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IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011
Magnonics Crystal Composed by Magnetic Antivortices Confined in Antidots Carlo Ragusa1 , Mario Carpentieri2 , Federica Celegato3 , Paola Tiberto3 , Emanuele Enrico3 , Luca Boarino3 , and Giovanni Finocchio4 Department of Ingegneria Elettrica, Politecnico of Torino, Torino I-10129, Italy Department of Elettronica, Informatica e Sistemistica, University of Calabria, Rende (CS) I-87036, Italy Istituto Nazionale di Ricerca Metrologica, INRIM, Torino I-10135, Italy Department of Fisica della Materia e Ingegneria Elettronica, University of Messina, Messina I-98100, Italy A magnetic patterned system constituted by antidots has been synthesized by electron beam lithography and its static and dynamical properties have been studied. Magnetic-domain patterns related to the static hysteresis loop have been acquired by means of magnetic force microscopy. The dynamical response to a magnetic field pulse has been studied by means of micromagnetic simulations. We found the magnetic response of a single antidot (excitation of a single mode) is qualitatively different from the one of coupled antidots (excitation of two modes). In the latter configuration, micromagnetic simulations show the low-frequency mode related to the in-phase oscillation of the magnetization and the high-frequency mode related to the out-of-phase oscillation of the magnetization. Index Terms—Magnetic films, magnetic force microscopy, magnonics crystal, micromagnetics.
I. INTRODUCTION AGNONICS is a research field in nanoscience whose purpose is to explore spin waves in applications for the storage and the processing of the information [1]–[14]. The elementary spin wave excitations (called magnons) can propagate into a ferromagnetic strip for some particular conditions. In terms of applications, the possibility to have a wave with wavelength orders of magnitude shorter than the one of electromagnetic waves (photons) at the same frequency (gigahertz range) is one of the key advantages of the magnonics [3], [5]. From a technological point-of-view, the main configuration studied as magnonic crystal is a periodic lattice composed by magnetic nanodots [3]–[5]. If the distance between the dots is small enough (typically, lower than 300 nm), each nanodot interacts with the others by means of the dipolar coupling [15] leading to the excitation of collective modes. Experimental data and micromagnetic simulations show that magnonic lattices can exhibit wide magnonic band; in addition, acoustic and optical modes have been identified [11], [14]. In other words, periodically patterned ferromagnetic materials on the nanoscale offer an artificial band structure for spin waves, consisting of allowed frequency bands and forbidden frequency gaps. At low field, a magnetic vortex (V) as ground state for the dot of a magnonic crystal can be found. This magnetic state has been extensively studied in the last decade for applications as storage systems (the information can be stored either in the core polarity or in the chirality of the V) or spin-torque oscillators [16]–[20]. In this paper, we study experimentally and by means of micromagnetic simulations the magnetic behavior of a magnetic antidot system. In these geometries, the ground state at low applied
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Manuscript received February 21, 2011; revised May 15, 2011; accepted May 21, 2011. Date of current version September 23, 2011. Corresponding author: C. Ragusa (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2011.2158578
field is characterized by the presence of a magnetic antivortex (AV) [21], [22]. We found that the dynamical response to a magnetic field pulse of a single antidot is characterized by the excitation of one main mode. It has been observed that the response of a system of coupled antidots is qualitatively different being characterized by two main excited modes. In particular, micromagnetic simulations point out that the low-frequency mode is related to the in-phase oscillation of the magnetization (acoustic mode); the other one is related to the out-of- phase oscillation of the magnetization (optical mode) in the neighborhood antidots. This paper is organized as follows. Section II introduces experimental and numerical details of the antidots under investigation. Section III describes experimental and micromagnetic simulations results regarding the characterization under static conditions. Finally, micromagnetic simulations of the dynamical properties of a single antidot and a configuration with three coupled antidotes are compared. II. EXPERIMENTAL DETAILS AND MICROMAGNETIC MODELING The patterned system fabrication process starts with the RF thin film (thickness ) sputter deposition of a on a thermally oxidized Si substrate. Subsequently, the magnetic film is spin coated with a layer of negative resist. The desired pattern is produced by electron beam lithography technique using a scanning electron microscope (FEI QUANTA 3D with NPGS). The film is submitted to sputter etching in order to remove the magnetic films among patterns after the resist development process. Finally, by using a liftoff process, the resist on regions with the patterned structures is removed and designed shapes on the film surface have been obtained. Basically, the geometry is squared of 2 mm in side formed by four nonmagnetic circles with ratio of about 500 nm. We stress the fact that the choice of this particular geometry is related to the possibility to nucleate a stable magnetic antivortex in the central asteroid. A topographic image obtained by scanning electron microscopy (SEM) a single element of the nanodots array is shown in Fig. 1 In addition, atomic force microscopy (AFM, Digital Instruments-Nanoscope IIIa)
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RAGUSA et al.: MAGNONICS CRYSTAL COMPOSED BY MAGNETIC ANTIVORTICES CONFINED IN ANTIDOTS
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Fig. 2. Experimental room-temperature hysteresis loop of the whole antidots array measured by an AGFM in the parallel configuration. Fig. 1. SEM topological image of one asteroid nanostructure.
has been exploited to study the sample microstructure. Magnetic-domain patterns have been imaged by magnetic force microscopy (MFM). The measurements have been performed in lift-mode exploiting a commercially available ferromagnetic CoCr tip (MESP, coercive field 40 mT). In particular, the images have been acquired at the magnetic remanence from an applied field of 1.5 T perpendicular to the sample plane. Subsequently, external fields between 10 and 10 mT have been applied along 135 in-plane and simultaneously the magnetic-domain patterns have been imaged. Micromagnetic simulations have been performed by means of a parallel version of OOMMF public code using a multiprocessor hardware architecture composed by a double-quad-core processor [23]. The magnetic parameters used for the simulations are the saturation magnetization and the exchange constant ; no magnetocrystalline anisotropy has been taken into account. In order to correctly compute the magnetization and to isolate the numerical aspects from the physical ones, some simulation tests have been performed. In particular, the time step and the discretization size have been changed, using eventually a 5 nm cell size that is inside the range of validity of micromagnetic formalism. III. EXPERIMENTAL CHARACTERIZATIONS AND MICROMAGNETIC SIMULATIONS OF THE MAGNETIZATION DYNAMICS At first, the experimental hysteresis loop of the matrix of antidots has been measured (see Fig. 2). Room-temperature hysteresis loops of the whole antidot arrays have been measured by a alternating gradient field magnetometer (AGFM, ) in the parallel configuration. As can be observed, a field of 10 mT is large enough to reverse the magnetization [24]. Afterward, we considered some points in the hysteresis loop and studied numerically and experimentally the magnetization configuration at the same points. To nucleate a stable antivortex configuration in the central region of the antidot, a perpendicular magnetic field to saturate the sample magnetization has been applied and then it has been reduced to zero ( -remanence). In this state, the magnetic configuration is rather complex favoring the formation of different
Fig. 3. Micromagnetic simulations (left part) displayed as divergence of the magnetization compared to MFM image (right part) for different magnetic configurations: (a) z -remanence; (b) applied field -10 mT, 135 ; (c) applied field 10 mT, 135 . The color map represents the divergence of the magnetization (blue negative-red positive).
static vortices and antivortices. Fig. 3(a) shows a comparison between the computed micromagnetic configuration (plot of the divergence of the magnetization, blue negative—red positive) and the MFM image at the -remanence [compare Fig. 3(a) left to right], the discontinuities in the color are related to strongly nonuniform spatial configuration of the magnetization. From micromagnetic simulations, we observe in the central zone of the asteroid two different vortices (black circles) with
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Fig. 4. Polarity switching when an in-plane field pulse (x-direction) is applied, amplitude 100 mT, duration 10 ps. (a) Initial state. (b) After 25 ps. (c) After 124 ps. (d) After 830 ps (from left to right and from up to down).
opposite chirality and an antivortex (white circle). Starting from this configuration, a low in-plane external field (135 direction, amplitude 10 mT) is applied (for our convention negative field means applied from II to IV quadrant of the asteroid). The experimental and numerical data show that this field is able to induce an uniform configuration in the center of the antidot [compare the left and the right side of Fig. 3(b)]. On the other hand, a applied from IV to II quadrant is able to field induce a configuration with an antivortex only located near the boundary between the asteroid and the circle related to the IV quadrant [see Fig. 3(c) left side]. Once nucleated, the antivortex is also stable after the applied field is switched off and it moves toward the center of the asteroid. The comparison between micromagnetic simulations and MFM images shows a qualitative agreement in terms of potential configuration of the magnetization in the static hysteresis loop. The dynamical properties of the -remanence state for the single antidot and for a coupled system composed by three antidots have been studied. The magnetization dynamics is characterized by the excitation of a mode related to the spin-wave emission as described later in detail. Fig. 4 displays some snapshots of the magnetization process which occurs after the application of a field pulse (100 mT) for the single antidot. The system configuration starts at -remanence [see Fig. 4(a)] where it can be observed the central vortex in a stable configuration with core polarity. At 25 ps, a vortex–antivortex pair appears ( with and with ) [see Fig. 4(b)] and after 124 ps, annihilates with the and a spin-wave propagating to the boundary of the asteroid is observed [see Fig. 4(c)]. Finally, the switched moves toward the center of the system [see vortex Fig. 4(d)]. We also considered a structure composed by three antidots at distance 100 nm (the distance is small enough to allow coupling via the dipolar interaction). After the identification of the -remanence state of the coupled system, we simulated the mag-
IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011
Fig. 5. Power amplitude of the average magnetization dynamics due to an applied perpendicular field pulse of amplitude: (a)-(b) 100 mT, (c)-(d) 200 mT, (e)-(f) 300 mT and 10 ps pulse duration. Micromagnetic simulation of: (left panel) a single asteroid dot; (right panel): array of three asteroid dots (the pictures refer to the power in the central dot).
Fig. 6. Snapshot of magnetization dynamics excited by a short pulse (amplitude 100 mT, duration 10 ps) after 20 ns from the excitation. Two of the three dots are reported: (a) left and (b) central dot. The short field pulse is applied to the central dot (b).
netic response due to the application of a short field pulse of 10 ps (amplitude of 100–300 mT) applied to the central antidot of the array only. Fig. 5 shows the comparison between the power of the magnetization response (Fourier Transform) in a single antidot [(a), (c), (e)] and the central antidot [(b), (d), (f)] of the array, for three different applied field pulses (100, at 200, and 300 mT). The single antidot shows a main mode a frequency of 180 MHz (this value is near the ferromagnetic resonance frequency of 190 MHz). The main difference with into two difthe three antidots is the splitting of the peak ferent modes at frequencies and . Markedly, the frequency of the new excited modes is exactly 90 MHz smaller and larger than the excited mode in the single antidot. In order to identify the origin of these modes, we performed a combined time–frequency study of the magnetization response. The comparison of the snapshots (time-domain evolution of the spatial distribution of the magnetization) between two adjacent and are characterized by an antidots show the mode in-phase and an out-of phase oscillation of the magnetization
RAGUSA et al.: MAGNONICS CRYSTAL COMPOSED BY MAGNETIC ANTIVORTICES CONFINED IN ANTIDOTS
respectively [compare Fig. 6(a) and (b) for the mode where can be observed almost a mirror of the magnetization]. In addition, we find that the power of mode in the coupled antidots is about 50 times larger than the single antidot structure (compare Fig. 5 left panel and right panel). This power increase and the splitting of the modes are due to the dipolar coupling; in fact, the same micromagnetic simulations performed for three antidots at a distance of 600 nm did not show this dynamical behavior. In summary, we studied the magnetic behavior of antidots under static and dynamic conditions. In particular, as a response to a short magnetic pulse in the coupled antidots, we observed the excitation of two main modes, being the low frequency one related to the in-phase oscillation of the magnetization (acoustic mode) and the highest frequency mode related to an out-of-phase oscillation of magnetization (optical mode). ACKNOWLEDGMENT The authors would like to thank G. Barrera for MFM images and M. J. Donahue for providing version 1.2a4 (parallel version) of OOMMF public code. REFERENCES [1] Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, “Observation of frequency band gaps in a onedimensional nanostructured magnonic crystal,” Appl. Phys. Lett., vol. 94, p. 083112, 2009. [2] K. S. Lee, D. S. Han, and S. K. Kim, “Physical origin and generic control of magnonic band gaps of dipole-exchange spin waves in widthmodulated nanostrip waveguides,” Phys. Rev. Lett., vol. 102, p. 127202, 2009. [3] M. Krawczyk and H. Puszkarski, “Plane-wave theory of three-dimensional magnonic crystals,” Phys. Rev. B, vol. 77, p. 054437, 2008. [4] V. V. Kruglyak and R. J. Hicken, “Magnonics: Experiment to prove the concept,” J. Magn. Magn. Mater., vol. 306, pp. 191–194, 2006. [5] S. A. Nikitov, P. Tailhades, and C. S. Tsai, “Spin waves in periodic magnetic structures on magnonic crystals,” J. Magn. Magn. Mater., vol. 236, pp. 320–330, 2001. [6] A. Kozhanov, D. Ouellette, Z. Griffith, M. Rodwell, A. P. Jacob, D. W. Lee, S. X. Wang, and S. J. Allen, “Dispersion in magnetostatic CoTaZr spin waveguides,” Appl. Phys. Lett., vol. 94, p. 012505, 2009. [7] A. V. Chumak, A. A. Serga, S. Wolff, B. Hillebrands, and M. P. Kostylev, “Design and optimization of one-dimensional ferrite-film based magnonic crystals,” J. Appl. Phys., vol. 105, p. 083906, 2009. [8] Y. V. Gulyaev, S. A. Nikitov, and L. V. Zhivotovskii et al., “Ferromagnetic films with magnon bandgap periodic structures: Magnon crystals,” JETP Lett., vol. 77, pp. 567–570, 2003.
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[9] A. V. Butko, A. A. Klimov, and S. A. Nikitov et al., “Using the magneto-optical Kerr effect to study magnetization processes in two-dimensional magnonic crystals based on YIG thin films,” J. Commun. Technol. Electron., vol. 51, pp. 944–947, 2006. [10] H. Ulrichs, B. Lenk, and M. Munzenberg, “Magnonic spin-wave modes in CoFeB antidot lattices,” Appl. Phys. Lett., vol. 97, p. 092506, 2010. [11] G. Gubbiotti, S. Tacchi, and M. Madami et al., “Brillouin light scattering studies of planar metallic magnonic crystals,” J. Phys. D-Appl. Phys., vol. 43, p. 264003, 2010. [12] Y. J. Cao, G. H. Yun, and X. X. Liang et al., “Band structures of twodimensional magnonic crystals with different shapes and arrangements of scatterers,” J. Phys. D-Appl. Phys., vol. 43, p. 305005, 2010. [13] S. Neusser, G. Duerr, H. G. Bauer, S. Tacchi, and M. Madami et al., Phys. Rev. Lett., vol. 105, p. 067208, 2010. [14] F. S. Ma, H. S. Lim, Z. K. Wang, S. N. Piramanayagam, S. C. Ng, and M. H. Kuok, “Micromagnetic study of spin wave propagation in bicomponent magnonic crystal waveguides,” Appl. Phys. Lett., vol. 98, p. 153107, 2011. [15] E. Martinez, L. Torres, L. Lopez-Diaz, M. Carpentieri, and G. Finocchio, “Spin polarized current-driven switching in permalloy nanostructure,” J. Appl. Phys., vol. 97, p. 10E302-1-3, May 2005. [16] K. Y. Guslienko, K. Lee, and S. Kim, “Dynamic origin of vortex core switching in soft magnetic nanodots,” Phys. Rev. Lett., vol. 100, pp. 027203-1–027203-4, 2008. [17] V. S. Pribiag, G. Finocchio, B. Williams, D. C. Ralph, and R. A. Buhrman, “Long-timescale fluctuations in zero-field magnetic vortex oscillations driven by dc spin-polarized current,” Phys. Rev. B, vol. 80, p. 180411(R), 2009. [18] K. Y. Guslienko, B. A. Ivanov, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, J. Appl. Phys., vol. 91, p. 8037, 2002. [19] D. D. Sheka, Y. Gaididei, and F. G. Mertens, “Current induced switching of vortex polarity in magnetic nanodisks,” Appl. Phys., vol. 91, p. 082509, 2007. [20] B. C. Choi, J. Rudge, E. Girgis, J. Kolthammer, Y. K. Hong, and A. Lyle, “Spin-current pulse induced switching of vortex chirality in permalloy/Cu/Co nanopillars,” Appl. Phys., vol. 91, p. 022501, 2007. [21] A. Drews, B. Krüger, M. Bolte, and G. Meier, “Current- and fielddriven magnetic antivortices,” Appl. Phys. Lett., vol. 94, p. 062504, 2009. [22] K. Shigeto, T. Okuno, K. Mibu, T. Shinjo, and T. Ono, “Magnetic force microscopy observation of antivortex core with perpendicular magnetization in patterned thin film of permalloy,” Appl. Phys. Lett., vol. 80, pp. 4190–4192, 2002. [23] M. J. Donahue and D. G. Porter, OOMMF User’s Guide Natl. Inst. Standards Technol., Gaithersburg, MD, Interagency Rep. NISTIR 6376, 1999, Version 1.0. [24] E. Cardelli, E. Della Torre, and B. Tellini, “Direct and inverse Preisach modeling of soft materials,” IEEE Trans. Mag., vol. 36, no. 4, pp. 1267–1271, Jul. 2000. [25] B. Van Waeyenberge, A. Puzic, H. Stoll, K. W. Chou, T. Tyliszczak, R. Hertel, M. Fahnle, H. Bruckl, K. Rott, G. Reiss, I. Neudecker, D. Weiss, C. H. Back, and G. Schutz, “Magnetic vortex core reversal by excitation with short bursts of an alternating field,” Nature, vol. 444, pp. 461–464, 2006.
