  Infrared reflectivity spectra of cubic SrMnO$_{3}$ ceramics reveal 18 %
stiffening of the lowest-frequency phonon below the antiferromagnetic phase
transition occurring at T$_{N}$ = 233 K. Such a large temperature change of the
polar phonon frequency is extraordinary and we attribute it to an exceptionally
strong spin-phonon coupling in this material. This is consistent with our
prediction from first principles calculations. Moreover, polar phonons become
Raman active below T$_{N}$, although their activation is forbidden by symmetry
in $Pm\bar{3}m$ space group. This gives evidence that the cubic $Pm\bar{3}m$
symmetry is locally broken below T$_{N}$ due to a strong magnetoelectric
coupling. Multiphonon and multimagnon scattering is also observed in Raman
spectra. Microwave and THz permittivity is strongly influenced by hopping
electronic conductivity, which is caused by small non-stoichiometry of the
sample. Thermoelectric measurements show room-temperature concentration of free
carriers $n_{e}=$3.6 10$^{20}$ cm$^{-3}$ and the sample composition
Sr$^{2+}$Mn$_{0.98}^{4+}$Mn$_{0.02}^{3+}$O$_{2.99}^{2-}$. The conductivity
exhibits very unusual temperature behavior: THz conductivity increases on
cooling, while the static conductivity markedly decreases on cooling. We
attribute this to different conductivity of the ceramic grains and grain
boundaries.
