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The spin dynamic of the metallic A-type antiferromagnetic manganites isstudied. An effective nearest-neighbour Heisenberg spin wave dispersion isderived from the double exchange model taking into account the superexchangeinteraction between the core spins. The result of inelastic neutron scatteringexperiment on ${Nd}_{0.45}{Sr}_{0.55}{Mn} {O}_{3}$ is qualitatively reproduced.Comparing theory with experimental data two main parameters of the model:nearest-neighbour electron transfer amplitude and superexchange couplingbetween the core spins are estimated.Comment: to appear in Phys. Rev.

Theory of spin-wave excitations of metallicA-type antiferromagnetic manganites