We report the measurement of spin waves in the bilayer colossal magnetoresistive manganites ${\mathrm{La}}_{2-2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_2{\mathrm{O}}_7$ with $x=0.30\mathrm{}$, 0.35, and 0.40. For $x=0.35\mathrm{}$ and 0.40 the entire acoustic and optic dispersion relations are well described by those for a bilayer Heisenberg Hamiltonian with nearest-neighbor exchange only, which is explained together with the spin-wave lifetimes by the double exchange model. The in-plane exchange depends weakly on $x$, but that between the planes of a bilayer changes by a factor of 4, directly revealing a change from mixed $d_{{3z}^2{-r}^2}$ and $d_{x^2{-y}^2}$ orbital character to mostly $d_{x^2{-y}^2}$.

• Received 14 May 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.217201