
that of the Ho-Fe terms is opposite.
