"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 9, 2019

contents of issue      DOI  10.30898/1684-1719.2019.9.8     full text in Russian (pdf)  

UDC 537.874; 537.624




V. I. Shcheglov

 Kotelnikov Institute of Radioengineering and Electronics of RAS,

Mokhovaya 11-7, Moscow 125009, Russia


The paper is received on August 6, 2019


Abstract. The propagation of magnetostatic wave in classic geometry of Damon-Eshbach task which is established as ferrite plate magnetized by external field in its plane is investigated. The investigation is made in connection with dynamic demagnetization and nonuniform exchange interaction. It is found the tensor of magnetic permeability in consideration with the periodic character of propagating wave. It is found the mixed symmetrical-anti-symmetrical character of permeability tensor which is connected with the consideration of dynamic demagnetization. It is found the conditions of frequency divergence of tensor components wish are supplemented to the influence of direct field also by the nonuniform exchange action. It is investigated the whole organization of task about propagation of magnetostatic surface wave. It is established that the equality to zero of circle from dynamic magnetic field of wave allows to introduce the potential of this field. Also the equality to zero of divergence from magnetic induction of the same wave allows to found the Walker equation which is analog with the Laplace equation for magnetic medium. It is found the existence of mixed second derivation by coordinated in Walker excitation which is brought by the influence of demagnetization and exchange. It is shown that the mixed character of derivation leads to the ambivalent character of transverse wave number. For the geometry of Damon-Eshbach task the equations for potential in magnetic plate and surrounding its form both sides free half-spaces. It is described the boundary conditions on the surfaces between the material of plate and free spaces. As a result from the decision of established boundary task by variation division method the dispersion relation for surface wave propagating in plate plane in direction perpendicular to constant field is found. In details it is investigated the double character of transversal wave number which is connected with the mixed derivation in Walker equation. It is found the analytical expressions for both meanings of wave number which determined only the demagnetization without the exchange. It is shown that the founding of both components of wave number when exchange interaction is present require with the decision of eight degree algebraic equation which may be decided only by numerical method. It is described the general scheme of dispersion law founding as a functional dependence of wave frequency from the its longitudinal wave number. It is proposed the algorithm of calculation which consist of step by step assignment of longitudinal wave number with the determination of frequency value on each step by zero searching method. It is described the schemes of calculation algorithms of both paths of dispersion relation and also the real and imaginary paths of relation as a whole. It is demonstrated that described algorithm allows to found the functional dependence of wave propagating frequency from the longitudinal wave number which is the unknown dispersion law. It is described the results of calculation magnetostatic surfaces wave dispersion on the basis of received dispersion relation. As a point for comparison it is described the classic dispersion dependence for exchange wave in infinite space and its generalization for the case of thin plate. On the basis of founded dispersion relation are constructed the dispersion curves with the consideration of demagnetization and exchange interaction. The investigations are performed in the interval of longitudinal wave number from zero to 4x104 cm-1, which is more than traditionally realized range in experiments of dipole magnetostatic waves about of two orders. It is made the comparison of founded curves with the same for classic Damon-Eshbach task and also for classic exchange wave in infinite space and thin plate. It is shown that the consideration with demagnetization direct to the increasing of dispersion curves in the region of wave numbers having values more the inverse value of plate thickness. It is shown that the exchange interaction leads to the quadratic exchange of dispersion curves which is more increased from dispersion curves for surface waves founded in frames of classic Damon-Eshbach task. On the basis of founded dispersion relation with the consideration of demagnetization and exchange it is investigated the dependence of dispersion law for surface wave from the plate thickness. It is found that the dispersion curves for any thickness when the wave number is increased also increase by the law near to quadratic. In this case in region near the wave number values which are less from inverse value of plate thickness the steepness of dispersion curves increases when the thickness is decreases. In the region of wave number which are more than inverse value of plate thickness the steepness of dispersion curves when the thickness is decreases asymptotically try to attain the value which is determined by dispersion law when the demagnetization is absent. On the basis of founded dispersion relation with the consideration of demagnetization and exchange it is investigated the dependence of dispersion law for surface wave from the constant of exchange interaction. The investigation is made when the thickness of plate is equal to 1 micrometer. This choice ensures the visible influence of demagnetization about the middle of investigated range of wave number (so as 2x104 cm-1). As the standard it was established the value of exchange constant equal to the same in yttrium iron garnet. It is found the dispersion curves having different values of exchange constant in the region from unit to hundred standard values. It is shown that when constant value exchanged from unit near the standard value the dispersion curve positioned less higher from classic Damon-Eshbach curve but its quadratic character is in visible not maintained. It is founded that for visible manifestation of quadratic character it is necessary the increasing of exchange constant more than one order in comparison with standard value. In this case the exceeding of constant above standard to two orders brings to the whole predomination of quadratic law over the classic. It is mentioned the connected with numerical character of task decision technical reason of limitation of longitudinal wave number by the value of 4x104 cm-1. Its reasons is founded and the way of its overcoming is proposed. As a most important task for further investigation it is established the necessity of expansion of investigated region of longitudinal wave number no less than two orders of value.

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


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For citation:

V.I.Shcheglov. The influence of exchange interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Part 2. Dispersion relation. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No. 9. Available at http://jre.cplire.ru/jre/sep19/8/text.pdf

DOI  10.30898/1684-1719.2019.9.8