"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 2, 2019

contents of issue      DOI  10.30898/1684-1719.2019.2.3     full text in Russian (pdf)  



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 January 23, 2019


Abstract. The influence of demagnetizing field on dispersion properties of Damon-Eshbach surface wave is investigated. It is noted that in literature the attention to demagnetizing field of propagated wave is insufficient. This field is very perceptible for waves which length is so short as some nanometers. In the geometry of Damon-Eshbach task it is proposed the model of demagnetizing field formation for the wave propagated in thin plate. It is proposed that this field is originated from condensation of magnetic charges in wave crests. For quantitative description of this field it is proposed the presentation of its amplitude in the form of hyperbolic tangent which argument in the bend point is equal to zero. It is investigated the dependence of demagnetizing field from wave number. It is shown that by the plate thickness is decreased, the wave number from which the demagnetizing field consideration is necessary, is gradually increased. It is shown that by the wave numbers about 106 cm-1 and more (as it take place in most quantity of today papers about magnetostatic waves) the consideration of demagnetizing field of wave is necessary in principle. It is found the magnetic susceptibility tensor which takes in consideration the periodic character of propagating wave. For the potential of propagating wave field it is found the Walker equation which takes in consideration the demagnetizing field influence. The most difference from its classic variant in Damon-Eshbach task is the availability of mixed second order derivative over the coordinates which are normal to static field direction. The Walker equation is resolved by division of variable method. It is shown that the mixed derivative leads to complex structure of wave number component which is normal to the plane of magnetic plate. In the case of surface wave the whole decision for potential component along this coordinate is the multiplication of decreasing exponential coefficient on periodical factor having sinusoidal character. It is presented the whole formation of task about the propagation of surface wave by Damon-Eshbach type in presented geometry with taking into consideration the demagnetizing field of wave. As a result of boundary task decision it is found the dispersion relation in the exaction in form as dispersion relation in classical Damon-Eshbach task. From the equality to zero of real and imaginary parts of this dispersion relation in separate it is found two equations which connect the wave number and frequency. It is shown that the equation for real part of dispersion relation in the case when demagnetization is absent transfer to classic dispersion relation of Damon-Eshbach task. On the basis of obtained dispersion relation for the magnetic film having thickness of 10 micrometers it is investigated the dispersion of surface wave with taking into consideration the demagnetizing field of wave. It is shown that the demagnetizing field consideration brings to increasing of dispersion curve in region of high values of wave number. As a quality cause of frequency increasing is proposed the supposition about the increasing of effective hardness of spin system. This increasing is caused by additional coercion on magnetization vector form demagnetizing field which try to attain do not deflect this vector from equilibrium position. It is investigated the character of dispersion curve deformation when demagnetizing field parameter is varied. It is shown that when the demagnetizing field parameter is increased the dispersion curve improvement is also increased. When demagnetizing field parameter is more then 0,02 the dispersion curve improvement acquires the two-steps character. In this case the first step describes the surface wave dispersion which is cased by demagnetizing factor of magnetic plate as a whole. The second step describes the influence of demagnetizing field of wave itself. When the demagnetizing field parameter is increased the first step is nit varied but the second step also is increased on the same manner as the value of this parameter. It is investigated the structure of dynamic magnetization distribution inside of magnetic plate which id determined by complex character of transverse wave number. It is shown that the real part of transverse wave number depend on longitudinal wave number completely linear with angle coefficient equal to unit. The imaginary part of this wave number by the demagnetizing field parameter is increased experience the expansion to upper which in first is small but after this is more and slowed and try to attain to linear low. The observed motion of these curves is explained on the basis of analytical forms structure of dependence imaginary part of wave number from longitudinal wane number and demagnetizing field parameter. It is investigated the structure of dynamical potential inside of magnetic plate. It is shown that the multiplication of exponential end sinusoidal parts of wave number the potential near the both surfaces of magnetic plate acquire the depressions having a-periodic character. In brief it is described the special feature of founded distribution which is caused by nonreciprocal character of surface wave propagation. As example to the magnetostatic wave application to information processing devises it is described the degree of influence of demagnetizing field on dispersion magnetostatic waves by the plate thickness variation. In the case of most important on today the wave length range as some units of nanometers it is established the necessity of demagnetizing field taking into consideration begin from wave number 105 cm and particularly for wave numbers 106 cm and more.  

Key words: magnetostatic wave, demagnetizing field, 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. ruglyak V.V., Demokritov S.O., Grundler D. Magnonics.  J. Phys. D: Appl. Phys. 2010. Vol. 43. No. 26. 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. JETP Letters. 2007. Vol. 87. No. 5. P. 160-164.  

  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.  JETP Letters. 2011. 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. Vol. 98. No. 12. 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 perekhoda. [Ferromagnetic resonance in conditions of orientation transition]. M.: Fizmatlit. 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. Antonets I.V., Kotov L.N., Kirpicheva O.A., Golubev E.A., Kalinin Yu. E., Sitnikov A.V., Shavrov V.G., Shcheglov V.I. Dynamic conductivity mechanism in amorphous nanogranulated “metal-dielectric” films in microwave frequencies. // Zhurnal Radio Electroniki – Journal of Radio Electronics. 2014. No. 4. Available at: http://jre.cplire.ru/jre/apr14/12/text.pdf

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


For citation:

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

DOI  10.30898/1684-1719.2019.2.3