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We present analytic expressions for the temperature dependent magnetizationand magnon dispersion relation of the antiferromagnetic (AFM) EuTe and theferromagnetic (FM) EuO. These bulk semiconductors represent concentrated spinsystems for which the interaction between magnons has to be taken into account.We do this using the renormalized spin wave theory. A higher order Green'sfunction according to Tjablikov is used for their description. As a result, weobtain a modified Bloch- T3/2 law, for low temperatures and high magneticfields. A full analytic expression is given for the sublattice magnetization ofthe AFM EuTe (B0=0), with a N\'eel temperature of TN = 9.81 K. Themagnetization curves {\sigma}N(T) of EuO (for 0 \leq T \leq 0.68TC) and{\sigma}R(T) (for 0.82TC < T < TC) agree well with experiment. The spin waveexcitation energy perfectly matches experimental data from inelastic neutronscattering. In the case of EuTe the magnon excitation energies exhibit acharacteristic maximum. For q = 0, an energy gap Eg occurs in the spin wavespectrum, a consequence of the AFM exchange interaction J2(T). Such energy gapsexist in the spectrum of magnon excitation energies only in systems with AFMinteractions.

Magnetization and magnon excitation energies of the magnetic semiconductors EuTe and EuO on the basis of the renormalized spin wave theory