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The Brillouin light scattering was used to investigate elastic properties of the zinc blende, MBE-grown MnTe layer that was deposited on a (001) GaAs substrate covered by CdTe buffer layer. The three elastic constants of the zinc blende MnTe, namely c_{11}, c_{12}, and c_{44}, were directly determined for the first time from the frequency of the Rayleigh mode, of the pseudo-surface mode, and of the shear horizontal bulk mode traveling parallel to the layer surface. The value of c_{11} was checked using the frequency of longitudinal bulk waves propagating at different angles from the normal of the layer plane. This value was also independently determined by results of the folding of acoustic phonons, observed for MnTe/CdTe superlattices by the Raman scattering. Finally, the bulk modulus given by the formula B=(c_{11}+2c_{12})/3 was determined for zinc blende MnTe by ab initio calculations making use of the density functional theory and atomic pseudopotentials; spin polarization of MnTe was taken into account. A satisfactory agreement between theoretical and experimental values was obtained.
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