Theory of propagation of nonlinear spin wave through an antiferromagnetic magnonic crystal with four-sublattice interfaces

The purpose of the research is constructing an analytical model of a nonlinear spin wave propagating through a single antiferromagnet/antiferromagnet boundary as well as in one-dimensional antiferromagnetic magnonic crystal comprised of two sorts of antiferromagnets (AFM). Both AFMs that comprise the magnonic crystal are assumed to be two-sublattice uniaxial ones. The Landau-Lifshitz equations have been used in the sigma model with account for the exchange bias between magnetic sublattices of both AFMs, the magnetic anisotropy, the magnetic dipole–dipole interaction and the Dzyaloshynskyi-Moriya interaction. As a result, the allowed discrete sets of frequencies and velocities for the considered spin wave are obtained. In the process of investigation, the boundary conditions for the Néel vector on the interface between two AFMs are derived with the exchange bias between magnetic sublattices of both AFMs taken into account. These boundary conditions are, in particular, applied for both fully uncompensated interface and fully compensated one for the illustration purposes. Analysis of the results show that the considered wave is reflectionless (thus, energy losses on reflection on the interfaces are absent), phase-coherent and possess a number of parameters that can be considered as degrees of freedom for encoding information. These findings open up new possibilities of digital data processing utilizing nonlinear spin waves propagating through antiferromagnetic magnonic crystal.