The phenomenon of even bulk modes variance in a ferromagnetic A--A bilayer system

The eigenproblems of spin waves in a symmetricalferromagnetic bilayered system with periodic boundary conditions aresolved using the interface-rescaling approach (IRA). The resultsshow that interface coupling between two sublayers would notchange the excitation energy of odd bulk modes, but changeexcitation energy of even bulk modes. We call this peculiarphenomenon the phenomenon of even bulk mode variance (PEBMV).There are two kinds of mechanisms which cause PEBMV:phase reversal and phase translation of the magnon at theinterface, corresponding, respectively, to the antiferromagnetic andferromagnetic interface coupling cases. PEBMV embodies the selectiveeffect of the interface on different bulk magnons.