Dyakonov surface magnons and magnon polaritons

We predicted one Dyakonov surface magnon (DSM) and two Dyakonov magnon polaritons (DSMPs) localized at the antiferromagnet (AF)-air interface. Their concise dispersion equations and necessary conditions of existence were obtained. The DSM is the magnetostatic limit of the first DSMP, which are situated inside the AF reststrahlen frequency band. The second DSMP has no magnetostatic limit and lies outside the frequency band. The specifical frequency ranges occupied by the DSM and DSMPs were analytically found. The DSMPs are hybrid-polarization surface polaritons and the DSM is a hybrid-polarization surface magnetostatic mode. The first DSMP possesses large attenuation constants so that it is highly localized at the surface. Compared with it, the second DSMP exhibits relatively small attenuation constants. According to the features of polarization obtained for either DSMP, we used the TE and TM radiations incident on the AF surface to calculate attenuated total reflection (ATR) spectra, respectively. These ATR spectra not only further prove the existence of the DSMPs but also demonstrate their observability in experiment. However, the DSM should be detected by means of a light-scattering technique.

Figure 1

Configurations and coordinate system used in the theoretical derivation and calculation, where the AF easy axis lies in the y-z plane or the AF surface and the space above the surface is filled with air. (a) For the derivation of dispersion equation, where θ is the propagating angle of DSMP with respect to the easy axis. (b) For the ATR calculation, where the AF and prism are separated by the air spacer, and $\beta$ is the incident angle.

Figure 2

Dispersion curves of DSMPs for various propagating angles, where $\mathrm{\Delta }\theta$ is the propagating-angle difference between two adjacent curves and the vertical dashed lines represent the scanning lines for numerical calculating ATR. (a) Dispersion curves of the first DSMP, where the topmost curve is related to $\theta ={90}^{\circ }$ and the dotted curve is the left boundary of the area where the first DSMP exists. (b) Dispersion curves of the second DSMP, where the topmost curve corresponds to $\theta =5^{\circ }$ and the two dotted lines are the left and right boundaries of the region in which the second DSMP appears.

Figure 3

(a) The permittivity and frequency regions occupied by DSMPs, where the first DSMP is situated in the light-gray region and the second DSMP lies in the gray region. The horizontal solid line corresponds to ${\varepsilon }_a^{-1}$, and the two horizontal dashed lines indicate the 0 line and −1 line. The solid curve shows the permittivity. (b) The dispersion curve of Dyakonov surface magnon; it occupies the light-gray region in (a).

Figure 4

Attenuation constants of DSMPs vs $k$ for various propagating angles. (a) For the first DSMP and (b) for the second DSMP, where a pair of solid curves with the same color indicates ${\mathrm{\Gamma }}_{+}$ and ${\mathrm{\Gamma }}_{-}$ in the AF, but the dotted line represents ${\mathrm{\Gamma }}^{\prime }$ above the surface.

Figure 5

The magnetic-field amplitude of the first DSMP vs $k$ for various propagating angles. Its $x$ components above and below the surface are imaginary and are different, and further the imaginary part is negative below the surface and positive above the surface. The $y$- or $z$ components above and below the surface are real and the same.

Figure 6

The magnetic-field amplitude of the second DSMP vs $k$ for various propagating angles. The $x$ components above and below the surface are imaginary and different, and further the imaginary parts below and above the surface both are negative. The curves below the break indicate the amplitude in the AF. The $y$- or $z$ components above and below the surface are real and the same.

Figure 7

The attenuated total reflective ratio vs frequency for various propagating angles. (a) is obtained from the transversely electric incidence. The four sharp dips show the first DSMP for the four propagating angles and correspond to the four intersections of the dispersion curves and the scanning line in Fig. 2, respectively. (b) comes from the transversely magnetic incidence. The five sharp dips demonstrate the second DSMP for the five propagating angles and correspond to the five intersections between the dispersion curves and the scanning line in Fig. 2, respectively.