content_image/329010.jpg content_image/329009.jpg content_image/329008.jpg
An implicit surface mode dispersion relation is calculated by requiring continuity of tangen- tial ⃗ H and normal ⃗ B at the interface z = 0. Using Eq.(29) and (30), we find 

<img src='content_image/329010.jpg'>

The dispersion implied by Eq. (31) involves mainly of magnetic permeabilities, and so describes magnetic surface polaritons for the weak ferromagnet. From symmetry, we know that magnetic surface polaritons can be nonreciprocal[19], and this is the case here as well. The direction of ⃗ k$_{y}$ matters in Eq. (31) and indicates nonreciprocal propagation. 

A key point is that the nonreciprocity of the surface modes depends strongly on the canting angle. If the canting angle is zero, then µ$_{yz}$ → 0 and µ$_{z}$ → 1, and the dispersion relation in Eq. (31) becomes 

<img src='content_image/329009.jpg'>

illustrating the dispersion of the surface modes in this case is reciprocal under reversal of ⃗ k , and propagation of the surface modes is reciprocal. 

<img src='content_image/329008.jpg'>

