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Field dependences of the frequencies of magneto-dielectric oscillations and spin excitations in the disk BF resonator

Frequency splitting effect of degenerate modes in ferrite resonators

Igor V. Zavislyak, Hryhorii L. Chumak


The splitting of magneto-dielectric modes frequency in disk ferrite resonators in a magnetic field is considered. A simplified formula is obtained for estimation of the splitting magnitude. Theoretical and experimental results of the frequency splitting effect in magneto-dielectric modes in the millimeter wave range are compared. The use of the splitting of the magneto-dielectric modes frequencies as an alternative to ferromagnetic resonance in devices with magnetic frequency tuning is suggested, with values of the magnetization fields being an order of magnitude lower than for ferromagnetic resonance. The features of the splitting modes effect in different ferrite classes are investigated and it is shown that it occurs in both microwave and optical ranges. The estimated magnitude of the mode frequency splitting in the iron-yttrium garnet (YIG) transparency window can reach 9 GHz, which is comparable to the 5 GHz splitting in the millimeter range. The frequency ranges where frequency splitting effect is of practical interest are discussed. In particular, the effect in barium hexaferrite can be used both in post-resonance and pre-resonance regions, which is almost impossible for ferrogarnates and ferrospinels.


modes splitting; YIG; barium hexaferrite; ferrite disk resonators; nonreciprocal devices

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NIKOLSKIY, V.V.; NIKOLSKAYA, T.I. Elecrodynamics and Radio Wave Propagation [in Russian]. Moscow: Nauka, 1989.

GRIGORIEV, A.D. Electrodynamics and Microwave Equipment [in Russian]. Moscow: Vyssh. Shkola, 1990.

LEBEDEV, I.V. Microwave Equipment and Devices [in Russian]. Moscow: Vyssh. Shkola, 1970.

ILCHENKO, M.Y.; VZYATYSHEV, V.F.; GASSANOV, L.G.; ET. AL. Dielectric Resonators [in Russian]. Moscow: Radio i Svyaz’, 1989.

BEZBORODOV, Y.M.; NARYTNIK, T.N.; FEDOROV, V.B. Microwave Filters Based on Dielectric Resonators [in Russian]. Kiev: Tekhnika, 1989.

ILYINSKI, A.S.; SLEPYAN, G.Y.; SLEPYAN, A.Y. Propagation, Scattering and Dissipation of Electromagnetic Waves. London: IET, 1993.

GUREVICH, A.G. Magnetic Resonance in Ferrites and Antiferromagnetics [in Russian]. Moscow: Nauka, 1973.

BOSMA, H. On the principle of stripline circulation. Proc. IEE - Part B: Electronic and Communication Engineering, v.109, n.21, p.137-146, 1962. DOI:

ZHANG, Zhizhi; LIU, Jieling; DING, Hao; FENG, Zekun; NIE, Yan. Microwave bandpass filters tuned by the magnetization of ferrite substrates. IEEE Magnetic Lett., v.8, 2016. DOI:

ARABI, Eyad; GHAFFAR, Farhan A.; SHAMIM, Atif. Tunable bandpass filter based on partially magnetized ferrite LTCC with embedded windings for SoP applications. IEEE Microwave Wireless Compon. Lett., v.25, n.1, p.16-18, Jan 2015. DOI:

CHATTOPADHYAY, Taraprasad; BHATTACHARYYA, Prosenjit; DAWN, Santosh Kumar. Frequency tuning of an active microwave bandpass filter by a monotone microwave carrier. Int. J. Electronics Lett., v.5, n.2, p.212-220, 2017. DOI:

NIKYTENKO, A.L.; CHEVNYUK, L.V.; GRYGORUK, V.I.; KOSTENKO, V.I.; ROMANIUK, V.F. Tunable bandpass filter based on single-crystal platelet of BaFe12O19 in multidomain area. Proc. of 9th Int. Kharkiv Symp. on Physics and Engineering of Microwawes, Millimeter and Submillimeter Waves, 20-24 June 2016, Kharkiv, Ukraine. IEEE, 2016. DOI:

CAO, Weiping; JIANG, Di; LIU, Yupeng; YANG, Yuanwang; GAN, Baichuan. A microwave tunable bandpass filter for liquid crystal applications. Frequenz, v.71, n.7-8, June 2017. DOI:

ZHANG, Yuanyuan; FENG, Xixi; ZHU, Kaiqiang; YANG, Xi; LI, Houmin. An X-band tunable circulator based on Yttrium iron garnet thin film. Proc. of IEEE Int. Conf. on Microwave and Millimeter Wave Technology, 5-8 Jun 2016, Beijing, China (IEEE, 2016). DOI:

BELYAEV, B.A.; LEMBERG, Konstantin V.; SERZHANTOV, Alexey M.; LEKSIKOV, Aleksandr A.; BAL’VA, Yaroslav F.; LEKSIKOV, Andrey A. Magnetically tunable resonant phase shifters for UHF band. IEEE Trans. Magnetics, v.51, n.6, June 2015. DOI:

USTINOV, A.B.; KALINIKOS, B.A.; SRINIVASAN, G. Nonlinear multiferroic phase shifters for microwave frequencies. Appl. Phys. Lett., v.104, n.5, Feb 2014. DOI:

PARK, Byeong-Yong; KIM, Tae-Wan; ARYA, A.K.; PARK, Seung-Young; PARK, Seong-Ook. Theory and design of a cylindrical ferrite resonator antenna using HE11d mode splitting behavior. IEEE Trans. Antennas Propag., v.64, n.12, p.5547-5552, Dec 2016. DOI:

BOURHILL, J.; KOSTYLEV, N.; GORYACHEV, M.; CREEDON, D.L.; TOBAR, M.E. Ultrahigh cooperativity interactions between magnons and resonant photons in YIG sphere. Phys. Rev. B, v.93, n.14, p.144420-1-144420-8, Apr 2016. DOI:

KIM, Tae-Wan; PARK, Byeong-Yong; PARK, Seung-Young; PARK, Seong-Ook. Calculation of magnetization value and permeability tensor of a partially magnetized cylindrical ferrite resonator. IEEE Magnetics Lett., v.7, Feb 2016. DOI:

KLOPFER, Klaus; ACKERMANN, Wolfgang; WEILAND, Thomas. Computation of complex eigenmodes for resonators filled with gyrotropic materials. IEEE Trans. Magnetics, v.51, n.1, Jan 2015. DOI:

LAUR, Vincent; VERISSIMO, Gregory; QUEFFELEC, Patrick; FARHAT, eo Arij; ALAAEDDINE, Hussain; REIHS, Jean-Claude; LAROCHE, Eric; MARTIN, Gilles; LEBOURGEOIS, Richard; GANNE, Jean-Pierre. Modeling and characterization of self-biased circulators in the mm-wave range. Proc. of IEEE MTT-S Int. Microwave Symp., 17-22 May 2015, Phoenix, AZ, USA. IEEE, 2015. DOI:

GUREVICH, A.G.; MELKOV, G.A. Magnetization Oscillations and Waves. CRC Press, 1996.

HELSZAJN, J. Passive and Active Microwave Circuits. Wiley-Interscience Pub., 1978.

KAGANOV, M.I.; PUSTYL’NIK, N.B.; SHALAEVA, T.I. Magnon, magnetic polaritons, magnetostatic waves. Phys. Usp., v.40, n.2, p.181, 1997. DOI:

HOW, H.; VITTORIA, C. Microwave phase shifter utilizing nonreciprocal wave propagation. IEEE Trans. Microwave Theory Tech., v.52, n.8, p.1813-1819, 2004. DOI:

GREEN, J.J.; SANDY, F. Microwave characterization of partially magnetized ferrites. IEEE Trans. Microwave Theory Tech., v.22, n.6, p.641-645, Jun 1974. DOI:

DANILOV, V.V.; ZAVISLYAK, I.V.; BALINSKIY, M.G. Spinwave Electrodynamics [in Russian]. Kyiv: Lybid’, 1991.

YAKOVLEV, Y.M.; GENDELEV, S.S. Ferrite Monocrystals in Radioelectronics [in Russian]. Moscow: Sov. Radio, 1975.

BUDAK, B.M.; FOMIN, S.V. Multiple Integrals and Series [in Russian]. Moscow: Nauka, 1965.

POPOV, M.A.; ZAVISLYAK, I.V.; SRINIVASAN, G. Sub-THz dielectric resonance in single crystal yttrium iron garnet and magnetic field tuning of the modes. J. Appl. Phys., v.110, n.2, p.24112, Jun 2011. DOI:

MOVCHAN, N.N.; ZAVISLYAK, I.V.; POPOV, M.A. Splitting axially heterogeneous modes in microwave gyromagnetic and gyroelectric resonators. Radioelectron. Commun. Syst., v.55, n.12, p.549-558, 2012. DOI:

YOUNG, D.; TSAI, C.S. GHz bandwith magneto-optic interaction in yttrium iron garnet-gadolinium gallium garnet waveguide using magnetostatic forward volume waves. Appl. Phys. Lett., v.53, n.18, p.1696-1698, 1988. DOI:

LE GALL, H.; JAMET, J.P. Theory of elastic and inelastic scattering of light by magnetic crystals. I. First-Order Processes. Phys. Stat. Sol. (B), v.46, n.2, p.467-482, 1971. DOI:

DIONNE, G.F.; ALLEN, G.A.; HADDAD, P.R.; ROSS, C.A.; LAX, B. Circular polarization and nonreciprocal propagation in magnetic media. Lincoln Laboratory J., v.15, n.2, p.323-340, 2005. URI:

KRINCHIK, G.S.; CHETKIN, M.V. Transparent ferromagnets. Sov. Phys. Usp., v.12, n.3, p.307-319, 1969. DOI:

PLANT, J.S. ‘Pseudo-acoustic’ magnon dispersion in yttrium iron garnet. J. Phys. C: Solid State Phys., v.16, n.36, p.7037-7051, 1983. DOI:

MARSHALL, S.P.; SOKOLOFF, J.B. Spin-wave spectrum for barium ferrite. J. Appl. Phys., v.67, n.4, p.2017-2023, 1990. DOI:

MARSHALL, S.P.; SOKOLOFF, J.B. Phonon spectrum for barium ferrite. Phys. Rev. B, v.44, n.2, p.619-627, 1991. DOI:

POPOV, M.A.; ZAVISLYAK, I.V.; TATARENKO, A.S.; SRINIVASAN, G.; BALBASHOV, A.M. Magnetic and dielectric excitations in the W-band in aluminum substituted barium and strontium hexaferrites. IEEE Trans. Magnetics, v.45, n.5, p.2053-2058, May 2009. DOI:

POPOV, M.; ZAVISLYAK, I.; USTINOV, A.; SRINIVASAN, G. Sub-terahert magnetic and dielectric excitations in hexagonal ferrites. IEEE Trans. Magnetics, v.47, n.2, p.289-294, Feb 2011. DOI:

POPOV, M.A.; ZAVISLYAK, I.V.; MOVCHAN, N.N.; GUDIM, I.A.; SRINIVASAN, G. Mode splitting in 37-42 GHz barium hexaferrite resonator: Theory and device applications. IEEE Trans. Magnetics, v.50, n.6, June 2014. DOI:



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