Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars

It is demonstrated that collective spin waves (SWs) propagating in complex periodic arrays of dipolarly coupled magnetic nanopillars existing in a saturated (single-domain) ground state in a zero bias magnetic field could be nonreciprocal. To guarantee the SW nonreciprocity, two conditions should be fulfilled: (i) existence of a nonzero out-of-plane component of the pillars' static magnetization and (ii) a complex periodicity of array's ground state with at least two elements per a primitive cell, if the elements are different, and at least three elements per a primitive cell, if the elements are identical.