Abstract. On the basis of whole
electrodynamics it is investigated the dispersion properties of electromagnetic
waves propagating on in-plane magnetized ferrite plate having bigyrotropic
properties. The investigation is made in supposition that the magnetic plate
has dissipation. In Damon-Eshbach geometry it is investigated the general wave
equation for gyromagnetic wave. It is found the dispersion relation expressed
through the wave vector components which are normal to the plate surface. The
structure of these dispersion relation is transformed to the appearance of
Damon-Eshbach relation which connects the magnetostatic wave frequency with
wave number in the direction of wave propagation. It is investigated the
special feature of dispersion relation for the medium having dissipation. The
dispersion relation is transformed to the appearance having real and imaginary
parts which sum is equal to zero. The equality of each these parts may be able
to found the system of equations for real and imaginary parts of wave number
which have the components of magnetic permeability tensor. It is established
the universal character of these equation system which in equal degree is
maintained in whole electrodynamics and magnetostatic approximation. It is
established that in the case of whole electrodynamics the separation of whole
system to two independent equations is not possible and the numeric calculation
must be consist of zero search over two variable quantity. It is proposed the
simplified variant of calculation which is consist of whole dispersion relation
real and imaginary parts and zero search by variation only real part of wave
number. It is established that when dissipation is absent the dispersion curves
except of usual branch of surface Damon-Eshbach wave there is other branch
having more high frequency. It is investigated the special feature of
gyromagnetic wave dispersion in ferrite plate by small values of wave number.
In the region of surface waves it is found two branches – low-frequency and
high-frequency. This low-frequency branch is correspond to magnetostatic
Damon-Eshbach wave and high-frequency branch in magnetostatic approximation is
absent. In the region of volume waves which is disposed higher then
Damon-Eshbach wave it is found two branches of forward waves having over the
wave number limited character which is limited by the light speed in the space. It is shown that with
dissipation the character of Damon-Eshbach branches is not changed. The both
branches of volume waves which frequency is more then Damon-Eshbach frequency
turned to the sin of wave number decrease and make the regions of backward
waves. It is found the mutual pushing of these branches creates the forbidden
zone which is connected with anomalous dispersion known in optics. It is investigated
the dispersion curves for gyromagnetic wave in dissipative medium in the region
of large wave number values. It is shown that the Damon-Eshbach branch has the
limitation by wave number which is analog to the limitation in magnetostatic approximation.
When the frequency is increased above the frequency of wave number limitation
this branch turns to the small wave number values and forms the region of
backward waves. When the wave number decreases this branch connects with
high-frequency branch which is lying higher then Damon-Eshbach branch.
Key words: equations of
electrodynamics, magnetostatic approximation, bigyrotropic medium, gyromagnetic
wave.
References
1. Adam J.D. Analog
signal processing with microwave magnetics Proc. IEEE. 1988. Vol.76.
No.2.
P.159.
2. Ishak W.S.
Magnetostatic wave technology: a review. Proc. IEEE. 1988. Vol.76. No. 2. P.171.
3. Adam J.D.,
Davis L.E., Dionne G.F., Schloemann E.F., Stitzer S.N. Ferrite devices and
materials. IEEE Trans. on Microwave Theory and Techniques. 2002. Vol.50.
No.3.
P.721.
4. Gurevich
A.G. Ferrity na sverkhvysokikh chastotakh [Ferrites on microwave frequencies]. Moscow,
FIZMATLIT Publ., 1960 (In Russian)
5. Gurevich
A.G. Magnitnyi rezonzns v ferritakh i antiferromagnetikakh [Magnetic resonance in ferrites and antiferromagnetics]. Moscow, Nauka
Publ., 1973 (In Russian)
6. Gurevich
A.G., Melkov G.A. Magnitnye kolebaniya i volny [Magnetic oscillations and waves]. Moscow, Nauka. Fizmatlit.
Publ., 1994. (In Russian)
7. Kirilyuk
A., Kimel A.V., Rasing T. Ultrafast optical manipulation of magnetic order. Rev.
Mod. Phys. 2010. Vol.82. No.3. P.2731.
8. Walowski
J., Münzenberg M. Perspective: Ultrafast magnetism and THz spintronics. Journ.
Appl. Phys. 2016. Vol.120. No.14. P.140901(16).
9. Janusonis
J., Chang C.L., Jansma T., Gatilova A., Vlasov V.S., Lomonosov A.M., Temnov
V.V., Tobey R.I. Ultrafast magnetoelastic probing of surface acoustic transients.
Phys. Rev. B. 2016. Vol.94. No.2. P.024415(7).
10. Janusonis
J., Jansma T., Chang C.L., Liu Q., Gatilova A., Lomonosov A.M., Shalagatskyi
V., Pezeril T., Temnov V.V., Tobey R.I. Transient grating spectroscopy in
magnetic thin films: simultaneous detection of elastic and magnetic dynamics.
Scientific reports. 2016. 6:29143. DOI:
10.1038/serp29143. Available at:
www.nature.com/scientificreports. P.1-10.
11. Chang
C.L., Lomonosov A.M., Janusonis J., Vlasov V.S., Temnov V.V., Tobey R.I.
Parametric frequency mixing in a magnetoelastically driven linear ferromagnetic
oscillator. Phys. Rev. B. 2017. Vol.95. No.6. P.060409(5).
12. VlasovV.S.,
Makarov P.A., Shavrov V.G., ShcheglovV.I. The orientational characteristics of
magnetoelastic waves excitation by femtosecond light pulses. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2017. No.6. Available at:
http://jre.cplire.ru/jre/jun17/5/text.pdf
(In Russian).
13. 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.1128-1134.
14. Damon
R.W., Eshbach J.R. Magnetostatic modes of a ferromagnet slab. J. Phys. Chem.
Solids. 1961. Vol.19. No.3/4. P.308.
15. Shavrov
V.G., Shcheglov V.I. Magnitostaticheskie volny v neodnorodnykh polyakh [Magnetostatic waves in nonuniform magnetic fields]. Moscow, Fizmatlit
Publ., 2016 (In Russian).
16. Vashkovsky
A.V., Lock E.H. The magnetostatic surface waves characteristics in
ferrite-dielectric structure displaced to slowly changed nonuniform magnetic
field. Journal of Communications Technology and Electronics. 2001. Vol.46.
No.10.
PP.1163-1170.
17. Vashkovsky
A.V., Lock E.H. The magnetostatic surface waves in serrate-dielectric structure
surrounded by semi-surface having negative dielectric permeability. Journal
of Communications Technology and Electronics. 2002. Vol.47. ¹1. PP
87-91
18. Lock E.H.
Magnetostatic waves in ferrite films and based on its structures. Doctor’s
thesis on physics and mathematic science. Moscow. IRE RAS. 2007. (In Russian)
19. Vashkovsky
A.V., Lock E.H. About the transformation mechanism of magnetostatic wave to
electromagnetic wave. Journal of Communications Technology and Electronics. 2009.
Vol.54. No. 4. P.456-467.
20. Vashkovsky
A.V., Lock E.H.
On the relationship between magnetostatic
wave energy and dispersion characteristics in ferrite structures. Phys. Usp. 2011. Vol.54.
No.3. P.281-290
21. Shavrov
V.G., Shcheglov V.I. Magnotostatticheskie i elektromagnitnye volny v slozhnykh
strulturakh [Magnetostatic and electromagnetic waves in complex
structures]. Moscow, Fizmatlit Publ., 2017 (In Russian).
22. Keller Yu.I.,
Makarov P.A., Shavrov V.G., Shcheglov V.I. The dispersion properties of
electromagnetic waves on in-plane magnetized ferrite plate. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2014.
No. 7. Available at:
http://jre.cplire.ru/jre/apr18/7/text.pdf
(In Russian).
23. Vizulin S.A., Rozenson A.E., Sheh S.A, About the spectrum of magnetostatic surface waves in ferrite
film with dissipation. Journal of Communications Technology and Electronics.
1991. Vol.36. No.1. P.164. (In Russian)
24. Vizulin
S.A. Generalized flat waves in the tasks of electrodynamics magnetic-gyrotropy
media. Doctor’s thesis on physics and mathematic science. Krasnodar.
2000.
25. Polzikova
N.I., Raevsky A.O. The special features of surface spin waves dispersion laws
in structures contained superconductor. Phys.Stat.Sol. 1996. Vol.38. No.10.
P.2037.
26. Annenkov
A.Yu., Gerus S.V. Book of Abstracts of Moscow International Symposium on
Magnetism (MISM). 2014. Published by Physical Faculty of Moscow State
niversity, Moscow, P.863.
27. Annenkov
A.Yu., Gerus S.V. Book of papers of International conference «Electromagnetic
field and materials. Moscow, NIU MEI Publ., 2014. P.99.
28. Makarov
P.A., Shavrov V.G., Shcheglov V.I. Influence of dissipation on magnetostatic
surface waves in tangent magnetized ferrite plate. Zhurnal Radioelectroniki
– Journal of Radio Electronics. 2014. No.7. Available at:
http://jre.cplire.ru/jul14/8/text.pdf
(In Russian).
29. Keller
Yu.I., Makarov P.A., Shavrov V.G., Shcheglov V.I. The magnetostatic surface
waves in ferrite plate with dissipation. Part 1. Dispersion relations. Zhurnal Radioelectroniki – Journal of Radio Electronics. 2016.
No. 2. Available
at: http://jre.cplire.ru/jre/feb16/2/text.pdf (In Russian).
30. Keller
Yu.I., Makarov P.A., Shavrov V.G., Shcheglov V.I. The magnetostatic surface
waves in ferrite plate with dissipation. Part 2. Propagation of wave in
perpendicular to field direction. Zhurnal Radioelectroniki – Journal of
Radio Electronics. 2016. No.3. Available at:
http://jre.cplire.ru/jre/mar16/1/text.pdf
(In Russian).
31. Keller
Yu.I., Makarov P.A., Shavrov V.G., Shcheglov V.I. The magnetostatic surface
waves in ferrite plate with dissipation. Part 3. Propagation of wave in arbitrary
direction relatively to field. Zhurnal Radioelectroniki – Journal of Radio
Electronics. 2016. No.3. Available at:
http://jre.cplire.ru/jre/mar16/2/text.pdf
(In Russian).
32. Keller
Yu.I., Makarov P.A., Shavrov V.G., Shcheglov V.I. Dispersion properties of
magnetostatic surface waves in ferrite plate with dissipation. Journal of
Communications Technology and Electronics. 2018. Vol.63. No.6. P.570-576.
33. Keller
Yu.I., Makarov P.A., Shavrov V.G., Shcheglov V.I. Propagation of magnetostatic
surface waves in a dissipative ferrite plate. Journal of Communications
Technology and Electronics. 2018. Vol.63. No.9. P.1035-1041.
34. Makarov
P., Maltceva L., Kotov L., Shcheglov V. Magnetostatic waves in a medium with
damping. Eur. Phys. Journ. 2018. Vol.185. P.02012(3).
35. Makarov
P., Maltceva L., Kotov L., Shcheglov V. Dispersion of the magnetostatic volume
waves in a medium with damping. Eur. Phys. Journ. 2018. Vol.185. P.02015(4).
36. Dwight
H.B. Tables of integrals and other mathematical data. New York. The Macmillan
Company. 1961.
37. Gilbert T.L.
A phenomenological theory of damping in ferromagnetic materials. IEEE Trans.
on Magn. 2004. Vol.40. No.6. P.3443.
38.
Kalashnikov S.G. Elektrichestvo [Electricity]. Moscow, Nauka Publ., 1964.
(In Russian)
39. Sivukhin
D.V. Obshchiy kurs fiziki. Tom 1. Elektrichestvo [Whole course of physics. Vol.3. Electricity]. Moscow,
Nauka Publ., 1977. (In Russian)
40. Landau
L.D., Lifshits E.M. Teoriya polya [Theory of field]. Moscow, Nauka Publ., 1967.
(In Russian)
41. Levich
V.G. Kurs teoreticheskoi fiziki. Tom 1 [Course of theoretial physics.
Vol.1]. Moscow, Nauka Publ., 1969. (In Russian)
42. Landsberg
G.S. Optika [Optics]. Moscow, Nauka Publ., 1976.(In Russian)
43. Born M.,
Volf E. Principles of Optics.
Cambridge University Press, 1999. 987 p.