  We demonstrate that we can determine the antiferromagnetic anisotropies and
the bulk Dzyaloshinskii-Moriya fields of the insulating iron oxide hematite,
{\alpha}-Fe2O3, using a surface sensitive spin-Hall magnetoresistance (SMR)
technique. We develop an analytical model that in combination with SMR
measurements, allow for the identification of the material parameters of this
prototypical antiferromagnet over a wide range of temperatures and magnetic
field values. Using devices with different orientations, we demonstrate that
the SMR response strongly depends on the direction of the charge current with
respect to the magneto-crystalline anisotropies axis. We show that we can
extract the anisotropies over a wide temperature range including across the
Morin phase transition. We observe that the electrical response is dominated by
the orientation of the antiferromagnetic N\'eel order parameter, rather than by
the emergent weak magnetic moment. Our results highlight that the surface
sensitivity of the SMR allows accessing the magnetic anisotropies of
antiferromagnetic crystals and in particular thin films where other methods to
determine anisotropies such as bulk-sensitive magnetic susceptibility
measurements do not provide sufficient sensitivity.
