Spectral characteristics of equilibrium position precession of magnetization in normal magnetized ferrite plate.
Authors:   Syktyvkar State University, Oktyabrskiy prosp. 55, Syktyvkar 167001, Russia, Vlasov V.S. , Shavrov V.G. ,   Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia, Shcheglov V.I. ,   Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia
Published: March 2021

The investigation of spectral characteristics of precession equilibrium balance position of magnetization is the main subject of this work. The geometry of task is normal magnetized ferrite plate. In this case the parametrical excitation of exchange spin waves is not possible and the angle of precession cone may be about some tens of degree. It is established that in the condition of orientational transition the switching of alternating magnetic field having circular polarization leads to precession of equilibrium position of magnetization. In this case the magnetization vector takes part in two precession motions: the first – along the large ring, the second – along the small ring. The radius of large ring is determined by the equilibrium angle between of magnetization vector direction and the external magnetic field direction. The radius of small ring is determined by the angle of deflection of magnetization vector from equilibrium position which moves along the large ring. As a result the precession portrait consist of large circular ring which is filled along its environment by small rings. The formula for specific energy which consist of interaction of magnetization with constant and alternating fields and also with demagnetization field is derived. On the basis of Landau-Lifshits equation the system of nonlinear equations of motion for three components of magnetization is derived. By the numerical solution of this system by Rounge-Cutta method the evolutions in time and corresponded precession portraits for magnetization are found. The possibility of founding the spectral characteristics of magnetization equilibrium position precession by the standard mathematical package “Matlab” which based by fast Fourier transformation is demonstrated. The program algorithm of this calculation using the evolutions in time which are found from the system of equations for magnetization is described. The evolutions in time, precession portraits and spectrums for five basis regimes are found. This regimes are: №1 – the small-amplitude circular precession; №2 – precession of equilibrium position without the envelop of centre; №3 – non-fading precession of equilibrium position with the envelop of centre; №4 – fading precession of equilibrium position with the envelop of centre; №5 – comprehensive circular precession. It is established that for the spectrum of all regimes the most typical line are on two frequencies – on the frequency of excitation which is equal to the frequency of alternate field and on the frequency of precession of equilibrium position which is more less then the frequency of excitation. The comparative investigation of amplitudes of both spectral lines shows that in the regime №1 and especially in the regime №2 the amplitude of line on the frequency of equilibrium position precession is more then the amplitude of line on the frequency of excitation. In the regime №3 and especially №4 the amplitude of line on the excitation frequency is more larger then the amplitude of line on the equilibrium position precession and in the regime №5 the line on the frequency of equilibrium position precession is absent. The dependencies of amplitude of spectrum line on the frequency of excitation from the level of alternative field in different regimes are investigated. As a control also the measuring of the same values from the evolutions in time are executed. It is found that the measuring by the spectrums in the middle part of whole interval where the equilibrium precession take place gives out the values which are a few smaller then the same values which are found from the evolutions in time. For the compensation of this divergence the correcting addition in the form of quadratic polynomial having negative sign is proposed. The dependencies of amplitude spectrum line on the frequency of precession equilibrium from the amplitude of excitation field are investigated. It is found that the using of correction slightly increases the level of dependence (about of 20%) in the whole interval of equilibrium precession presence. In this case the general character of curve is not changed. The character indication of this dependency is the initial horizontal path which occupies the most path of regime №2 and has subsequent abatement in the regime №3, №4 with decreasing to zero in the regime №5. The mechanism of formation of horizontal path is explained on the basis of vector model. It is found that by small amplitude of excitation the precession of equilibrium takes place along the cone which angle is determined by the value of equilibrium inclination of magnetization vector from the field. This motion is the reason of horizontal path of investigated dependence. The increasing of excitation level leads to the increasing of cone angle around the equilibrium position. By this reason the both cones of precession connect together and amplitude on the frequency of equilibrium precession decrease to zero. The investigation of dependence of equilibrium precession frequency from the amplitude of excitation is made. The main measuring are made by spectrum which are founded by whole five regimes. The control measuring are made by analysis of geometrical parameters (periods) of evolutions in time. The good agreement between both dependencies is found. The discrepancy was not more then 5%. The comparison of measured dependence with the analytical formula having quadratic character founded by the basis of vector model is made. It is found that in the regimes №1 and №1 analytical formula describes the measured dependencies to the approximation of 5% but in regimes №3 and №4 the quadratic increasing of explored dependencies is slowed down and the formula gives the excessive values on 20% and more. It is established that the reason of this discrepancy is the lowering the precision of formula so as by its derivation it is accepted the supposition about a small value of equilibrium precession angle. The introduction of correction into index of degree of alternating field which decreases this index when excitation level increases is proposed. Some possible questions for new investigations is proposed. In the first place it is mentioned that the large enrichment of spectrum may be expected from violation of symmetry of equilibrium precession by constant or alternate fields. In this case the evolutions in time acquire the view of pulses having complex form. In this case in the spectrum of equilibrium precession must be appear large quantity additional frequencies harmonic character. The large variety of spectrum may introduce the investigation of equilibrium precession in anisotropic media. It is mentioned that the investigation of spectrum in these conditions may demand for interpretation of results the elaboration of new models which will be different from models which applied in symmetrical case.