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IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002
Magnetic Properties of Submicron Circular Permalloy Dots Gianluca Gubbiotti, Giovanni Carlotti, Fabrizio Nizzoli, Roberto Zivieri, Takuya Okuno, and Teruya Shinjo
Abstract—Both the static and the dynamical magnetic properties of a square array of circular permalloy dots, characterized by a magnetic vortex configuration of the magnetization, have been investigated by means of magneto-optical Kerr effect and of Brillouin light scattering (BLS) from thermally excited spin waves. The measured hysteresis loop can be satisfactorily reproduced by micromagnetic simulations, showing that the vortex configuration is stable over a wide range of applied field. The high frequency response of the dots was analyzed by BLS measurements performed under external magnetic field intensity large enough to uniformly magnetize the dots. Evidence is given of a marked discretization of the spin wave spectrum with respect to the case of the continuous permalloy film, where only one peak, corresponding to the Damon–Eshbach mode, was detected. The experimental frequencies have been compared to those calculated using a recently developed analytical model for a flat uniformly magnetized cylindrical dot. Index Terms—Brillouin light scattering (BLS), magnetic vortex, permalloy, spin waves.
I. INTRODUCTION
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T HAS BEEN recently found that a curling magnetic structure with perpendicular magnetization at the core may be realized in permalloy (PY) [1]–[4] and Co [5]–[7] dots with appropriate aspect ratio, over a wide range of applied fields. This flux-closure state reduces the magnetostatic interaction between individual magnets and therefore such isolate magnetic dots may have a potential application for high density magnetostorage devices. The vortex core displacement in the applied magnetic field has been observed [8] by magnetic force microscopy (MFM) and Lorentz microscopy and theoretically calculated by minimizing the total magnetic energy [9], [10]. Concerning the high frequency dynamical properties of patterned magnetic films, it has been recently shown that they can be successfully investigated by Brillouin light scattering (BLS) from spin waves. Most of the BLS study of patterned arrays of wires and dots has been carried out by the group of Hillebrands at Kaiserslautern [11]. In particular, the BLS technique has been used to measure the spin-wave dispersion on a regManuscript received February 25, 2002; revised May 10, 2002. This work was supported by MURST-COFIN 2000 and INFM-PAIS MAGDOT. G. Gubbiotti is with the National Institute of Physics of Matter (INFM), 06123 Perugia, Italy (e-mail:
[email protected]). G. Carlotti is with the Department of Physics, Perugia University, and also with the National Institute of Physics of Matter (INFM), 06123 Perugia, Italy (e-mail:
[email protected]). F. Nizzoli and R. Zivieri are with the Department of Physics of the University of Ferrara, 44100 Ferrara, Italy, and also with the National Institute of Physics of Matter (INFM), 06123 Perugia, Italy T. Okuno and T. Shinjo are with the Institute for Chemical Research, Kyoto University, Uji 611-0011, Japan. Digital Object Identifier 10.1109/TMAG.2002.801920.
ular square array of tangentially magnetized circular dots of permalloy (1 or 2 micron diameters) [12]. Although a detailed calculation of the spin-wave frequency is quite complicated because of the finite lateral shape of the dots, a theoretical model has been recently proposed in [13] which enables one to calculate the spin-wave frequency in tangentially magnetized cylindrical dots, under the hypothesis of uniform magnetization. The frequency quantization is thus explained as a direct consequence of the radial boundary conditions at the lateral edges of the magnetic dots. In this paper, the results on both the static and the dynamic magnetic properties of PY circular dots with a vortex domain nm; configuration are presented. The dots thickness is m. Hysteresis loops of the patterned array the radius is and the continuous PY film were obtained by using magneto-optical Kerr effect (MOKE) in the longitudinal geometry. Numerical simulations based on micromagnetic theory have been performed to achieve a deeper insight into the evolution of magnetic vortex with the applied field and to reproduce the shape of the measured hysteresis loops. The high frequency dynamical properties of the dots have been studied by BLS with applied field large enough to stabilize a single domain state within each dot. A quantitative comparison between the measured spin-wave frequencies and those expected from the theoretical model [13] is presented. II. SAMPLE PREPARATION AND EXPERIMENTAL SETUP Samples of ferromagnetic Ni Fe (PY) alloy dots were prepared by means of electron–beam lithography and evaporation in ultrahigh vacuum using an electron beam gun. The desidered patterns were printed in a spin-coated layer of resist on thermally oxidized Si substrate and subsequently topped by a layer of PY. By a liftoff process, the resist was removed and permalloy dots as designed remain on top of the Si surface. Several arrays with circular permalloy dots were prepared with radius ranging between 0.1 and 0.5 m even if in this paper we focus on results relative to smallest dot diameter, only. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) images confirmed that the morphology of the patterns was of good quality, as far as both the uniformity and the dimensional control of the diameter and periodicity were concerned. Part of the magnetic film was left unpatterned to compare the consequences of patterning as measured by Kerr magnetometry and BLS. Magnetic hysteresis loops were measured in the longitudinal Kerr effect configuration, i.e., with the external field applied in the film plane. The nearly crossed polarizers method was used, including a laser modulated in amplitude at 450 Hz and a lock-in amplifier. The BLS measurements were carried
0018-9464/02$17.00 © 2002 IEEE
GUBBIOTTI et al.: MAGNETIC PROPERTIES OF SUBMICRON CIRCULAR PERMALLOY DOTS
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Fig. 2. BLS spectra relative to the patterned film (upper spectrum) and unpatterned film (lower spectrum). An external field of 1.8 kOe was applied 26 . Note that the two in-plane while the incidence angle of light was peaks close to the central elastic peak are artifacts produced by the closing of the mechanical shutter on the primary laser beam at the entrance of the interferometer. The inset shows the magnetization vector plot calculated for the same field used to record the BLS spectrum of the patterned film.
=
Fig. 1. Measured (open circles) and simulated (continuous curve) hysteresis loops for the 0.1-m radius dots. The insets show the SEM image of the sample and the orientation of the applied field with respect to the dot arrays. In the upper part of the figure, the vector plots obtained from a two—dimensional numerical micromagnetic calculations using the NIST OOMMF code are shown for 0.6, 0, and 0.6 kOe applied field.
0
out in backscattering geometry at the GHOST laboratory, Perugia University, Perugia, Italy [14], using a Sandercock 3)-pass model tandem Fabry–Pérot interferometer in a (3 configuration. The light source was a single-mode Argon laser operating at the 514.5 nm with incident power in the range between 100–200 mW. The spectra were acquired using crossed polarizations between the incident and the scattered beams, in order to take advantage of the selection rules for the magnon spectra and to prevent phonon lines to appear. A magnetic field with intensity variable from 0 to 10 kOe was applied parallel to the film plane and perpendicular to the incident light beam. The sample was mounted on a goniometer to allow rotation around the field direction, i.e., to vary the incidence angle of light, and, thus, the spin-wave wave number . III. RESULTS AND ANALYSIS A typical loop is shown in Fig. 1. In order to achieve an understanding of such a loop in terms of the evolution of the magnetization configuration, we have used the publicly available National Institute of Standards and Technology micromagnetic simulator [15] in which a numerical finite-element method which is used to find the equilibrium magnetization vector solves the Landau–Lifshitz equation. The integration is stopped reaches a sufficiently low value so that when the torque is less than 10 ( is the saturation magnetization). The cell size was 5 nm. The crystalline anisotropy was set to zero since the measured in-plane anisotropy in our continuous layer was very small. The absence of interdot coupling
has been experimentally verified by measuring the longitudinal Kerr hysteresis loops for different in-plane orientations of the applied magnetic field. The main features of the hysteresis loop are fairly well reproduced by our micromagnetic simulations (continuous curve in Fig. 1), where we used the magnetic parameters of PY derived by the BLS study of the continuous film (see below). At zero applied field, the remanence is vanishing, a typical feature of the vortex remanent state of soft PY dots of circular shape. As the external field is switched on, the gradual increase of the magnetization corresponds to the displacement of the vortex core from the center. This is evident in the two-dimensional vector plots obtained from numerical micromagnetic calculations shown in the upper part of Fig. 1. At zero field the vortex is in the center and during the reversible part of the loop (up to about 1 kOe) the vortex core movement is perpendicular to the applied field and displaced toward the dot edges; on further increasing the applied field the saturation is reached through a jump of magnetization at about 1.3 kOe. When the field is reduced from saturation, the cycle is nonreversible and a second jump takes place at about 0.7 kOe. The slight discrepancy between the measured and the simulated value of this second jump is typical of micromagnetic simulations and depends on the parameters of the model (cell size, convergence parameter, loop step). The existence of a vortex spin distribution was confirmed by magnetic force microscopy observation of magnetic domains [1]. Concerning the dynamical magnetic properties, in Fig. 2 the BLS spectrum of the array of circular dots with radius m together with the spectrum of the unpatterned PY film is shown. The two spectra are taken in the same experimental
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conditions: incidence angle of light and applied magnetic field 1.8 kOe. Such a field is large enough to ensure sample saturation, as shown by the domain configuration calculated by the micromagnetic simulation, seen in the inset of Fig. 2. For the patterned film (upper spectrum), one notes the well-resolved discretization of the peaks, indicated by the arrows, on both the Stokes and the anti-Stokes sides of the spectrum, while for the continuous films only one peak associated to the DamonEshbach (DE) is present. The measured frequency are: 8.05, 9.30, 11.62, 14.65, and 16.02 GHz. We have found that the discrete modes are dispersionless, i.e., their frequencies do not change as a function of the magnon wave vector while the frequencies monotonously increase with the intensity of the magnetic field. In order to calculate the spin-wave frequency of the quanm and tized modes of a cylindrical PY dot of radius nm, the formalism recently proposed in [13] has height been exploited. The model is valid for an isolated cylindrical magnetic dot with in-plane magnetization in the presence of intradot dipolar and exchange interactions. The quantization condition on the parallel magnon wavevector has been introduced through the usual radial boundary condition at the dot boundary in the absence of pinning on the cylindrical lateral surface. The four lowest modes frequencies have been calculated using the analytical frequency equation [13]. From a best fit procedure of the frequency dependence of the DE mode of the continuous film on both the field intensity and the magnon wave vector, we could estimate the values of the satGauss, of the exchange stiffuration magnetization cm and of the gyromagness constant GHz/kOe. These values have been used netic ratio both in the micromagnetic simulation (solid line in Fig. 1) and in the spin-vave frequency calculation. For the aspect ratio of , [13] also enour dots the effective demagnetizing factor tering into the frequency expression, can be calculated using an . The lowest diagonal analitical formula which gives frequencies calculated in the cosine basis correspondent to the ) are Brillouin experimental geometry ( perpendicular to the following: 11.51, 12.73, 14.00, and 16.73 GHz. In addition, the expected frequency of the uniform mode of a single disk for “free spins” boundary conditions is 9.51 GHz; for its determination the Kittel’s formula [16] with averaged demagnetizing factor was used. The aforementioned calculated frequencies compare fairly well with those of the five modes detected experimentally, except for the two lowest modes whose frequencies are overestimated. The reason for this disagreement may be due to the fact
IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002
that in our dots the condition is not well fulfilled. In addition, the pinning at the lateral surface, neglected in our calculations, could reduce the calculated frequencies of the low frequency modes. In spite of this slight discrepancy, however, these results are better than those which would have been obtained using the simple quantization model used in the past [11], where the quantization condition for ferromagnetic wires was extended to the case of a cylindrical dot, just replacing the wire , width with the dot diameter, i.e., imposing the rule . with REFERENCES [1] T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science, vol. 289, pp. 930–932, 2000. [2] R. P. Cowburn, D. K. Kolsov, A. O. Adeyeye, M. E. Welland, and D. M. Tricker, “Single-domain circular nanomagnets,” Phys. Rev. Lett., vol. 83, pp. 1042–1045, 1999. [3] R. Pulwey, M. Rahm, J. Biberger, and D. Weiss, “Switching behavior of vortex structures in nanodisks,” IEEE Trans. Magn., vol. 37, pp. 2076–2078, July 2001. [4] M. Schneider, H. Hoffmann, and J. Zweck, “Lorentz microscopy of circular ferromagnetic permalloy nanodisks,” Appl. Phys. Lett., vol. 77, pp. 2909–2911, 2000. [5] A. Lebil, S. P. Li, M. Natali, and Y. Chen, “Size and thickness dependencies of magnetization reversal in Co dot arrays,” J. Appl. Phys., vol. 89, pp. 3892–3896, 2001. [6] J. Raabe et al., “Magnetization pattern of ferromagnetic nanodisks,” J. Appl. Phys., vol. 88, pp. 4437–4439, 2000. [7] A. Fernandez and C. J. Cerjan, “Nucleation and annihilation of magnetic vortices in submicron-scale Co dots,” J. Appl. Phys., vol. 87, pp. 1395–1401, 2000. [8] K. Ounadjela, I. L. Prejbeanu, L. D. Buda, U. Ebels, and M. Hehn, “Observation of micromagnetic configurations in mesoscopic magnetic elements,” in Spinelectronics, M. Ziese and M. Thornton, Eds. Berlin, Germany: Springer-Verlag, 2001, Series lectures notes in Physics, pp. 332–378. [9] K. Y. Guslienko, Y. Novosad, Y. Otani, H. Shima, and K. Fukamichi, “Field evolution of magnetic vortex state in ferromagnertic disks,” Appl. Phys. Lett., vol. 78, pp. 3848–3850, 2001. [10] K. Yu Guslienko and K. L. Metlov, “Evolution and stability of a magnetic vortex in a small cylindrical ferromagnetic particle under applied fiedl,” Phys. Rev. B., vol. 63, pp. 100403-1–100403-4, 2001. [11] S. Demokritov and B. Hillebrands, “Spinwaves in laterally confined magnetic structures,” in Spin Dynamics in Confined Magnetic Structures I, B. Hillebrands and K. Ounadjela, Eds. Berlin, Germany: SpringerVerlag, 2002, Topics in Applied Physics, pp. 65–92. [12] J. Jorzick et al., “Spin-wave quantization and dynamic coupling in micron-size circular magnetic dots,” Appl. Phys. Lett., vol. 75, pp. 3859–3861, 1999. [13] K. Y. Guslienko and A. N. Slavin, “Spin-wave in cylindrical magnetic dots arrays with in-plane magnetization,” J. Appl. Phys., vol. 87, pp. 6337–6339, 2000. [14] [Online]. Available: http://www.fisica.unipg.it/infm/ghost/ghost.htm [15] [Online]. Available: http://math.nist.gov/oommf [16] C. Kittel, “On the theory of ferromagnetic resonance absorption,” Phys. Rev., vol. 73, pp. 155–161, 1948.
