Magnetic excitations in dipolar pyrochlore antiferromagnet Gd${}_2$Sn${}_2$O${}_7$

The spin dynamics in the geometrically frustrated pyrochlore antiferromagnet $\mathrm{G}{\mathrm{d}}_2\mathrm{S}{\mathrm{n}}_2{\mathrm{O}}_7$ is studied by means of the electron spin resonance. In the ordered phase ($T_N=1$ K), we have detected three gapped resonance modes. Their values agree well with the developed spin-wave theory which takes into account the Heisenberg nearest-neighbor exchange, the single-ion anisotropy and the long-range dipolar interactions. The theory also predicts a fourth lowest-frequency gap, which lies beyond the experimental range of frequencies, but determines the exponential decrease of the specific heat at low temperature.