−400 −200 0 200 400 0 10 20 30 40 k  (cm −1 ) /2 c  (cm −1 ) $_{ez}$  $_{oz}$  ’$_{ey}$  $_{i}$  ’$_{m}$  SP  −A  A  −L  L  (a)Dispersion relation. −200 0 200 39 40 41 42 k  (cm −1 ) /2 c  (cm −1 ) ’$_{ey}$ $_{i}$  −A   A  −L L  (b)’Window’ where surface modes exist. 175.782 175.784 175.786 40.7525 40.7526 40.7527 k  (cm −1 ) /2 c  (cm −1 ) $_{i}$  SP  (c)Narrow gap at ω i . 175.776 175.78 175.784 40.7525 40.7526 40.7527 k  (cm −1 ) /2 c  (cm −1 ) $_{Ly}$  (d)Narrow gap with bigger coupling. FIG. 2. Dispersion relation without external field. In (a) he dispersion relation without the external field is shown. The surface modes are indicated by“SP”. The shaded regions represent bulk bands, which are limited by frequencies ´ ω$_{m}$ , ω$_{ez}$ , ω$_{oz}$ , ´ ω$_{ey}$ and ω$_{i}$ . In (b) The “window” where the surface modes exist is shown. In (c) a narrow gap around ω$_{i}$ is expanded. In (d) the narrow gap is wider when the ME coupling is increased by a factor of 10. and ( ζ$_{1}$ + 3 ζ$_{2}$P 2 $_{o}$) f = ω 2 $_{ey}$, the soft phonon frequency along the spontaneous polarisation. With the inverse phonon mass 4 as f = 2 . 7 × 10 24 statC $^{2}$/g cm3 and transversal phonon frequency 19 ω$_{ey}$ = 7.73 THz, this gives ζ$_{1}$ =-10.528 g cm $^{3}$/statC$^{2}$s2 and ζ$_{2}$ = 1 . 934 × 10 -8 erg cm $^{5}$/statC$^{4}$. The suceptibility χ e z is calculated by using the transverse phonon frequency for z polarization $^{4}$, ω$_{ez}$ = 33 . 7 cm − $^{1}$. The parameters C$_{c}$ and C$_{αf}$ in Eq.(24) and (33) are converted to frequency units in cm − $^{1}$. 10