"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki)  ISSN 1684-1719, N 11, 2019

contents of issue      DOI  10.30898/1684-1719.2019.11.4     full text in Russian (pdf)  

UDC 537.874; 537.624

THE INFLUENCE OF EXCHANGE INTERACTION AND DYNAMIC DEMAGNETIZING FIELD ON DISPERSION PROPERTIES OF DAMON-ESHBACH SURFACE WAVE

PART 3. SPECIAL CASES OF DISPERSION

 

V. I. Shcheglov

Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia

 

The paper is received on October 29, 2019

 

Abstract. The propagation of magnetostatic surface waves along in-plane biased magnetic plate with dynamic demagnetization and nonuniform exchange interaction is investigated. The magnetic susceptibility tensor is described, and on the base of this tensor the dispersion relation is found under given boundary conditions.. This dispersion relation is investigated in connection with the double-mention and complex character of transverse wave number. The wave dispersion by large wave numbers up to 107 cm-1, where the wavelength becomes comparable with the interatomic distances in the material of the magnetic plate, is investigated. It is shown that in a wide range of changes in the exchange constant the dispersion curves have an increasing quadratic character. It is shown that wave numbers of the order of 10-7 cm-1, i.e., lengths of the exchange waves of the order of interatomic distances, correspond to frequencies of the order of tens and small hundreds of THz. The comparison is made between founded dispersion law for longitudinal magnetized plate and classic form of dispersion for infinite space which is the product of exchange constant and square of wave number. It is founded that the dispersion curve without the transversal wave number is placed on frequency upper than the classic curve in twice but taking into account the transversal wave number decreases this value to only 20%. On the basis of the comparison of the dispersion in infinite space with the dispersion in a thin plate, the necessity of more precise determination of nonuniform exchange constant, as well as a deeper elaboration of the physical role of the transverse wave number, is noted. Besides the principal solution of dispersion relation, the additional solution of the same relation is found. It is shown that the main curve transforms to the classic Damon-Eshbach dispersion curve in the absence of exchange and demagnetization. The additional frequency curve lies upper than the main one. Moreover, in the region of small wave numbers the excess is about 0,5 of the normalized frequency of the main curve. The slope of initial region of additional curve is absent and it does not change with changing of plate thickness. Both curves have the similar quadratic character. When the wave number is increased the distance between these curves gradually decreases and by large wave numbers both curves become one. The geometry configuration of additional curve does not depend on the plate thickness. When the bias field changes, the displacement of additional curve on frequency is the similar to the displacement of the main curve. Based on the analysis of dispersion relation structure, it is shown that the existence of two of its solutions is due to the passage through zero of the dependence of its left side on frequency. In this case the main dispersion curve is formed by smooth intersection of left part through zero. But the intersection of additional dispersion curve is formed between divergence to both its branches, which opposite ends goes to plus and minus infinity. We investigated the problem of the practical realization of limitation of maximum value of wave number due to dissipation, noted in a number of theoretical works. It is established that the reason of this limitation is the decreasing of wave group velocity on plane region of dispersion curve to the value by which wave subside on the distance is equal to wave length. We made the comparative analysis of experimental results known to the author. It is established that the limitation of wave number by large dissipation levels in investigated experiments is absent. We suppose that in real materials the quadratic increasing of dispersion curve prevents the group velocity to decrease to the value when the wane is subsided on its length. As the possible task it is suggested to find a correlation criterion between the wave distance where it subsides and the wave length depending on dissipation parameter. The structure of magnetostatic surface wave potential in connection with exchange and demagnetization, when the wave propagates in longitudinal magnetized plate, is discussed. It is shown that the real character of transversal wave number demands the limitation of wave existence region by two parallel planes where the potential takes the limited value. In the infinite space the transversal wave number must have imaginary character, which makes possible the limited periodic sinusoidal dependence of potential from normal coordinate to the surface of magnetic plate. In connection with this fact the two tasks are formulated as the aim of possible investigations:  (1) the investigation of wave propagation with exchange and demagnetization in longitudinally biased plate in arbitrary direction relatively to field direction and founding the possible cutting directions; (2) the investigation of the same wave propagation in infinite space in arbitrary direction relatively to field direction and also founding the possible cutting directions. Some possible applications of exchange magnetostatic waves are discussed. As a traditional direction, the creation of devices for processing analog information, primarily delay lines, is mentioned. It is shown that the use of exchange waves instead of dipole waves will allow to decrease the dimensions of wave-guiding parts on two-three orders and to decrease device dimensions to values about tens and units nanometers and also to increase the working frequency of devices to some terra-hertz without the increasing the dc bias magnetic field. The possibility of decreasing the exchange waves to several nanometers allows us to consider such a wave as possible instrument for constructing a microscope with a spatial resolution that is two to three orders of magnitude higher than the resolution of an optical microscope. Another possible application of such short waves can be the study of the structure of matter at the atomic-molecular level. In this case, for the theoretical interpretation of these phenomena a transition from continual consideration to microscopic on quantum level is required.

Key words: magnetostatic wave, demagnetizing field, exchange interaction, wave dispersion, nanoscale.

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For citation:

Shcheglov V.I. The influence of exchange interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Part 3. Special cases of dispersion. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No. 11. Available at http://jre.cplire.ru/jre/nov19/4/text.pdf

DOI  10.30898/1684-1719.2019.11.4