Large magnonic band gaps and spectra evolution in three-dimensional magnonic crystals based on magnetoferritin nanoparticles

We study magnonic crystals based on magnetoferritin nanoparticles. These nanoparticles self-assemble to form crystals of highly ordered fcc structure with a lattice constant of ten-odd nanometers. Filling the interparticle space by a ferromagnetic material should stabilize the ferromagnetic order in such a crystal at room temperature. We use the plane wave method to demonstrate that the introduction of a ferromagnetic matrix can also lead to the opening of a complete band gap, referred to as a magnonic band gap, in the spin-wave spectrum. We use a model based on a homogeneous medium with effective parameters to interpret the characteristics of the obtained spin-wave spectra in the long wave limit. We also study in detail the width of the band gap and its central frequency versus the matrix material and the lattice constant. The occurrence of a maximum width in the lattice-constant dependence is shown to be closely related to the specific behavior of the dynamic magnetization profiles of the lowest excitations in the spin-wave spectrum. On the basis of our results we determine the conditions conducive to the occurrence of a complete magnonic band gap. We also show that the crystallographic structure and the lattice constant of the crystals produced by the protein crystallization technique are almost optimized for the occurrence of a magnonic band gap.