Nanostructured Magnonic Crystal with Magnetic-Field

Copyright © 2011 American Scientific Publishers All rights reserved Printed in the United States of America

Journal of Nanoscience and Nanotechnology Vol. 11, 2657–2660, 2011

Nanostructured Magnonic Crystal with Magnetic-Field Tunable Bandgap V. L. Zhang1 , Z. K. Wang1 , H. S. Lim1 , S. C. Ng1 , M. H. Kuok1 ∗ , S. Jain2 , and A. O. Adeyeye2 1

2

Department of Physics, National University of Singapore, 117542, Singapore Department of Electrical and Computer Engineering, National University of Singapore, 117576, Singapore

RESEARCH ARTICLE

Most experimental investigations into magnonic bandgaps are based on structures composed of single-constituent magnetic materials. Here we report Brillouin and numerical studies of the spin dynamics of a bi-component magnonic crystal, viz. a one-dimensional periodic array of alternating permalloy and cobalt 150 nm-wide nanostripes. Our measurements, together with those for a Delivered by Ingenta to: similar crystal composed Institute of 250 nm-wide nanostripes, suggest that for a of Molecular and Cell Biology stripe width ratio of 1:1, the bandgap width of such magnonicIP arrays increases with crystal lattice constant. The bandgap : 137.132.123.69 parameters are strongly dependent on external magnetic field. This magnetic-field tunability of the Wed, 23 Mar 2011 10:17:29 bandgap is expected to be a crucial property of devices based on magnonic crystals. The agreement between numerical calculations, based on finite element analysis, and the experimental data is generally good.

Keywords: Magnonic Crystal, Magnonics, Tunable Bandgap, Brillouin Light Scattering.

1. INTRODUCTION Photonic crystals are a well known class of materials that possesses special properties arising from their optical band gap. In contrast, information on their magnetic analog, known as magnonic crystals, is relatively scarce. In particular, little experimental research has been conducted on magnonic crystals.1–8 The role of information carrier in them is played by magnons (quantized spin waves), and they possess bandgaps within which spin waves cannot propagate. Magnonic crystals form the basis of magnonics, an emerging field which aims to control the generation and propagation of magnons by means analogous to the control of photons in photonic crystals. It is foreseen that magnonic crystals have wide-ranging applications such as in spin wave logic and magneto-electronic devices.8 In analogy to a photonic crystal, which is a periodic composite of materials with different dielectric constants, a magnonic crystal can be regarded as a periodic composite composed of different magnetic materials. Except for our earlier work on a bi-material magnonic crystal,3 experimental studies reported on magnonic bandgaps are

∗

Author to whom correspondence should be addressed.

J. Nanosci. Nanotechnol. 2011, Vol. 11, No. 3

based on structures with exchange-decoupled arrayed elements composed of only one constituent magnetic material, or modulated yttrium iron garnet (YIG) films. These structures include micron-size shallow grooves etched on YIG films,6 7 and one-dimensional (1D) arrays of micronsize metal stripes on YIG films.9 Structures in the form of 1D periodic arrays of nano-size permalloy stripes have also been studied, but these stripes are non-contacting and hence exchange-decoupled as well.10 11 The sample used in this study is a laterally patterned bi-component magnonic crystal. Specifically, it is a laterally patterned periodic array of alternating contacting cobalt and permalloy (Ni80 Fe20 ) nanostripes, each of width 150 nm. As adjacent stripes are in contact with each other, they are exchange-coupled. Theoretical studies by Puszkarski and Krawczyk1 2 indicate that the more contrasting the magnetic properties of the constituent materials of a magnonic crystal are, the wider would be its bandgap. The saturation magnetization and exchange constant of cobalt are some two times those of permalloy. Also, as wider bandgaps are more readily detectable, our sample was synthesized from these two materials. A tunable electronic bandgap is a desirable property of semiconductors because it permits flexibility in the design and optimization of semiconductor devices like transistors.

1533-4880/2011/11/2657/004

doi:10.1166/jnn.2011.2730

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Nanostructured Magnonic Crystal with Magnetic-Field Tunable Bandgap

This is especially so if the bandgap can be tuned by the application of an external electric field. Analogously, frequency bandgap tunability in magnonic crystals should facilitate the control of the propagation of spin waves in magnonic devices. Hence, for applications purposes, these crystals should be designed so that their frequency bandgap is readily modifiable by an external magnetic field. Here we report the results of an experimental and theoretical investigation into the spin dynamics of a nanostructured magnonic crystal composed of materials with two different magnetic properties. In particular, the tunability of its magnonic bandgap with applied magnetic field will be studied, and compared with that of a similar structure with wider nanostripes. Brillouin light scattering, an excellent technique for studying low-frequency (gigahertz range) magnetic excitations in nanostructures,10 12 13 will be employed in this study. Numerical calculations, based on finite element analysis, will be performed to determine Delivered by the spin waves modes of the sample.

Zhang et al.

z H y

x

q

Fig. 1. Orientation of applied magnetic field H relative to the magnon wavevector q and nanostripes of the nanostructured magnonic crystal.

wave modes. The frequencies of these modes were plotted against their respective wavevectors to give the measured dispersion relations, and are presented in Figure 2(b) which reveals that there is a frequency range of 1.7 GHz, within which propagation of spin waves is disallowed. Interestingly, this measured frequency bandgap width for Ingenta to:(lattice constant a = 300 nm) is narrower than the sample Institute of Molecularthe andcorresponding Cell Biology value of 2.1 GHz observed for a similar IP : 137.132.123.69 magnonic crystal (a = 500 nm) composed of alternating 2. EXPERIMENTAL DETAILS Wed, 23 Mar 2011 250 10:17:29 nm-wide cobalt and permalloy stripes.3 This suggests The one-dimensional magnonic crystal structure studied that for a 1:1 stripe-width ratio of the cobalt-permalloy was synthesized on oxidized Si(001) substrate using highmagnonic arrays studied, the bandgap width increases with resolution multilevel electron beam lithography, deposition crystal lattice constant. and lift-off techniques. Details of the fabrication processes Brillouin spectra were also recorded under various involved are described in Ref. [3]. The resulting sample is applied magnetic fields, with a typical spectrum, one a laterally-patterned 100 m × 100 m periodic array of contacting, alternating cobalt and permalloy stripes. The width and thickness of each stripe are 150 and 30 nm (a) (b) respectively, and the magnonic crystal thus has a lattice constant a = 300 nm. All Brillouin spectra were excited with the = 5145 nm radiation of an argon-ion laser. They were measured in the 180 -backscattering geometry and in p–s polarization using a 6-pass tandem Fabry-Perot interferometer. A continuous stream of pure argon gas was directed at the irradiated spot on the surface of the magnonic crystal to cool it and to keep air away from it. Prior to the start of an experiment, the sample was saturated in a onetesla field directed parallel to the long axes of the nanostripes (z-axis in Fig. 1(a)). In magnetic field dependence experiments, the applied static field H was generated with a computer-controlled electromagnet. The dispersion relations were mapped across the Brillouin zone, i.e., over the range of the magnon wavevector q (= 4 sin /) from zero to 2/a, by changing the incidence angle of the laser light. Fig. 2. (a) Brillouin spectra of the magnonic crystal recorded, under

3. RESULTS AND DISCUSSION Figure 2(a) shows the Brillouin spectra, measured under zero magnetic field, for three different magnon wavevectors. As the positions of the spectral peaks are dependent on applied magnetic field, they are ascribed to spin 2658

zero applied field, at various magnon wavevectors. The shaded region represents the frequency bandgap. All spectra were fitted with Lorentzian functions (dotted curves), and the resultant fitted spectra are shown as solid curves. (b) Measured and calculated magnonic band structure of the sample with lattice constant a = 300 nm. Measured and calculated data are denoted by symbols and solid curves respectively. The measured frequency bandgap is represented by a shaded band. The Brillouin zone boundary (q = /a) is represented by a dashed line.

J. Nanosci. Nanotechnol. 11, 2657–2660, 2011

Zhang et al.

(a)

Nanostructured Magnonic Crystal with Magnetic-Field Tunable Bandgap (b)

where = / 0 H Q = 2A/ Ms 0 H , A is the exchange constant, Ms the saturation magnetization, the gyromagnetic ratio, H the applied magnetic field, mx and my the components of the dynamic magnetization m, the spin wave angular frequency and r the 3D position vector. The magnetic potential (r), within the magnetic stripes, is given by 2 r =

mx r my r

+ x y

(3)


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while outside the stripes, it satisfies the Laplace equation. For simplicity, the surface anisotropy and interface (c) (d) exchange coupling are neglected. Hence, the exchange boundary conditions are satisfied if the magnetization m and (A/Ms m/ x 15 are both continuous at the interface between the cobalt and permalloy stripes. Magnetostatic boundary conditions also require that (r) and the Delivered by Ingenta to: normal component of the magnetic induction be continuInstitute of Molecularous andacross Cell interfaces Biology between two adjacent stripes. As the IP : 137.132.123.69 propagating spin waves are modulated by the periodicity Wed, 23 Mar 2011 10:17:29 of the magnonic crystal, the Bloch-Floquet theorem can be applied to give m(x + a) = m(x)exp iqa . Thus, only a unit cell of the repeating structure needs to be considered and with the periodic boundary conditions imposed, the Fig. 3. (a) Magnetic-field dependence of spin wave frequencies at first effects of the periodic images are included. The dispersion Brillouin zone boundary (q = /a), featuring bandgap. The dots and relations (q) are then obtained by numerically solving squares represent measured data for the respective lowest-frequency and second lowest-frequency spin wave modes. (b) Brillouin spectrum Eqs. (1) to (3), with the above-stated interface and surface recorded at H = 0175 T/0 for q = /a. (c) Dependence of the bandgap boundary conditions. center frequency on applied magnetic field. (d) Dependence of the The theoretical dispersion relations, presented in bandgap width on applied magnetic field. Measured and calculated data Figure 2(b), were calculated based on magnetic paramare represented by symbols and solid curves respectively. eters Ms = 658 × 105 A/m, A = 111 × 10−11 J/m, = measured at H = 0175 T/0 , shown in Figure 3(b). The 1905 GHz/T for permalloy, and Ms = 115 × 106 A/m, plot of magnon frequencies, measured at the Brillouin zone A = 288 × 10−11 J/m, = 1988 GHz/T for cobalt. These boundary (q = /a), as a function of H is displayed in data were obtained from Brillouin measurements of respecFigure 3(a) which reveals that the frequencies rise sharply tive 30 nm-thick permalloy and cobalt reference films. with increasing magnetic field. The corresponding variaThe magnetic field dependence of the spin wave modes, tions, of the center frequency and width of the bandgap, at the Brillouin zone boundary (q = /a), was also comwith magnetic field are presented in Figures 3(c) and puted and is presented in Figure 3(a). The resulting theo(d) respectively. It can be seen from the figures that the retical H -dependences of the width and center frequency gap width decreases, while the gap center increases with of the bandgap were then plotted in Figures 3(c) and (d) increasing applied field. respectively. In general, as can be seen from Figure 3, The following approach was used to calculate the disthe agreement between theory and experiment is fairly persion relation (q) of spin waves in the magnonic crystal good, indicating that the theoretical treatment employed under an applied homogeneous magnetic field. The magcaptures the observed magnetic-field dependent features. netic stripes are treated as being infinitely long in the The observed discrepancy could be partly due to interz-direction (see Fig. 1(a)). Linearization of the Landau14 face/surface anisotropy being neglected in the computaLifshitz equation then yields tions. Although exchange interaction within a stripe has Ms r

been considered in our model, interface exchange couimx r + · Q my r − my r − = 0 (1) H y pling between adjacent contacting stripes has been ignored, and which could be another reason for the discrepancy. A comprehensive calculation however would entail data on the M r

− · Q mx r + mx r + imy r + s = 0 (2) inter-stripe cobalt-permalloy exchange constant as well as H x

Nanostructured Magnonic Crystal with Magnetic-Field Tunable Bandgap

RESEARCH ARTICLE

the interface/surface anisotropy, information which are not currently available.

Zhang et al.

References and Notes

1. M. Krawczyk and H. Puszkarski, Phys. Rev. B 77, 054437 (2008). 2. H. Puszkarski and M. Krawczyk, Solid State Phenom. 94, 125 (2003). 4. CONCLUSIONS 3. Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, Appl. Phys. Lett. 94, 083112 (2009). We have performed Brillouin studies on the spin dynam4. S. A. Nikitov, C. S. Tsai, Y. V. Gulyaev, Y. A. Filimonov, S. L. ics of a bi-component magnonic crystal, viz. a laterally Vysotskii, and P. Tailhades, Mater. Res. Soc. Symp. Proc. 834, 87 patterned array of alternating permalloy and cobalt (2005). 150 nm-wide nanostripes. Brillouin data show that it 5. S. A. Nikitov, P. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001). exhibits a 1.7 GHz bandgap which is narrower than that 6. A. V. Chumak, A. A. Serga, S. Wolff, B. Hillebrands, and M. P. of a similar crystal composed of 250 nm-wide permalKostylev, Appl. Phys. Lett. 94, 172511 (2009). loy and cobalt stripes. This implies that, for a 1:1 stripe7. A. V. Chumak, A. A. Serga, B. Hillebrands, and M. P. Kostylev, width ratio of such magnonic arrays, the bandgap width Appl. Phys. Lett. 93, 022508 (2008). increases with crystal lattice constant. The bandgap param8. V. V. Kruglyak and A. N. Kuchko, Physica B 339, 130 (2003). 9. M. E. Dokukin, K. Togo, and M. Inoue, J. Magn. Soc. Jpn. 32, 103 eters were also found to be strongly dependent on exter(2008). nal magnetic field. Just as the electric-field tunability of 10. G. Gubbiotti, S. Tacchi, G. Carlotti, N. Singh, S. Goolaup, semiconductor bandgaps is of paramount importance in A. O. Adeyeye, and M. Kostylev, Appl. Phys. Lett. 90, 092503 semiconductor device applications, the magnetic-field tun(2007). ability of magnonic bandgaps, like the one observed here, 11. M. Kostylev, P. Schrader, R. L. Stamps, G. Gubbiotti, G. Carlotti, Delivered by Ingenta to: A. O. Adeyeye, S. Goolaup, and N. Singh, Appl. Phys. Lett. is expected to be crucial to the performance of devices Institute of Molecular and Cell Biology 92, 132504 (2008). based on magnonic crystals. The agreement between our IP : 137.132.123.69 12. Z. K. Wang, M. H. Kuok, S. C. Ng, D. J. Lockwood, M. G. numerical calculations, based on solving the linearized K. Nielsch, R. B. Wehrspohn, and U. Gosele, Phys. Rev. Wed, 23 Mar 2011 Cottam, 10:17:29 Landau-Lifshitz equation, and the experimental data was Lett. 89, 027201 (2002). found to be generally good. It is hoped that this study will 13. Z. K. Wang, H. S. Lim, H. Y. Liu, S. C. Ng, M. H. Kuok, L. L. Tay, D. J. Lockwood, M. G. Cottam, K. L. Hobbs, P. R. Larson, J. C. spur more research into magnonics, a field which shows Keay, G. D. Lian, and M. B. Johnson, Phys. Rev. Lett. 94, 137208 great promise in applications. (2005). 14. J. O. Vasseur, L. Dobrzynski, B. Djafari-Rouhani, and H. Puszkarski, Acknowledgments: This work was funded by the Phys. Rev. B 54, 1043 (1996). Ministry of Education Singapore under research projects 15. V. V. Kruglyak, R. J. Hicken, A. N. Kuchko, and V. Y. Gorobets, J. Appl. Phys. 98, 014304 (2005). R144-000-205-112 and R144-000-239-112.

Received: 23 June 2009. Accepted: 20 November 2009.

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