Magnonic Crystal Theory of the Spin-Wave Frequency Gap in Low-Doped La_{1-x}Ca_{x}MnO₃ Manganites

A theory of three-dimensional (3D) hypothetical magnonic crystal (conceived as the magnetic counterpart of the well-known photonic crystal) is developed and applied to explain the existence of a spin-wave frequency gap recently revealed in low-doped manganites $La_{1-x}Ca_{x}MnO_{3}$ by neutron scattering. A successful confrontation with the experimental results allows us to formulate a working hypothesis that certain manganites could be regarded as 3D magnonic crystals existing in nature.