  We present a theory for surface polaritons on ferroelectric-antiferromagnetic
materials with canted spin structure. Canting is assumed to be due to a
Dzyaloshinkii-Moriya interaction with the electric polarisation and weak
ferromagnetism directed in the plane parallel to the surface. Surface and bulk
modes for a semi-infinite film are calculated for the case of transverse
magnetic polarisation. Example results are presented using parameters
appropriate for BaMnF4. We find that the magnetoelectric interaction gives rise
to "leaky" surface modes, i.e. pseudosurface waves that exist in the pass band,
and that dissipate energy into the bulk of material. We show that these
psuedosurface mode frequencies and properties can be modified by temperature,
and application of external electric or magnetic fields.
