Magnon energy gap in a three‐layer ferromagnetic superlattice

Abstract

The magnon energy band in a three-layer ferromagnetic superlattice is studied by using the linear spinwave approach and Green's function technique. It is found that two modulated energy gaps exist in the magnon energy band along K x direction perpendicular to the plane of the superlattice. The spin quantum numbers and the interlayer exchange couplings all affect the two energy gaps. The disappearance of one of the energy gaps corresponds to a high symmetry among the interlayer exchange couplings, while the vanishing of another energy gap corresponds to a high symmetry of the system, which belongs to the type III Shubnikov group or the polychromatic group of magnetic group. This magnetically structural symmetry includes not only the symmetry of crystallographic point-groups or space-groups, but also the symmetry of strength and direction of spins. Comparing with the previous results for a three-layer ferrimagnetic superlattice, it is concluded that the energy gap of the ferromagnetic/ferrimagnetic superlattices is dominated by different symmetries originated from ferromagnetic/antiferromagnetic interlayer exchange couplings.

Effects of competition between the anisotropy and the spin quantum number on the magnon energy gap in a four-layer ferromagnetic superlattice

“…Our point of view can be compared with that in literatures [31][32][33][34][35]. The magnon gap is a function of the magnetic anisotropy: the stronger the anisotropy is, the bigger the magnon gap [31].…”

“…Schwenk et al [32,33] also thought that the vanishing of gaps could be understood by a C 2 symmetry operation around the zaxis. In three-layer ferrimagnetic superlattice [34] and FM one [35], two zero energy gaps correspond to different higher magnetically structural symmetry. The previous results [31][32][33][34][35] agree well with the viewpoint of the present work.…”

“…Spin-wave propagation through this structure is prohibited within restricted bands. In magnetic superlattice systems, the magnon as a kind of spin excitations has been an interesting subject [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Rejection frequency bands were clearly observed in the experimental study on scattering of backward volume magnetostatic spin waves from a 1-D magnonic crystal, realized by a grating of shallow grooves etched into the surface of an yttrium iron garnet film [24].…”

“…It was presented that the magnon energy gap derives mainly from the exchange interaction [32,33]. In our previous work [34,35], the magnon energy band was studied for ferrimagnetic [34] and FM [35] superlattices with three layers in a unit cell. The results showed that there are two modulated energy gaps, and the absence of the energy gap means that the system has a high magnetically structural symmetry [34,35].…”

“…In our previous work [34,35], the magnon energy band was studied for ferrimagnetic [34] and FM [35] superlattices with three layers in a unit cell. The results showed that there are two modulated energy gaps, and the absence of the energy gap means that the system has a high magnetically structural symmetry [34,35]. Usually, the classical approaches ignore quantum fluctuations that might significantly affect the magnon excitation.…”