Band gap controlling in layered structures based on magnonic crystals
Band gap controlling in layered structures based on magnonic crystals
Laboratory «Metamaterials» Saratov State University, Saratov 410012, Russia
A.Yu. Sharaevskaia,1,2 M.A. Morozova,1A.V. Sadovnikov,1,2, ,
E.N. Beginin,1 D.V. Romanenko,1 Yu.P. Sharaevskii,1 and S.A. Nikitov1,2
1) Laboratory ”Metamaterials”, Saratov State University, Saratov 410012, Russia
2) Kotel’nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia
The results of theoretical and experimental investigations of spin wave propagation in the coupled magnonic crystals are presented. Analytical and numerical model has been developed to describe the propagation of magnetostatic waves in a periodic structure consisting of two one-dimensional magnonic crystals. It is demonstrated, that up to three bandgaps in the first Bragg resonance can be formed in such structure. Also it is shown, that effective coupling between two magnonic crystals and magnonic crystal/ferromagnetic film permits to govern the selective properties of spin waves. We demonstrate a good agreement between predicted and experimentally observed data. Fabricated complex structures cab be used as a magnonic platform for new spin-wave devices.
Currently, researchers pay much attention to periodic structures formed on the surface of ferromagnetic films: magnonic crystals (MCs) [1−3]. In contrast to photonic crystals, which are used in the optical range , MCs have been generally investigated in the microwave range. Their properties can be controlled by external magnetic field. The presence of spatial period leads to the formation of band gaps in the spin-wave spectrum for the wavenumbers satisfying the Bragg resonance condition . The presence of band gaps in the spin-wave spectra allows to design the devices based on magnonic crystals and tuned by magnetic field for processing and generating microwave signals [1-3].
Actually, we considered a possibility of controlling characteristics of band gaps in the spectra of magnetostatic waves, which allows functionality extending of devices based on magnonic crystals. In recent years controlling characteristics of band gaps in MCs can be carry out a variety of ways: by changing geometric and magnetic parameters of the structures , structures symmetry , boundary conditions , creation of defects  due to propagate of electric current .
In this letter we presented the results of theoretical and experimental study of layered periodic structure in form of a magnonic crystals separated by dielectric layer. Special attention is paid to influence of connection between layers and asymmetry on mechanisms of formation band gaps. In particular, we investigated structure of magnonic crystals with shifted to each other periods and layered structure, such as magnonic crystal – ferromagnetic film (FF). The results obtained on basis of wave model and numerical simulation are in agreement with the results of an experimental study.
Model and numerical simulation
The structure under consideration (see schematic diagram in Fig. 1a) consists of two magnonic crystals, separated by a dielectric layer (spacer). Each MC is a ferromagnetic film having saturation magnetization and thickness with a periodic structure deposited on its surface in the form of protrusions of height. It is generally assumed that the periods in MCs are shifted relative to each other. The structure is infinite in the directions of the x and y axes. The system is placed in an external magnetic field H0, applied along the x-axis. Thus the surface magnetostatic waves (MSW) propagates in each of the MC. The system of equations for such structures is a system of coupled equations with periodically varying coefficients.
For solving system of equations we used approach based on method coupled waves, waves propagating in the forward and backward directions in the periodic system, and a periodic structure provides their connection. In Fig.1b we showed the dependence of the width of band gap in the spectra of magnetostatic waves on coupling coefficient K between ferromagnetic structures. We show that three band gaps G-1, G-2, G-3 can be formed. As the coefficient K is increased, the central frequency of G-1 is shifted upward, central frequencies of G-2 and G -3 are shifted down. It should be noted that similar situation exists for MCs structure with phase shift. Thus, these results demonstrate the ability to control of band gaps characteristics by the tuning of parameter K in asymmetrical structure based on MC.
For experimental study of wave propagation in periodic structures were used sample on the basis of 12 microns thick yttrium-iron garnet (YIG) films with the saturation of magnetization of 1750 G. The film is grown by liquid-phase epitaxy on the 0.5 mm thick gadolinium gallium garnet (GGG) substrate. Periodic system of grooves with a period of 200 microns and width of 100 microns was fabricated on the surface of YIG film. MC had a rectangular shape: MC width is 3 mm, length is 13 mm.
For propagating of spin wave in MC we used 30 microns width microstrip transducers, which are located on the surface of the MC at a distance of 7 mm from each other. The 25 microns dielectric spacer was placed between MCs. The uniform static magnetic field H0=250 Oe was applied in the plane of the waveguide along the z-direction for the effective excitation of the magnetostatic surface wave.
First, experiment was conducted using time- and space-resolved BLS technique. We have demonstrated that the selected thickness of dielectric plate of 25 microns provides a sufficient amount of coupling and layered structure behaves as a coupled system . Fig. 2a shows intensity of the scattered light for layered structure MC-FF at frequency of band gap f = 2340 MHz. The focus of optical system was set up on a layer of MCs. We can see alternating maxima and minima of intensity along the propagation direction. This can be described by the periodic power exchange between MC and FF along the direction of wave propagation. In this case maxima alternates with the period L = 1.2 mm.
In Fig. 2b we showed the results of experimental study of band gaps formation in MC-FF in amplitude-frequency characteristics (AFC) (blue curve 2). From the results in Fig. 2b we can sight that in such structure three band gaps formed in the first Bragg resonance at the frequencies of f1 = 2334 MHz, f2 = 2220 MHz and f3 = 2270 MHz and formation of three band gaps in first Bragg resonance structure MC - FF based on theoretical results due to asymmetry of the structure. Black curve in Fig.2b is AFC for a single MC.
In this letter we have shown the main features of band gaps formation in the periodic layered ferromagnetic structures. For the first time we have shown the possibility of effective control of the parameters of band gaps in layered structures based on magnonic crystals by changing the coupling between the ferromagnetic layers. It was shown that the two band gaps are formed in the structure consist of two MCs separated by dielectric layer near first Bragg resonance band. In the case of symmetry breaking we observed formation of three band gaps near the first Bragg resonance. It can be explained by a changing of the phase shift between the MCs, geometrical parameters one of the MCs in the structure of MC-FF. The good agreement between the theoretical results, numerical simulations and experimental data was shown. The proposed structure based on vertical coupled MCs can be used in information processing systems as a frequency-selective device in microwave range.
The work was supported by the Grant RSF № 16-19-10283.
- M. Krawczyk and D. Grundler, J. Phys. D 26, 123202 (2014).
- S.A. Nikitov, Ph. Tailhades, C.S. Tsai “Spin waves in periodic magnetic structures - magnonic crystals”, JMMM, vol. 236, no. 3, 320-330, 2001.
- V.V. Kruglyak, S. O. Demokritov and D. Grundler, “Magnonics”, Journal of Physics D, vol. 43, 264001, 2010.
- R. Kashyap, Fiber Bragg Gratings, San Diego, USA: Acad. Рress., 1999.
- D. Marcuse Light transmission optics. Van Nostrand Reinhold Company. New York.1972.
- M. Arikan, Y. Au, G. Vasile, S. Ingvarsson, V.V. Kruglyak “Broadband injection and scattering of spin waves in lossy width-modulated magnonic crystal waveguides”, J. Phys. D, vol. 46, 135003, 2013.
- Q. Wang, H. Zhang, X. Tang, H. Su, F. Bai, Y. Jing, andZ. Zhong, J. Phys. D 47, 065004 (2014).
- E. N. Beginin, Yu. A. Filimonov, E. S. Pavlov, S. L. Vysotskii, and S. A. Nikitov “Bragg resonances of magnetostatic surface spin waves in a layered structure: Magnonic crystal-dielectric-metal”, Appl. Phys. Lett., vol. 100, 252412, 2012.
- V. V. Kruglyak, M. L. Sokolovskii, V. S. Tkachenko, and A. N. Kuchko, J. Appl. Phys. 99, 080906 (2006).
- A. V. Chumak, T. Neumann, A. A. Serga, B. Hillebrands and M. P. Kostylev, “A current-controlled, dynamic magnonic crystal”, J. Phys. D: Appl. Phys., vol. 42, 205005, 2009.
- M.A. Morozova, S.V. Grishin, A.V. Sadovnikov, Yu.P. Sharaevskii, and S.A. Nikitov Magnonic Band Gap Control in Coupled Magnonic Crystals// Transaction on magnetics. 2014. 2321611.
- S. O. Demokritov, B. Hillebrands, and A. N. Slavin, Brillouin light scattering studies of confined spin waves: linear and nonlinear confinement Phys. Rep. 348, 441 (2001).