content_image/338820.jpg
is discussed in the next section, and relevant magnetic and dielectric susceptibilities are calculated in section III. Results for surface and bulk mode dispersions are presented and discussed in the final section IV. 

## II. GEOMETRY AND MAGNETIC SUB-LATTICE CANTING 

<img src='content_image/338820.jpg'>

The geometry used is shown in Fig. 1. A semi-infinite film of a multiferroic with a two sub-lattice antiferromagnet fills the half space z < 0 while the other half space is assumed to be vacuum. The magnetocrystalline easy axis for a uniaxial anisotropy is directed out of plane along the z axis. The spin system cants symmetrically in the x − z plane, and the sublattices are assumed to have the same magnitude of magnetisation, | ⃗ m$_{a}$ | = | ⃗ m$_{b}$ | = M$_{s}$ . The nett magnetisation, ⃗ M corresponding to the weak ferromagnet due to spin canting, lies along the x axis in a plane parallel to the surface. The spontaneous dielectric polarisation is oriented in the perpendicular direction, also in the x − z plane. An external magnetic field is applied parallel to the weak ferromagnetic moment. 

The transverse electric (TE) mode is associated with the condition where the electric part of electromagnetic waves propagate along the surface is parallel to the surface. We assume that the surface modes propagate on the surface along the ˆ y direction, hence the electric components lie on the surface in the ˆ x direction while the magnetic part has H$_{y}$ and H$_{z}$ 

