Geodesic
Asymptotic analysis of a multiferroic model
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 26-39
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We consider a system of nonlinear autonomous differential equations that describe the orientation of the antiferromagnetic vector in a multiferroic film and find the conditions for the existence of spatially modulated structures of the cycloid type. We investigate the stability of such structures under spatial perturbations.
Keywords: multiferroics, nonlinear equation, variational problem, small parameter, asymptotics. 
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L. A. Kalyakin; A. K. Zvezdin; Z. V. Gareeva. Asymptotic analysis of a multiferroic model. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 26-39. http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a2/

[1] Y. Tokura, S. Seki, “Multiferroics with spiral spin order”, Adv. Mater., 22:14 (2010), 1554–1565 | DOI

[2] N. A. Spaldin, R. Ramesh, “Advances in magnetoelectric multiferroics”, Nature Mater., 18:3 (2019), 203–212 | DOI

[3] I. Sosnowska, T. Neumaier, E. Steichele, “Spiral magnetic ordering in bismuth ferrite”, J. Phys. C, 15:23 (1982), 4835–4846 | DOI

[4] Yu. A. Izyumov, Difraktsiya neitronov na dlinnoperiodicheskikh strukturakh, Energoatomizdat, M., 1987

[5] V. V. Nemytskii, V. V. Stepanov, Kachestvennaya teoriya differentsialnykh uravnenii, OGIZ, M.-L., 1947 | MR

[6] K. Lantsosh, Variatsionnye printsipy mekhaniki, M., Mir, 1965 | MR | Zbl

[7] E. M. Galeev, V. M. Tikhomirov, Optimizatsiya: teoriya, primery, zadachi, Editorial URSS, M., 2000

[8] B. V. Levitan, V. V. Zhikov, Pochti periodicheskie funktsii i differentsialnye uravneniya, Izd-vo Mosk. un-ta, M., 1978 | MR | Zbl

[9] N. I. Akhiezer, Lektsii po teorii approksimatsii, Nauka, M., 1965 | DOI | MR | MR | Zbl | Zbl

[10] N. E. Kulagin, A. F. Popkov, A. K. Zvezdin, “Prostranstvenno-modulirovannye antiferromagnitnye struktury v legkoploskostnom multiferroike”, FTT, 53:5 (2011), 912–918 | DOI

[11] N. E. Kulagin, A. F. Popkov, S. V. Solovev, A. K. Zvezdin, “Indutsirovannye magnitnym polem spin-modulyatsionnye perekhody v epitaksialnykh plenkakh BiFeO$_3$ s orientatsiei (001)”, FTT, 61:2 (2019), 248–256 | DOI

[12] M. V. Fedoryuk, Metod perevala, Nauka, M., 1977 | MR | Zbl

[13] V. A. Yakubovich, V. M. Starzhinskii, Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh primenenie, Nauka, M., 1972 | MR | MR | Zbl | Zbl

[14] A. P. Shvartsman, “K voprosu ob ogranichennosti reshenii differentsialnogo uravneniya $y''+p(x)y=0$”, PMM, 18:4 (1954), 404–408