Frequency Dependencies of the Exchange Spin Wave Reflection Coefficient on a One-Dimensional Magnon Crystal with Complex Interfaces

Serhii O. Reshetniak, Anastasiia V. Lysak

Abstract


Background. This work is devoted to theoretical study of the behavior of spin waves passing through multilayer ferromagnetic with complex interfaces.

Objective. The aim of the paper is to calculate the reflection coefficient of multilayer ferromagnetic with complex interfaces as function of spin wave frequency at variable material parameter and constant value of external magnetic field. The formalism of geometric optics allows describing the spin wave refraction process and the reflection coefficient, as well as controlling this process by changing the frequency of the spin wave for given parameters of the medium.

Methods. To find the reflection coefficient from a multilayer ferromagnetic the mathematical apparatus of geometric optics was used. To describe the dynamics of the magnetization vector the formalism of the spin density order parameter was used allowing for the use of methods of quantum mechanics to calculate the reflection coefficient from a semi-infinite multilayer structure.

Results. The spin wave reflection coefficient of semi-infinite multilayer structure of ferromagnetic materials with complex interfaces has been found. The dependency graphs of the reflection coefficient from the frequency of the spin waves at different parameters of magnetic anisotropy inhomogeneity and constant value of the external magnetic field were obtained.

Conclusions. It is shown that the frequency dependencies are periodic, points of full transmission and areas, full of reflection. Decreasing exchange parameter value in interface causes the increase of reflectance coefficient. Changing the material parameters we get the necessary intensity value of the reflection coefficient depending on the frequency at a constant value of the external magnetic field.

Keywords


Spin waves; Multilayer ferromagnetic; Reflection coefficient; Complex interface; Magnetization vector

References


D.D. Stancil and A. Prabhakar, Spin Waves: Theory and Applications. New York: Springer, 2009.

G. Csaba et al., “Spin-wave based realization of optical computing primitives”, J. Appl. Phys., vol. 115, no. 17, pp. 115–118, 2014. doi: 10.1063/1.4868921

A.V. Chumak et al. (2014, Aug. 21). Magnon transistor for all-magnon data processing [Online]. Available: https://www.nature.com/articles/ncomms5700. doi: 10.1038/ncomms5700

M. Jamali et al. (2013, Nov. 7). Spin wave nonreciprocity for logic device applications [Online]. Available: https://arxiv.org/ftp/arxiv/papers/1311/1311.1881.pdf. doi: 10.1038/srep03160

V.E. Demidov et al. (2011). Excitation of short-wavelength spin waves in magnonic waveguides [Online]. Available: http://aip.scitation.org/doi/pdf/10.1063/1.3631756. doi: 10.1063/1.3631756

A.B. Ustinov et al., “Multifunctional nonlinear magnonic devices for microwave signal processing”, Appl. Phys. Lett., vol. 96, no. 14, pp. 96–98, 2010.

B. Lenk et al., “The building blocks of magnonics”, Phys. Rep., vol. 507, no. 4-5, pp. 107–136, 2011. doi: 10.1016/j.physrep.2011.06.003

T. Balashov et al. (2014, Sept. 12). Magnon dispersion in thin magnetic films [Online]. Available: http://iopscience.iop.org/article/10.1088/0953-8984/26/39/394007/pdf. doi: 10.1088/0953-8984/26/39/394007

V.V. Kruglyak et al. (2014, Oct. 8). Magnetization boundary conditions at a ferromagnetic interface of finite thickness [Online]. Available: http://iopscience.iop.org/article/10.1088/0953-8984/26/40/406001/pdf. doi: 10.1088/0953-8984/26/40/406001

S.A. Reshetnyak, “Refraction of spin wave surface in spatially inhomogeneous ferrodielectrics with biaxial magnetic anisotropy”, Fizika Tverdogo Tela, vol. 46, no. 6, pp. 1061–1067, 2004 (in Russian).

J.D. Adam et al., “Ferrite devices and materials”, IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 721–737, 2002. doi: 10.1109/22.989957

B.A. Kalinikos and A.N. Slavin, “Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions”, J. Phys. C, vol. 35, no. 19, pp. 7013–7033, 1986.

K. Perzlmaier et al. (2008, Feb. 20). Observation of the propagation and interference of spin waves in ferromagnetic thin films [Online]. Available: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.77.054425. doi: 10.1103/PhysRevB.77.054425

K. Tanabe et al. (2014, Apr. 9). Real-time observation of Snell’s law for spin waves in thin ferromagnetic films [Online]. Available: http://iopscience.iop.org/article/10.7567/APEX.7.053001/pdf. doi: 10.7567/APEX.7.053001

S.O. Reshetnyak and O.M. Andriyevska, “Behavior of surface spin waves at reflection from uniaxial multilayer ferromagnet”, Naukovi Visti NTUU KPI, no. 4, pp. 56–61, 2014.

O.Yu. Gorobets and S.A. Reshetnyak, “Reflection and refraction of spin waves in uniaxial magnets in the approximation of geometric optics”, Zhurnal Tehnicheskoj Fiziki, vol. 68, no. 2, pp. 60–63, 1998 (in Russian).

Yu.I. Gorobets et al., “Formation of nonlinear magnetization oscillations by spin waves transmission through the boundary of two uniaxial ferromagnets”, Commun. Nonlinear Sci. Numer. Simul., vol. 15, no. 12, pp. 4198–4201, 2010. doi: 10.1016/j.cnsns.2010.01.045

J.M. Pereira and R.N. Costa Filho, “Dipole-exchange spin waves in Fibonacci magnetic multilayers”, Phys. Lett. A, vol. 344, no. 1, pp. 71–76, 2005. doi: 10.1016/j.physleta.2005.06.042

V.G. Bar’yakhtar and Yu.I. Gorobets, Bubble Domains and their Lattices. Kyiv, Ukraine: Naukova Dumka, 1988 (in Russian).

V.K. Ignatovich, “Sketch about one-dimensional periodic potential”, Uspehi Fizicheskih Nauk, vol. 150, pp. 880–887, 1986 (in Russian).


GOST Style Citations


 

 





DOI: https://doi.org/10.20535/1810-0546.2017.4.105143

Refbacks

  • There are currently no refbacks.




Copyright (c) 2017 Igor Sikorsky Kyiv Polytechnic Institute