On magnon energy branches of multilayer ferrimagnetic superlattices [Reply to the comment “Boson Green's functions treatment of three‐layer ferrimagnetic superlattice”, phys. stat. sol. (b) 244, No. 10, 3750–3753 (2007)]

Abstract

The magnon energy branches of multilayer ferrimagnetic superlattices are discussed, as regards the linear spin-wave approach and Green's function technique. It is argued that negative energy branches in the spin-wave spectra of the ferrimagnetic systems have physical significance, which is responsible for the zero-point motion (i.e. the quantum fluctuations) in the ground state, since the sign of ω l (k) indicates the direction in which the spin-wave mode propagates. On boson Green's function treatment, the results calculated for physical properties with consideration of negative energy spectra are correct and the consequent conclusions do not need to be re-examined. Even for the definition of energy gaps, nothing is wrong from the theoretical point of view if one considers both negative and positive energy spectra, but one may need to consider two different definitions (one considers the negative/positive energy spectra; the other only the positive ones), from the experimental point of view, to compare both of them with experimental data, in an attempt to detect whether the negative energy branch does excite or not.

Magnon energy gap in a three‐layer ferromagnetic superlattice

“…But in the present work there are only three positive spectra branches, because of the use of the Holstein-Primakoff and Green function techniques. For ferrimagnetic superlattices, different results of the two methods were discussed in [29,30]. Furthermore, there are two magnon energy gaps ∆ 12 ω and ∆ 23 ω in the present system.…”

The analytical treatment of magnetic properties of three-layer ferrimagnetic superlattice

“…The same results were obtained in Ref. [19]. The layer magnetizations can be evaluated also from the second set of BGFs.…”

“…OperatorĈ just as the operatorB can be chosen depending on the purposes. In their previous work on the similar problems a group of authors [14][15][16][17][18][19][20] claimed that set I having two positive and one negative energy solution is the only meaningful one, while set II has no meaning at all. There also appear the works of other authors with a similar statement [21,22].…”

Quantum competitions between the effects of the interlayer exchange couplings and the magnetically structural symmetry in a four-layer ferrimagnetic superlattice

“…This suggests that the negative energy branch is the character of the spinwave spectra of the ferrimagnetic systems. If one considered only the positive energy branch, it would lead to wrong results for physical properties of the ferrimagnetic systems [28,29]. There have been many reports on the negative energy branches of the spin waves [21,22,[30][31][32][33].…”