On the question about the limitation of wave number in Damon-Eshbach task with exchange and demagnetization
The influence of nonuniform exchange interaction and demagnetization field on the limitation of wave number in the Damon-Eshbach task about the propagation of magnetostatic surface wave in tangentially magnetized plane ferrite plate having dissipation is investigated. It is found that in the case when the wave number is increased in large degree, the wave frequency approaches to the upper boundary of its spectrum. In this case the wave group velocity approaches zero and the wave on the distance of its length dissipate, and its propagation becomes impossible. This dissipation manifests itself restriction of dispersion law by wave number. It is shown that introduction the exchange interaction and demagnetization in classic Damon-Eshbach task leads to the quadratic increase of upper boundary of wave spectrum. In this case the a-periodic character of wave is not take place and the limitation by wave number is absent. We found the dispersion relation, group velocity and time which is necessary for wave propagation on a distance equal to its own length. The relaxation time is found from the solution of auxiliary task about the excitation of uniform magnetic vibrations in normal magnetized plate. The obtained relaxation time is compared with the wave’s own travel time when the remaining parameters of the main and auxiliary problems coincide. It is shown that the necessary condition of wave propagation is the less value of own running time in comparison with relaxation time. We investigated the own running time of wave when the frequency and field are varied. It is shown that in frequency interval from 2 to 7 GHz for the material like yttrium-iron garnet the own running time and the character of its dependence on wave number does not depend on frequency and corresponding field. We investigated the dependence of relaxation time on frequency in the region from 2 to 100 GHz. It is shown that up to the frequency about 10 GHz the relaxation time is decreased according to a law close to inverse proportionality, then it has a minimum near the frequency 30 GHz, then it increases smoothly to the frequency 100 GHz. It is shown that in the region of minimum the own running time may be less than the relaxation time and as a result the limitation along wave number is absent. The influence of plate thickness on the limitation of wave number is investigated. It is shown that the decrease of plate thickness leads both to large broadening of frequency range and to the complete removal of the limitation of the wave number. It is shown that this removal of the limitation for yttrium-iron garnet takes place by the thickness less to 2-3 micrometers and for other ferrites - by the thickness about 1 micrometer and less. Some recommendations are proposed for using described phenomena in practice. It is noted that to remove the limitation, a plate of small thickness should be selected from a material with small dissipation.