Theory of Spin-Wave Frequency Gaps in 3D Magnonic Crystals. Application to Manganites

his study is an investigation of spin wave spectrum in macrostructures composed of two ferromagnetic materials and showing a 3D periodicity: spherical ferromagnetic grains disposed in the nodes of a 3D crystal lattice are embedded in a matrix with different ferromagnetic properties. Frequency ranges forbidden to spin wave propagation are found in the calculated magnonic spectra. Both the position and the width of the gaps are found to depend on the magnetic (exchange and magnetization) contrasts in the composite material, as well as on its structural parameters (filling fraction, crystal lattice type). Having applied our theory to interpretation of the existence of a spin wave gap in doped manganites, recently revealed in neutron scattering experiments by S. Hennion {\em et al.}, we obtained a good (though approximate) quantitative agreement with the experimental results. A working hypothesis is proposed on this basis, supposing that certain manganites can be treated as natural 3D magnonic crystals.