Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2021. No. 3
ContentsFull text in Russian (pdf)
DOI https://doi.org/10.30898/1684-1719.2021.3.2
UDC 537.874; 537.624
Spectral characteristics of equilibrium position precession of magnetization in normal magnetized ferrite plate
V. S. Vlasov 1, V. G. Shavrov 2, V. I. Shcheglov 2
1 Syktyvkar State University, Oktyabrskiy prosp. 55, Syktyvkar 167001, Russia
2 Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia
The paper was received on March 9, 2021
Abstract. 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: ¹1 – the small-amplitude circular precession; ¹2 – precession of equilibrium position without the envelop of centre; ¹3 – non-fading precession of equilibrium position with the envelop of centre; ¹4 – fading precession of equilibrium position with the envelop of centre; ¹5 – 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 ¹1 and especially in the regime ¹2 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 ¹3 and especially ¹4 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 ¹5 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 ¹2 and has subsequent abatement in the regime ¹3, ¹4 with decreasing to zero in the regime ¹5. 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 ¹1 and ¹1 analytical formula describes the measured dependencies to the approximation of 5% but in regimes ¹3 and ¹4 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.
Key words: precession of magnetization, orientation transition, spectrum analysis.
References
1. Gurevich A.G. Ferrity na sverkhvysokikh chastotakh [Ferrites on microwave frequencies]. Moscow, FIZMATLIT Publ. 1960. (In Rusian)
2. Gurevich A.G. Magnitnyy rezonans v ferritakh i antiferromagnetikakh [Magnetic resonance in ferrites and antiferromagnetics]. Moscow, Nauka Publ. 1973. (In Russian)
3. Gurevich A., Melkov G. Magnitnyye kolebaniya i volny [Magnetic oscillations and waves]. Moscow, Nauka-Fizmatlit Publ. 1994. (In Russian)
4. Gurevich A.G., editor. Ferrity v nelineynykh sverkhvysokochastotnykh ustroystvakh [Ferrites in nonlinear microwave devices]. Moscow, Inostrannaya Literatura Publ. 1961. (In Russian)
5. Pippin J.E. The doubling and transformation of frequency in ferrites. Proc. IRE. 1956. Vol.44. No.8. P.1054.
6. Skomal E.N., Medina M.A. Investigation of multiple transformation of frequency in ferrites. Journ. Appl. Phys. 1959. Suppl. to Vol.30. No.4. P.161S.
7. Jaffe D., Cacheris J.C., Karayianis N. Ferrite detector of microwaves. Proc. IRE. 1958. Vol.46. No.3. P.594.
8. Simon J.C., Broussaud G. Detection with microwave ferrites. Compt. Rend. Acad. Sci. 1954. Vol. 238. No.24. P.2294.
9. Weiss M.T. Ferrite amplifier and generator of microwaves. Phys. Rev. 1957. Vol.107. No.1. P.317.
10. Suhl H. Theory of ferromagnetic resonance by large levels of microwave power. Journ. Phys. Chem. Sol. 1957. Vol.1. No.4. P.209.
11. Monosov Ya.A. Nelineynyy ferromagnitnyy rezonans [Nonlinear ferromagnetic resonance]. Moscow, Nauka Publ. 1971. (In Russian)
12. L’vov V.S. Nelineynyye spinovyye volny [Nonlinear spin waves]. Moscow, Nauka Publ. 1987. (In Russian)
13. Zakharov V.E., L’vov V.S., Starobinets S.S. Spin-wave turbulence beyond the parametric excitation threshold. Sov. Phys. Usp. 1975. Vol.18. No.4. P.896-919.
14. Nielsen J.W., Dearborn E.F. The growing of mono-crystal of magnetic ferrites having garnet structure. Journ. Phys. Chem. Sol. 1958. Vol.5. No.3. P.202.
15. LeCraw R.C., Spencer E.G., Porter C.S. The width of ferromagnetic resonance line in mono-crystals of yttrium- iron-garnet ferrites. Phys. Rev. 1958. Vol.110. No.6. P.1311.
16. Temiryasev A.G., Tikhomirova M.P., Zil’berman P.E. “Exchange” spin waves in nonuniform yttrium iron garnet films. JAP. 1994. Vol.76. No.9. P.5586-5588.
17. Zil’berman P.E., Temiryasev A.G., Tikhomirova M.P. Excitation and propagation of exchange spin waves in yttrium-iron-garnet films. JETP.1995. Vol.108. No.1(7). P.281.
18. Gulyaev Yu.V., Zil’berman P.E., Temiryazev A.G., Tikhomirova M.P. Principal mode of the nonlinear spin-wave magnetized ferrite films. Physics of the Solid State. 2000. Vol.42. No.6. P.1094.
19. Gerrits Th., Schneider M.L., Kos A.B., Silva T.J. Large-angle magnetization dynamics measured by time-resolved ferromagnetic resonance. Phys.Rev.B. 2006. Vol.73. No.9. P.094454(7).
20. Alvarez L.F., Pla O., Chubykalo O. Quasiperiodicity, bistability, and chaos in the Landau-Lifshitz equation. Phys.Rev.B. 2000. Vol.61. No.17. P.11613-11617.
21. Shuty A.M., Sementsov D.I. Nonlinear effects of precession motion of magnetization in the region of ferromagnetic resonance. Physics of the Solid State. 2000. Vol.42. No.7. P.1268.
22. Shuty A.M., Sementsov D.I. Dynamics of magnetization in conditions of nonlinear ferromagnetic resonance in film type of (111). Physics of the Solid State. 2002. Vol.43. No.8. P.1439.
23. Shuty A.M., Sementsov D.I. Dynamics of nonlinear precession motion of magnetization in ferrite-garnet film type of (100). Physics of the Solid State. 2002. Vol.44. No.4. P.734.
24. Sementsov D.I., Shuty A.M. Nonlinear regular and stochastic dynamics of magnetization in thin-film structures. Physics - Uspekhi. 2007. Vol.50. No.8. P.793.
25. Karpachov S.N., Vlasov V.S., Kotov L.N. Nonlinear dynamics of magnetic and elastic sub-systems of thin ferrite film near the acoustic resonance. Vestnik MGU. Ser.3 [Bulletin of Moscow State University. Series 3]. 2006. No.6. P.60. (In Russian)
26. Vlasov V.S. Issledovaniye relaksatsionnoy i nelineynoy dinamiki magnitnykh i magnitouprugikh kolebaniy plenok i chastits [Investigation of relax and nonlinear dynamics of magnetic and magnetoelastic vibrations of films and particles]. PhD thesis in physics and mathematics. Syktivkar. 2007. (In Russian)
27. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Forced nonlinear precession of the magnetization vector under the conditions of an orientation transition. Journal of Communications Technology and Electronics. 2011. Vol.56. No.1. P.73.
28. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Asymmetric forced nonlinear precession of the magnetization under the conditions for the orientation transition. Journal of Communications Technology and Electronics. 2011. Vol.56. No.6. P.670.
29. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Multiregime character of the nonlinear precession of the second-order magnetization under the conditions for the orientational transition. Journal of Communications Technology and Electronics. 2011. Vol.56. No.9. P.1117.
30. Belov K.P., Zvezdin A.K., Kadomtseva A.M., Levitin P.Z. Oriyentatsionnyye perekhody v redkozemel'nykh magnetikakh [Orientational transitions in rare-earth magnetic]. Moscow, Nauka Publ. 1979. (In Russian)
31. Vlasov V.S., Kotov L.N., Shcheglov V.I. Nelineynaya pretsessiya vektora namagnichennosti v usloviyakh oriyentatsionnogo perekhoda [Nonlinear precession of magnetization vector in conditions of orientation transition]. Syktivkar, Syktyvkar State University. 2013. (In Russian)
32. Shavrov V.G., Shcheglov V.I. Ferromagnitnyy rezonans v usloviyakh oriyentatsionnogo perekhoda [Ferromagnetic resonance in conditions of orientation transition]. Moscow, Fizmatlit Publ. 2018. http://jre.cplire.ru/jre/library/Shavrov-Shcheglov_3.pdf. (In Russian)
33. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Nonlinear excitation of hypersound in a ferrite plate under the ferromagnetic-resonance conditions. Journal of Communications Technology and Electronics. 2009. Vol.54. No.7. P.821.
34. Gulyaev Yu.V., Temiryazev A.G., Tikhomirova M.P., Zilberman P.E. Magnetoelastic interaction in yttrium iron garnet films with magnetic inhomogeneities through the film thickness. JAP. 1994. Vol.75. No.10. P.5619.
35. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Nonlinear dynamics of the magnetization in a ferrite plate with magnetoelastic properties under the conditions for orientational transition. Journal of Communications Technology and Electronics. 2010. Vol.55. No.6. P.645.
36. Korn G.A., Korn T.M. Mathematical handbook for scientists and engineers. New York. McGraw-Hill Book Company. 1968.
37. Poteomkin V.G. Systema MATLAB. Spravochnoye posobiye [MATHLAB System. Handbook]. Moscow, DIALOG-MIFI Publ. 1998. (In Russian)
38. Harkevich A.A. Osnovy radiotekhniki [Foundations of radio engineering]. Moscow, Fizmatlit Publ. 2007. (In Russian)
For citation:
Vlasov V.S., Shavrov V.G., Shcheglov V.I. Spectral characteristics of equilibrium position precession of magnetization in normal magnetized ferrite plate. Zhurnal Radioelektroniki [Journal of Radio Electronics]. 2021. No.3. https://doi.org/10.30898/1684-1719.2021.3.2 (In Russian)