3D magnonic crystals

Magnetic micro- and nanostructures are extensively investigated due to their potentials as candidates for future spintronic and magnonic devices [1–4]. Main carriers of signals used for information processing in such structures are magnons and, in particular, magnetostatic spin waves (MSW). They are also possible candidates for beyond-CMOS (complementary metal-oxide semiconductor) technologies [5], as they are free of Joule heating and, respectively, free of power loss associated with traditional electronics [6, 7]. Here, the concept of three-dimensional (3D) magnonic crystals is discussed for the first time. A meander type ferromagnetic film which can be grown at the top of the structured substrate can be a candidate for such 3D crystal (see Fig.1). Propagating wave dispersion and band structure in such crystals are calculated using finite elements method and by the means of micromagnetic simulation. Amplitudes of magnetostatic potentials as functions of frequencies are also deduced. Wave reflections and transmissions at the corners of parts of the meander waveguide are discussed and estimated within the model of transfer matrix method [8]. Furthermore, the properties of coupled 3D magnonic crystals are also considered. We considered the meander type structure with isotropic ferromagnetic layer saturated by in-plane magnetic field. We restrict ourselves by dipole approximation eliminating the exchange interactions. The calculation of the magnetic field within one cell of the periodic structure was provided using magnetostatic equations as well as periodic boundary conditions using finite elements method (FEM) [9]. In order to calculate dispersion of the propagating MSW in such structures we used Maxwell's equations in a magnetostatic approximations with electrodynamic boundary conditions. It has been shown that the band gaps have clearly appeared in dispersion of magnetostatic surface spin waves (MSSW) propagating in such 3D structures. They were at the frequencies of Bragg resonances when the MSSW wavelength is equal to two periods of the periodic structure. Dispersion characteristics of MSSW are shown in Fig. 2 at various meander depths. Two main conclusions can be made based on the results of this Figure. Namely, as the depth of the groove is increased the width of the band gap is also increased. Second conclusion concerns that fact at fixed wavenumbers (or wave lenghts) the dispersion curves are shifted in the lower frequencies and this is due to decrease of the MSSW phase velocities. Authors acknowledge the financial support from RFBR through the grant 18-57-76001.