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 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 illustrating the dispersion of the surface modes in this case is reciprocal under reversal of ⃗ k , and propagation of the surface modes is reciprocal. FIG. 2. Attenuation constant and Dispersion relation. In (a) the attenuation constant is shown for two values of wavevector in the absence of external fields. The solid line represents k = 0 cm − $^{1}$, while the dashed line correspond to k = 16 cm − 1 . In (b) bulk and surface mode dispersions are shown. Surface modes are indicated by SP. The shaded regions represent bulk bands, limited by frequencies ω$_{m}$ , ω$_{p}$ and ω$_{z}$ . The dashed lines denote by vertical and horizontal arrows represent ATR light lines for incident angles of 30 o and 70 $^{o}$. The asymptotic boundaries and lightline are represented by dashed lines which are indicated as A and by L. 8 2.9 3 3.1 3.2 0 10 20 30 /2 c  (cm −1 )  (cm −1 )  k  = 0 cm −1 $_{m}$   k  = 16 cm −1 $_{z}$  $_{p}$  (a)Attenuation constant. −20 −10 0 10 20 2.9 3 3.1 3.2  k  (cm −1 ) /2  (cm −1 ) −A  −L  L   A  $_{z}$  $_{p}$  SP  $_{m}$  (b)Dispersion relation. β + µ$_{y}$β$_{o}$ = 0 (32) µ$_{z}$β + ( µ$_{y}$µ$_{z}$ − µ 2 yz ) β$_{o}$ + µ$_{yz}$ k$_{y}$ = 0 . (31)