The influence of exchange interaction and dynamic demagnetizing field on the dispersion of Damon-Eshbach surface wave. Part 1. Transverse wave number
The influence of demagnetizing field and nonuniform exchange interaction on dispersion properties of Damon-Eshbach surface wave is investigated. On the basis of short review of to-day works level by investigation of magnetostatic waves it is found the necessity of the investigation waves which long is about some nanometers and less. It is established that for investigation of so short waves it is necessary to take into account the dynamic demagnetizing and exchange fields. The quantity description of demagnetizing field is made in the form of hyperbolic tangent which argument is the multiplication of wave number on plate thickness. In the linear approximation it is decided the equation of motion for magnetization with the consideration of demagnetizing and exchange fields. It is found the magnetic sensibility tensor which components have resonance character. In the geometry of Damon-Eshbach task for potential of propagating wave field it is found the Walker equation which considers the influence of demagnetization and exchange. The most difference of this equation from its classic variant is the existence of mixed second order derivative by coordinates which are normal to constant field direction. It if found the Walker equation solution be division of variable quantity method. It is shown that the mixed second order derivative lead to complex character of wave number component which is perpendicular to the plane of magnetic plate. It is found the double character of transverse wave number which is caused by two possible decisions of Walker equation for the wave component which propagates perpendicular to plane of magnetic plate to its depth. For the case of exchange absence the transverse wave number is presented as a sum of real and imaginary parts. It is found the dependencies of real and imaginary transverse wave number components from longitudinal wave number by different values of demagnetization parameter. It is investigated the possibility of presentation of transverse wave number as a sum of real and imaginary parts in the case of exchange interaction presence. It is found that in this case the transverse wave number having complex character is defined by the decision of algebraic equation having eight degree. The whole complex equation is reduced to the system of two eight degree equations which roots are real. It is proposed the algorithm of this system the step by step decision which consist of variation of first variable value and founding on the each step two meaning of other value and with the following minimization of difference between its. With the assistance of this algorithm it is found the dependencies of real and imaginary transverse wave number components from the value of longitudinal wave number. It is shown that the exchange interaction leads to raising of both components transverse wave number dependencies from longitudinal wave number value relatively to same dependencies when exchange is absent. It is established three fundamental affirmations which determine the character of observed phenomena: 1) the influence of demagnetization causes the formation of imaginary part of transverse wave number; 2) when the demagnetization is increased the absolute value of imaginary part of transverse wave number is increased; 3) when the exchange interaction is increased the absolute value of imaginary part of transverse wave number is increased. For the quality interpretation of these affirmations it is proposed the model which considers the propagating wave as progressive moving of periodic flat planes having maximum deflection of magnetization. When these planes crops out of magnetic plate surface near this surface are forms the fields which are “get out” of the plate boundaries. It is voiced the supposition that in the process of wave propagation owing to these “getting out” fields the plates of maximum deflection acquires the inclined areas which falls behind the main part of moving surface. These inclined areas ensure the formation of transverse component of whole wave number. When the demagnetization is increased the deflection of inclined areas from the normal to the plane of magnetic plate the length of wave in these areas directed along the normal to plane of plate is decreased. The exchange interaction causes to difficulty of distortion of maximum deflections and so the wave length in inclined areas also is decreased. On the basis of mechanics it is voiced supposition that the increasing as demagnetization so exchange increases the hardness of system and this increasing causes the increasing of wave length. It is proposed the conclusion that the variation of transverse wave number by the variation of demagnetization and exchange is subjected to influence of two factors: the variation of maximum deflections plate form and variation of system hardness which both acts in opposite directions. So the resulted alteration of wave number may be determined by the compromises between these two factors. It is established that the more detailed investigation of question about mutual alignment both factors also on the model level may be established as a object for new separate task.