Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 8

Full text in Russian (pdf)

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DOI  https://doi.org/10.30898/1684-1719.2020.8.2

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 June 16, 2020


Abstract. The main result of this work is the interpretation of spin-wave resonance excitation by uniform alternating field in the case of the absence of surface anisotropy but on the basis of hardness of spin chain which is brought by non-uniform exchange interaction. In the geometry of normal magnetized film we investigated the classic variant of spin-wave resonance excitation on the basis of vibrations of change consisted from spins which are connected by exchange interaction. The task is solved about the vibrations of this chain in connection with the boundary conditions which consist of equality to zero of amplitude of vibrations on the film surfaces. These conditions correspond to attachment on spins on these surfaces. Based on the analysis of the overlap integral, it is shown that excitation is possible only of those modes for which an odd number of half-waves of oscillations fit over the film thickness. The insufficiency of the surface anisotropy model for the interpretation of a number of experimental results is noted. It is noted that in all versions of this model, there is no account of the hardness of the spin chain due to the exchange interaction. A model of spin chain vibrations is proposed, based on taking into account the hardness of the spin chain without introducing surface anisotropy. As a simplified analogy, a mechanical model of vibrations of a hard string is presented. It was found that the manifestation of string hardness consists in the emergence of a straighten force opposing the bending of the string. It is shown that the rectifying force is proportional to the second derivative of the displacement of the string along the coordinate along its main direction. A wave-type equation is obtained for the vibrations of a hard string, which contains the second-order coordinate and time derivatives in combination with a third-order derivative of the string displacement along the coordinate. It is noted that the third-order derivative corresponds to a straighten force that prevents the string from bending. The solution of the obtained third-order equation is performed by the method of separation of variables. Boundary conditions are proposed, which consist in the absence of a straighten force, that is, in the equality to zero of the second derivative of the coordinate displacement at the ends of the string. It is shown that taking into account the proposed boundary conditions leads to a solution that is a discrete set of modes, similar to that for a string with fixed ends, the main difference being the absence of such a fixation. The results obtained on the mechanical model were applied for analyzing vibrations of a chain of spins coupled by exchange interaction in a normally magnetized thin film. It is established that the field of non-uniform inhomogeneous exchange interaction is proportional to the second derivative of the transverse component of the magnetization along the coordinate along the chain. It was found that such a field is a mechanism for the generation of a force that straightens the spin chain during its bending. Boundary conditions are proposed, consisting in the absence of a straighten force, that is, in the equality to zero on the film surfaces of the second derivative of the transverse magnetization. Taking into account the boundary conditions, a discrete spectrum of vibration modes was found, similar to that obtained using the surface anisotropy model  with the main difference being the absence of spin pinning on the film surfaces. Some recommendations are given for the further development of the hard spin chain model.

Key words: spin-wave resonance, exchange interaction, curvature hardness. 


1. Suzdalev I.P. Nanotekhnologiya. Fiziko-khimiya nanoklasterov, nanostruktur i nanomaterialov [Nanotechnology. Physics and chemistry of nanoclusters, nanostructures and nanomaterials]. Moscow, KomKniga Publ. 2006.  (In Russian)

2. Rit M. Nanokonstruirovaniye v nauke i tekhnike. Vvedeniye v mir nanorascheta [Nanodesign in science and technology. Interaction to the nanocalculation world]. Moscow-Ijevsk, NITS “Regular and chaotic dynamics”.  2005. (In Russian)

3. Vendick I.B., Vendick O.G. Metamaterials and its application in microwave engineering. Journ Tech. Phys. 2013. Vol.83. No.1. P.3.

4. Vinogradov A.P. Elektrodinamika kompozitnykh materialov [Electrodynamics of composite materials]. Moscow, URSS Publ. 2001. (In Russian)

5. Vinogradov A.P., Dorofeenko A.V., Zukhdi S. To the question about effective materials parameters. Physics Uspekhi. 2008. Vol.178. No.5. P.511.

6. Veselago V.G. Waves in metamaterials: its role in modern physics. Physics Uspekhi. 2011. Vol.181. No.11. P.1201.

7. Golovanov O.S., Makeeva G.S., Rinkevich A.B. Interaction of electromagnetic waves with periodic lattices of micro and nanoribbons in teracycle per second microwave region. Journ Tech. Phys. 2016. Vol.86. No.2. P.119.

8. Makeeva G.S., Golovanov O.A. Matematicheskoye modelirovaniye elektronnoupravlyayemykh ustroystv teragertsovogo diapazona na osnove grafena i uglerodnykh nanotrubok [Mathematical modeling of electronics-controlled theracycle-microwave devices based on grapheme and carbon nano-tubes]. Penza. Penza State University. 2018. (In Russian)

9. Makeeva G.S., Golovanov O.S., Rinkevich A.B. The probability model and electro-dynamical analysis of resonance interaction of electromagnetic waves with 3D-magnetic nanocomposites.  J. Comm. Technol. Electron. 2014. Vol.59. No.2. P.139-144. https://doi.org/10.1134/S1064226913120139  

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

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

12. Kruglyak V.V., Demokritov S.O., Grundler D. Magnonics.  J. Phys. D: Appl. Phys. 2010. Vol.43. No.26. P.264001(14).

13. 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.

14. 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.

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

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

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

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

19. 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.

20. 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).

21. 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).

22. 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).

23. Gulyaev Yu.V., Zilberman 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). 2007. Vol.85. No.3. P.160.  

24. Gulyaev Yu.V., Zilberman 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.  

25. Vilkov E.A., Mikhailov G.M., Nikitov S.A., Safin A.P., Chigarev S.G., Fomin L.A., Chernikh A.V. The kinetic equation of spin polarization of non-equilibrium conductivity electrons in magnetic transitions. XXIII International conference “Novoye v magnetizme i magnitnykh materialakh (NMMM-2018) [«New in magnetism and magnetic materials (NMMM-2018»]. MIREA. Moscow, Buki Vedi Publ. 2018. P.298. (In Russian)

26. 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).

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

28. 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).

29. 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. Vol.98. No.12. P.122506(3).

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

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

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

33. 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)

34. 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)

35. Gurevich A.G. Ferrity na sverkhvysokikh chastotakh [Ferrites on microwave frequencies]. Moscow, Gos. Izd. fiz. mat. lit. 1960. (In Russian)

36. Gurevich A.G. Magnitnyi rezonans v ferritakh i antiferromagnetikakh [Magnetic resonance in ferrites and antiferromagnetics]. Moscow, Nauka Publ., 1973, 588 p. (In Russian)

37. Gurevich A.G., Melkov G.A. Magnitnye kolebaniya i volny [Magnetic oscillations and waves]. Moscow, Nauka Publ., 1994 (In Russian)

38. Shcheglov V.I. The influence of demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2019. ¹2. https://doi.org/10.30898/1684-1719.2019.2.3 (In Russian).

39. Shcheglov V.I. The influence of exchange interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Part 1. Transverse wave number. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2019. ¹7. https://doi.org/10/30398/1684-1719.2019.7.3 (In Russian).

40. Shcheglov V.I. The influence of exchange interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Part 2. Dispersion relation. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2019. No.9. https://doi.org/10/30398/1684-1719.2019.9.8  (In Russian)

41. Shcheglov V.I. The influence of exchange interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Part 3. Special cases of dispersion. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2019. No.11. https://doi.org/10.30898/1684-1719.2019.11.4  (In Russian)

42. Seavey M.H., Tannenwald P.E. Direct observation of spin-wave resonance. Phys. Rev. Lett. 1958. Vol.1. No.5. P.168.

43. Kittel C. Excitation of spin waves in ferromagnetics by uniform microwave field. Phys. Rev. 1958. Vol.110. No.9. P.1295.

44. Ament W.S., Rado G.T. Phys. Rev. 1955. Vol.97. No.6. P.1558.

45. Tihonov A.N., Samarsky A.A. Uravneniya matematicheskoy fiziki [Equations of mathematical physics]. Moscow, Nauka Publ., 1972 (In Russian) 46. Vonsovsky S.V., Shur Ya.S. Ferromagnetizm [Ferromagnetism]. Moscow, OGIZ Gostechizdat Publ. 1948. (In Russian)

47. Lugovskoy A.V., Shcheglov V.I. Spectrum of exchange and nonexchange spin-wave excitations in ferrite garnet films. J. Comm. Technol. Electron. 1982. V.27. No.3. P.518.  

48. Il’yin V.A., Poznyak E.G. Osnovy matematicheskogo analiza. Chast’ 1 [Foundations of mathematical analysis. Part 1]. Moscow, Nauka Publ., 1965 (In Russian). 

49. Strelkov S.P. Mekhanika [Mechanics]. Moscow, Nauka Publ. 1965. (In Russian)

50. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Nonlinear excitation of hypersound in ferrite plate by ferromagnetic resonance. Journal of Communications Technology and Electronics. 2009. Vol.54. No.7. P.821-832. https://doi.org/10.1134/S1064226909070110


For citation:

Shcheglov V.I. Excitation of spin-wave resonance in thin magnetic films in the absence of surface anisotropy. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 8. https://doi.org/10.30898/1684-1719.2020.8.2   (In Russian)