"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 7, 2019

contents of issue      DOI  10.30898/1684-1719.2019.7.3     full text in Russian (pdf)  

UDC 537.874; 537.624




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 July 9, 2019


Abstract. 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.

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


1. Serga A.A., Chumak A.V., Hillebrands B. YIG magnonics. J. Phys. D: Appl. Phys. 2010. Vol.43. P.264002(16).

2. Kruglyak V.V., Demokritov S.O., Grundler D. Magnonics. J. Phys. D: Appl. Phys. 2010. Vol.43. ¹26. P.264001(14).

3. Slonczewski J.C. Current-driven excitation of magnetic multilayers.  Journal of Magnetism and Magnetic Materials. 1996. Vol.159. No.1. P.L1-L7.

4. Berger L. Emission of spin waves by a magnetic multilayer traversed by a current.  Phys. Rev. B. 1996. Vol.54. No.13. P.9353-9358.

5. Gulyaev Yu.V., Zil’berman P.E., Krikunov A.I., Panas A.I., Epshtein E.M. Current-induced inverse population of spin subbands in magnetic junctions.  Journal of experimental and theoretical physics Letters (JETPL). 2001. Vol.93. No.5. P.160.  

6. Gulyaev Yu.V., Zil’berman P.E., Malikov I.V., Mikhailov G.M., Panas A.I., Chigarev S.G., Epshtein E.M. Spin-injection terahertz radiation in magnetic junctions.  Journal of experimental and theoretical physics Letters (JETPL). 2001. Vol.93. No.5. P.259.  

7. Beaurepaire E., Merle J.C., Daunois A., Bigot J.Y. Ultrafast spin dynamics in ferromagnetic nickel.  Phys. Rev. Lett. 1996. Vol.76. No.22. P.4250-4253.

8. Kirilyuk A., Kimel A.V., Rasing T. Ultrafast optical manipulation of magnetic order.  Rev. Mod. Phys. 2010. Vol.82. No.3. P.2731-2784.

9. Walowski J., Münzenberg M. Perspective: Ultrafast magnetism and THz spintronics.  Journ. Appl. Phys. 2016. Vol.120. No.14. P.140901(16).

10. Bigot J.V., Vomir M. Ultrafast magnetization dynamics of nanostructures.  Ann. Phys. (Berlin). 2013. Vol.525. No.1-2. P.2-30.

11. Ka Shen, Bauer G.E.W. Laser-induced spatiotemporal dynamics of magnetic films.  Phys. Rev. Lett. 2015. Vol.115. No.19. P.197201(5).

12. Chernov A.I., Kozhaev M.A., Vetoshko P.M., Zvezdin A.K., Belotelov V.I., Dodonov D.V., Prokopov A.R., Shumilov A.G., Shaposhnikov A.N., Berzhanskii V.N. Local probing of magnetic films by optical excitation of magnetostatic waves.  Physics of the Solid State. 2016. Vol.58. No.6. P.1128.

13. Dreher L., Weiler M., Pernpeintner M., Huebl H., Gross R., Brandt M.S., Goennenwein S.T.B. Surface acoustic wave driven ferromagnetic resonance in nickel thin films: theory and experiment.  Phys. Rev. B. 2012. Vol.86. No.13. P.134415(13).

14. Thevenard L., Gourdon C., Prieur J.Y., Von Bardeleben H.J., Vincent S., Becerra L., Largeau L., Duquesne J.Y. Surface-acoustic-wave-driven ferromagnetic resonance in (Ga,Mn)(As,P) epilayers.  Phys. Rev. B. 2014. Vol.90. No.9. P.094401(8).

15. Chang C.L., Tamming R.R., Broomhall T.J., Janusonis J., Fry P.W., Tobey R.I., Hayward T.J. Selective excitation of localized spin-wave modes by optically pumped surface acoustic waves.  Phys. Rev. Applied. 2018. Vol.10. No.3. P.034068(8).

16. Kim S.-K. Micromagnetic computer simulations of spin waves in nanometer-scale patterned magnetic elements.  J. Phys. D: Appl. Phys. 2010. Vol.43. P.264004(25).

17. Khitun A., Bao M., Wang K.L. Magnonic logic circuits.  J. Phys. D: Appl. Phys. 2010. Vol.43. P.264005(10).

18. Au Y., Ahmad E., Dmytriiev O., Dvornik M., Davison T., Kruglyak V.V. Resonant microwave-to-spin-wave transducer.  Appl. Phys. Lett. 2012. Vol.100. No.18. P.182404(5).

19. Au Y., Davison T., Ahmad E., Keatley P.S., Hicken R.J., Kruglyak V.V. Excitation of propagating spin waves with global uniform microwave fields.  Appl. Phys. Lett. 2011. V.98. ¹12. P.122506(3).

20. Damon R.W., Eshbach J.R. Magnetostatic modes of a ferromagnet slab.  J. Phys. Chem. Solids. 1961. Vol.19. No.3/4. P.308.

21. Joseph R.I., Schlömann E. Theory of magnetostatic modes in long, axially magnetized cylinders.  JAP. 1961. Vol.32. No.6. P.1001.

22. Schlömann E. Generation of spin waves in nonuniform magnetic fields. I. Conversion of electromagnetic power into spin-wave power and vice versa.  JAP. 1964. Vol.35. No.1. P.159.

23. Schlömann E., Joseph R.I. Generation of spin waves in nonuniform dc magnetic fields. II. Calculation of the coupling length.  JAP. 1964. Vol.35. No.1. P.167.

24. Schlömann E., Joseph R.I. Generation of spin waves in nonuniform magnetic fields. III. Magneto-elastic interaction.  JAP. 1964. Vol.35. No.8. P.2382.

25. Schlömann E., Joseph R.I., Kohane T. Generation of spin waves in nonuniform magnetic fields, with application to magnetic delay line.  Proc. IEEE. 1965. Vol.53. No.10. P.1495.

26. Schlömann E. Amplification of magnetostatic surface waves by interaction with drifting charge carriers in crossed electric and magnetic fields.  JAP. 1969. Vol.40. No.3. P.1422.

27. Adam J.D. Analog signal processing with microwave magnetics.  Proc. IEEE. 1988. Vol.76. No.2. P.159.

28. Ishak W.S. Magnetostatic wave technology: a review.  Proc. IEEE. 1988. Vol.76. No.2. P.171.

29. Schlömann E.F. Circulators for microwave millimeter wave integrated circuits.  Proc. IEEE. 1988. Vol.76. No.2. P.188.

30. Adam J.D., Collins J.H. Microwave magnetostatic delay devices based on epitaxial yttrium iron garnet.  Proc. IEEE. 1976. Vol.64. No.4. P.794.

31. Smith K.R., Kabatek M.J., Krivosik P., Wu M. Spin wave propagation in spatially nonuniform magnetic fields.  J. Appl. Phys. 2008. Vol.104. No.4. P.0439116(10).

32. Gruszecki P., Krawczyk M. Spin-wave beam propagation in ferromagnetic thin films with graded refractive index: mirage effect and prospective applications.  Phys. Rev. B. 2018. Vol.97. No.9. P.094424(9).

33. Kalinikos B.A., Slavin A.N. Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions.  J. Phys. C. 1986. Vol.19. P.7013-7033.

34. Grigoryeva N.Y., Popov D.A., Kalinikos B.A. Dipole-exchange spin wave spectrum in an anisotropic ferromagnetic waveguide with a rectangular cross section.  Physics of the Solid State. 2014. Vol.56. No.9. P.1806-1816.

35. Gurevich A., Melkov G. Magnitnie kolebania i volny [Magnetic oscillations and waves]. Moscow, “Nauka-Fizmatlit” Publ., 1994. (In Russian).

36. Monosov Ya.A. Nelineyny ferromagnitniy rezonans [Nonlinear ferromagnetic resonance]. Moscow, “Nauka” Publ., 1971. (In Russian).

37. Shavrov V.G., Shcheglov V.I. Magnitostaticheskie volny v neodnorodnih polyah [Magnetostatic waves in nonuniform magnetic fields]. Moscow, “Fizmatlit” Publ., 2016 (In Russian).

38. Shavrov V.G., Shcheglov V.I. Magnitostaticheskie I elektromagnitnie volny v sloshnih structurah [Magnetostatic waves in composite structures]. Moscow, “Fizmatlit” Publ., 2017 (In Russian).

39. Shavrov V.G., Shcheglov V.I. Ferromagnitniy resonans v usloviyah orientacionnogo perehoda [Ferromagnetic resonance in conditions of orientation transition]. Moscow, “Fizmatlit” Publ., 2018 (In Russian).

40. Shavrov V.G., Shcheglov V.I. Dinamika namagnichennosty v usloviyah izmeneniz eye orientacii [Dynamics of magnetization in conditions of its orientation changing]. Moscow, “Fizmatlit” Publ., 2019 (In Russian).

41. Shcheglov V.I. The influence of demagnetizing field on dispersion properties of Damon-Eshbach surface wave.  Zhurnal Radio electroniki – Journal of Radio Electronics. 2019. No.2. Available at: http://jre.cplire.ru/jre/feb19/3/text.pdf (In Russian).

42. Dwight H.B. Tables of integrals and other mathematical data. New York. The Macmillan Company. 1961.

43. Sushkevich A.K. Osnovi visshey algebry [Foundations of high algebra]. Moscow-Leningrad, “Gosudarstvennoe izdatel’stvo tekhniko-teoreticheskoy literatury” Publ., 1941. (In Russian).

44. Korn G.A., Korn T.M. Mathematical handbook for scientists and engineers. New York. McGraw-Hill Book Company. 1968.

45. Demidovich B.P., Maron I.A. Osnovy vychislitelnoy matematiki [Foundations of numerical mathematics]. Moscow, “Fizmatgiz” Publ., 1963. (In Russian).

46. Kalashnikov S.G. Elektrichestvo [Electricity]. M.: Nauka. 1964. (In Russian).

47. Sivukhin D.V. Obschiy kurs fiziki. Tom 3. Elektrichstvo [General physics course. Vol.3. Electricity]. Moscow, :Nauka” Publ., 1977. (In Russian).

48. Malozemoff A.P., Slonczewski J.C.  Magnetic domain walls in bubble materials. New York. Acad. Press. 1979.


For citation:

V. I. Shcheglov. The influence of exchange interaction and dynamic demagnetizing field on the dispersion of Damon-Eshbach surface wave. Part 1. Transverse wave number. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No. 7. Available at http://jre.cplire.ru/jre/jul19/3/text.pdf

DOI  10.30898/1684-1719.2019.7.3