Propagation of Spin Wave Through the Anisotropic Boundary of Two Uniaxial Ferromagnets in an External Magnetic Field

Оксана Юріївна Горобець, Юрій Іванович Горобець, Володимир Петрович Роспотнюк, Тетяна Юріївна Роспотнюк


This paper represents the investigation of the reflection of bulk spin waves at the interface of two uniaxial ferromagnetic media that propagate at an angle to the interface and their penetration from one ferromagnetic medium to another one. Thereby, the interaction similar to the interaction of two antiferromagnets is taken into account at the boundary interface between two media in an external constant uniform magnetic field. The problem is solved in the formalism of spin density based on equations of Landau–Lifshitz in the absence of dissipation in the system. The boundary conditions are proposed and imposed on the magnetization vector at the boundary of the interface of ferromagnets taking into account the energy of the boundary anisotropy. The expressions are also calculated for the reflection and transmission coefficients of spin waves in this case. It is shown that the intensity of the reflected spin waves and those that penetrated into the medium of another ferromagnet depends on the parameters characterizing the anisotropy of the interface section in the case of presence of the magnetic anisotropy of the boundary interface of ferromagnets.


Spin waves; Ferromagnet; The surface magnetic anisotropy; The boundary conditions for the magnetization; Landau–Lifshitz equation


B. Neite and H. Dotsch, “Dynamical conversion of optical modes in garnet films induced by ferrimagnetic resonan­ce”, J. Appl. Phys., vol. 62, pp. 648–652, 1987.

C.M. Rezende and F.M. Aguiar, “Spin-wave instabilities, auto-oscillations, and chaos in yttrium-iron-garnet”, Proc. IEEE, vol. 78, no. 6, pp. 893–908, 1990.

A.V. Kokin and S.A. Nikitov, “The influence of continuous-wave pumping on the propagation of envelope solitons of magnetostatic spin waves”, Physics of theSolidState, vol. 43, no. 5, pp. 884–887, 2001.

M.A. Tsankov et al., “Magnetostatic wave dynamic magnetization response in yttrium iron garnet films”, J. Appl. Phys., vol. 79, is. 3 pp. 1595–1604, 1996.

G. Consolo et al., “Excitation of self-localized spin-wave “bullets” by spin-polarized current in in-plane magnetized magnetic nano-contacts: a micromagnetic study”, Phys. Rev. B, vol. 76, p. 144410, 2008.

Yu. I. Gorobets et al., “Excitation of modulated spin waves by a model one-dimensional anisotropy defect”, Phy­sics of Metals and Metallography, vol. 85, no. 3, pp. 272–275, 1998.

Yu. I. Gorobets et al., “Spectrum of spin waves in magne­tic materials with a periodically modulated anisotropy”, Physics of the Solid State, vol. 34, pp. 790–792, 1992.

Yu. I. Gorobets et al., “Formation of nonlinear magnetization oscillations by spin waves transmission through the boundary of two uniaxial ferromagnets”, Commun. Nonlinear Sci. Numerical Simulatio, vol. 15, pp. 4198–4201, 2010.

Решетняк С.А. Преломление поверхностных спиновых волн в пространственно неоднородных ферродиэлек­триках с двуосной магнитной анизотропией // Фи­зика твердого тела. – 2004. – 46, № 6. – С. 1031–1037.

J.Y. Gan et al., “Spin wave theory for antiferromagnetic XXZ spin model on a triangle lattice in the presence of an external magnetic field”, Phys. Rev. B, vol. 67, p. 144427, 2003.

M. Buchmeier et al., “Spin waves in magnetic double layers with strong antiferromagnetic interlayer exchange coupling: Theory and experiment”, Ibid, p. 184404, 2003.

J. Fransson et al., “Theory of spin filtering through quantum dots”, Ibid, p. 205210, 2003.

Горобец Ю.И., Решетняк С.А. Отражение и преломление спиновых волн в одноосных магнетиках в при­ближении геометрической оптики // ЖТФ. – 1998. – 68, № 2. – С. 60–63.

L. Néel, “L’approche a la saturation de la magnétostric­-ti­on”, J. Phys. Rad., vol. 15, pp. 376–378, 1954.

U. Gradmann et al., “In-Plane Magnetic Surface Aniso­tro­pies in Fe(110)”, Appl. Phys. A, vol. 39, pp. 101–108, 1986.

H. Takayama et al., “Magnetic surface anisotropy of tran­si­tion metals”, Phys. Rev. B, vol. 14, pp. 2287–2295, 1976.

P. Bruno, “Dipolar magnetic surface anisotropy in ferroma­gnetic thin films with interfacial roughness”, J. Appl. Phys., vol. 64, p. 3153, 1988.

C. Chappert and P. Bruno, “Magnetic anisotropy in metallic ultrathin films and related experiments on cobalt films”, Ibid, p. 5736, 1988.

U. Gradmann, “Magnetic surface anisotropies”, J. Magn. Magn. Mat., vol. 54-57, pp. 733–736, 1986.

F.J.A. den Broeder et al., “Magnetic anisotropy of multilayers”, J. Magnet. Magnetic Mater. vol. 93, pp. 562–570, 1991.

U. Gradmann et al., “Magnetic surface anisotropizs of clean Ni(111)-surfaces and of Ni(111)/metal interface”, IEEE Trans. Magn., vol. 20, pp. 1840–1845, 1984.

B.P. Voznyuk et al., “Effect of the interaction of layers on a ferromagnetic resonance in two-layer ferromagnetics films”, FTT, vol. 33, no. 2, pp. 438–442, 1991.

А.М. Kosevich et al., Nonlinear magnetization waves. Dy­namic and topological solitons.Ukraine, Кyiv: Nau­ko­va dumka, 1983.

A.I. Akhiezer et al., Spin Waves. North Holland,Amsterdam, 1968.

Влияние динамического закрепления спинов на межслойной границе на распространение поверхностных спиновых волн в многослойных ферритовых пленках / С.Л. Высоцкий, Г.Т. Казаков, А.В. Маряхин и др. // Письма в ЖЭТФ. – 1995. – 61, № 8. – С. 673–677.

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