Spin Dynamics in Ferromagnetic Resonance for Nano ... - IEEE Xplore

IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

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Spin Dynamics in Ferromagnetic Resonance for Nano-Sized Magnetic Dot Arrays: Metrology and Insight Into Magnetization Dynamics SeungMo Noh1 , Daisuke Monma1 , Kousaku Miyake1 , Masaaki Doi1 , Tomoaki Kaneko2 , Hiroshi Imamura2 , and Masashi Sahashi1 Department of Electronic Engineering, Tohoku University, Sendai 980-8579, Japan Nanoscale Theory Group, NRI, AIST, Tsukuba 305-8568, Japan The ferromagnetic resonance response (FMR) in the variously sized magnetic dot arrays was measured by using network-analyzer by the ferromagnetic resonance technique. We first demonstrated that the magnetization excitation related to the susceptibility coplanar wave-guide (CPW). In this , the edge mode excitation modified the FMR response appreciably and found that the damping constant is strongly affected by the size of the nano-magnet. In larger nano-magnets, two edge modes were observed. We showed that this edge mode can be exploited as a means to separately characterize the magnetization state of the nano-magnet as well as the size variation. In addition, the simulation results are also presented here to account for the experimental observations. Index Terms—Coplanar waveguide (CPW), damping constant, magnetic dot array, magnetization dynamics, network analyzer ferromagnetic resonance (NA-FMR), rf magnetic susceptibility.

I. INTRODUCTION

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ICROWAVE assisted magnetic recording (MAMR) with a spin torque microwave oscillator is currently of high interest in research attempting to achieve next-generation hard-disk drives with high areal densities of over 1 Tbpsi [1]. For MAMR, a large-amplitude of AC stray field, coherent motion of magnetization, and low driving power are necessary for optimal performance of a nano-sized spin torque oscillator writing head. The field generation layer (FGL), in which the magnetization rotates, of the spin torque oscillator (STO) is a key element of MAMR for achieving a large amplitude for the AC field. In order to achieve a large amplitude for the AC field, magnetization in FGL must oscillate within a single domain. A synthetic FGL structure composed of the field generation layer and a layer with perpendicular anisotropy has been theoretically proposed [1] for generating large AC field. While, such technological application is of course important in its own right, there is also significant interest to understanding how magnetic material behaves when confined to nanoscale dimensions, how to interpret ferromagnetic resonance (FMR) spectra in arrays of nanostructures, how defect affects both the static and high frequency properties of nanostructures, how to measure and characterize such defect, how micro-magnetic simulation or model can be improved to better description for nanostructure, and how lateral confinement affects line-width and the intrinsic damping parameter. The determination of the damping parameter is critical for the development of high-speed switching technology and theory for spin-momentum transfer. It is also important to understand how scaling and fabrication process affects the switching field distribution, reversal mechanism, and switching rate. It was recently shown that the fabrication technique used to make perpendicularly magnetized Manuscript received February 21, 2011; accepted April 22, 2011. Date of current version September 23, 2011. Corresponding author: S. Noh (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.2011.2150741

nanostructures can significantly alter the anisotropy of the edge region [2]. This edge modification has significant effect on the magnetic reversal properties of the nanostructure that are critical for storage technology. This highlights the fact that magnetic nanostructure cannot be realistically modeled as a homogenous system with uniform magnetic properties throughout. Recently, it was also discovered that inhomogeneous dipole field at the edge of magnetic stripes creates the localized modes at the edges confined to a few tens of nanometers [3], [4]. The behavior of this edge modes differs significantly from the bulk excitations. Moreover extensive work has been carried out on characterizing this edge mode as well as the edge saturation field in magnetic stripes using an inductive FMR technique and it was shown that the edge saturation field, edge mode frequency, and edge mode line-width depend strongly depend on the edge roughness [5]. These results indicate that the edge properties can be separately measured from the bulk magnetic properties via spatially confined mode. However, this issue has not been addressed so far due to the difficulty related to a systematic experimental condition. Recently, network analyzer ferromagnetic resonance (NA-FMR) method using coplanar wave guide (CPW) demonstrated that the magnetic response of single patterned magnetic elements can be studied. In addition to vastly improved sensitivity for measuring magnetic fluctuation in small-sized structure, this technique allows the magnetic response to be probed over the continuous range of frequency when attached to a network analyzer, which provides a substantial advantage over conventional FMR. In this study, we investigated the mode structure in various sized magnetic dot arrays of a circular shape fabricated on CPW using the NA-FMR method and found a significant variation in line-width depending on size variation in line-width which depends on size and edge modes of two peaks in larger size. This well-controlled experimental situation enables us to study the magnetization precession comprehensively by measuring the resonance frequency, and the precession angle of component. Finally we discuss the agreement between theory and experiment.

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Fig. 1. Sample geometry set-up of NA-FMR measurement. (a) Schematic drawing of CPW, where w is width of signal line and h is radio frequency AC field. (b) SEM images of nominally 50 nm and 150 nm circular magnetic dot arrays. (c) The film structure of a magnetic dot sample.

II. EXPERIMENT: SAMPLE PREPARATION AND MEASUREMENT We fabricated a set of electrically shorted coplanar waveguide (CPW) transmission lines consisting of quartz sub./Ta(5 nm)/Cu(300 nm)/Ta(5 nm) using photolithography, the sample dot arrays (circularly lateral size of 50, 100, 150, of dots, 20 nm thickness) was 300, and 500 nm and 1, 3, 5 fabricated on CPW using e-beam lithography, Ar+ ion milling and a resist removal processes. Fig. 1 shows a diagram of the measurement system. The impedance of the CPW with a signal [see Fig. 1(a)] approximately matched line width of 50 . Fig. 1(b) shows scanning electron microscope (SEM) images of nominal 50 and 150 nm diameter magnet dot arrays as well as a schematic diagram of the idealized magnet dot array structure [see Fig. 1(c)]. SEM image analysis indicated that the root-mean-square size varies along the short and long axes. The circular shape of the dots was slightly varied to a non-uniform edge with an approximately 10 nm variation in diameter. The film. CPW and dot array pattern were insulated by a 10 nm The FMR measurements of the reflection at microwave frequencies were carried out using a network analyzer that can perform sweeps from 10 MHz up to 40 GHz. The FMR spectra of were measured as a functhe real and imaginary parts of tion of the applied magnetic field. The microwave and magnetic fields are applied perpendicular and parallel to the plane. The microwave drive was provided by a CPW excitation structure with the thin film sample deposited across the signal line (see Fig. 1(a)). NA-FMR was measured with an Agilent N5230A network analyzer and 40A-GSG-250 EDP of a high frequency probe in the frequency range of 0.01–26.5 GHz. Two ground-signalground (GSG) pin-type wafer probes were in mechanical contact with both ends of the CPW transmission line. Therefore, the ac magnetic field was caused by applying microwaves to the CPW and had an input power of 15 dBm. The microwave magnetic was generated in-plane by the ac current through the field signal line around CPW. was right-angled to the external . of 0–2 kOe was applied parallel to the signal field line during measurement. In order to extract the FMR absorption, parameter. We neglected the effect of the we used only the resonances on the impedance of the coplanar waveguide.


Fig. 2. Theoretically, simulated and measured microwave magnetic susceptiof 1 kOe. (a) Geometry of the bility dependence on h magnetic field at H setup. The stripline runs parallel along the Y -axis. The induced rf field is always ! =h and ! =h are susceptigenerated along the X -axis. Where bility ; respectively. (b) The simulated real (solid red line) and imaginary (solid blue line) parts of and . (c) Real (red circle) and imaginary (blue circle) parts of the measured susceptibility in a 100 nm circular magnetic in the thickness of 20 nm in 1 kOe applied field. dot array of

m()

m( )

Fe Co

In this case, the FMR response, representing the real and imaginary parts of rf magnetic susceptibility, can simply be defined as the difference between magnitudes of ( mag) at and out of the ferromagnetic resonance. Thus, we calculated the FMR response as where background of mag is the magnitude of the “background” , which is mag without magnetic dot arrays. only coplanar waveguide The background value is the maximum of S11 mag, measured in the maximum magnetic field. The difference found in the each FMR response can thus unambiguously be ascribed to the variation in the magnitude. III. RESULT AND DISCUSSION We present some measurements for the magnetic response of our samples in the frequency domain. We probed the response to the excitation of the magnetization precession driving field generated by the CPW. To describe the magnetization dynamics in the magnetic dot array for arbitrary orientations of the magnetirelative to the CPW, we refer to a theoretical descripzation tion in [6] for the rf magnetic susceptibility in magnetic nanosize as defined in dot, where we introduce a coordinate system Fig. 2(a). The frequency dependence of the rf magnetic susceptibility is shown in Fig. 2(b), (c). For the simulations, we used the , the exchange saturation magnetization , , stiffness and the damping constant , which are parameters for FeCo alloy. We can see the measured susceptibility dependence on fre. This quency is very similar to that of simulation result for allows to model the precession motion of magnetization as an . We remind that is additional impedance as is composed of both real and imagcomplex and therefore inary parts of inductance. G. Counil et al. have previously reported experiment result and theoretical calculated simulation for a different magnetization dynamics, which found magnetic

NOH et al.: SPIN DYNAMICS IN FMR FOR NANO-SIZED MAGNETIC DOT ARRAYS: METROLOGY AND INSIGHT

Fig. 3. Susceptibility as FMR response, Re (S ) and various applied external magnetic field for 20 nm thickness Fe Co in 100 nm diameter: (a) a simulated Re spectrum, (b) mode structure of simulated representative equilibrium magnetization states, (c) the measured spectrum of Re , (d) plots where the red solid line denotes the fitting of the Kittel equaof f vs H tion (1).

susceptibility in the xz plane precession of the static magin a Permalloy thin film [6]. On the other netization vector hand, we found that can be measured in the xz plane precession in our samples. As a check, we also verified that the resonance frequency obtained from our susceptibility measurements as a function of applied external magnetic field is consistent with Kittel’s formula shown in Fig. 3(c). The dependence of the resonance frequency on the external is defined in the Kittel equation [7] field

(1) , and where we have defined are effective demagnetizing factors and express the effect of magneto-crystalline anisotropy or induced anisotropy. This is exemplified in Fig. 3(a), which show the calculated of real parts for a 100 nm sized dot array of FMR spectra of a 20 nm thick FeCo alloy sample patterned on the CPW under the applied magnetic fields of 1, 1.25 and 1.5 kOe. The magnetization states at each calculated mode frequency with in-plane applied field of 1 kOe are given in Fig. 3(b), where a white arrow indicated the magnetization motion in each mode frequency corresponding to first, second and third peaks. Using deobtained by micro-magnetic simmagnetization factors ulations, is given by 10.2 GHz, 11.5 GHz and 12.8 GHz , 1.25 kOe and 1.5 kOe, respectively. Therefor fore, the second peak is the whole magnetization mode to agreement reasonably well with the Kittel formula. The other peaks show the magnetization mode of end region. It is seen that two edge modes show non-degenerate frequency over a wide range of applied field (see Fig. 3(a)). From the mode structure, shown in Fig. 3(b), we performed micro-magnetic simulation in order to understand the mode structure. Fig. 3(c) shows the experifor a 20 nm-thick for the mented spectra of Re 100 nm diameter. In Fig. 3(a) and (c), the two modes in simulation and experiment were observed and the field dependence of the simulated data (see Fig. 3(a)) agreed reasonably well

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Fig. 4. Magnetic dot array diameter versus: (a) the FMR spectra, (b) the resonance frequency, (c) full width of half maximum (FWHM), 1f , (d) damping of constant in 20 nm thick Fe Co under the applied magnetic field H 1.5 kOe.

with the experimental data. We speculate that the small frequency shifts between the simulations and data resulted from the fact that the simulations were performed. Fig. 3(d) shows vs , these fit to the Kittel equation except data for for edge mode. In the following, we move onto the size dependence of FMR spectra. Fig. 4(a) shows the spectra plots for the various diameter magnet arrays. At the smallest diameters (50 nm), the edge mode is not appeared. As the diameter increases, the resonance frequency with edge mode frequency increased. By performing this procedure on data recorded at different sized-dot diameters, we obtained the frequencies, line widths and damping constants as functions of the diameter as shown in Fig. 4(b)–(d). was obtained from FMR spectra. In order The line width to study quantitatively, the damping constant was obtained from frequency line width of FMR spectra and anisotropy fields obtained from the fitting of (1) using the following: (2) The damping constant decreases with the dot diameter decrease. The data suggest that the large increase in line-width is primarily due to increased in-homogeneity. The magnetization state of dot arrays depend on the balance of the spin alignment, the magnetic anisotropy favoring alignment of spins along a particular direction, and the demagnetizing field created by magnetization of the particles. Shape anisotropy is of special importance in lithographically defined elements. The demagnetizing field inside a magnetized body is proportional to its magnetization by a factor determined by the shape of the body. Therefore, geometrical details of a magnetic element, such as the in-plane aspect ratio, the critical size for a single domain element depends on the dot shape. This effect is maximal for square or rectangular dots. However, there are no systematic studies of this issue. Due to the sensitivity of the magnetic properties of dot array on the fabrication process that affects the microstructure or edge roughness, it is

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virtually impossible to draw any conclusion from the existing results on similar systems. IV. CONCLUSION We present a study on the ferromagnetic resonance response of patterned magnet dot arrays on CPW measured by NA-FMR. We demonstrated the magnetization excitation related to the rf magnetic susceptibility for patterned magnet dot arrays on CPW in the xz plane. Micro-magnetic simulations demonstrate that these observations can be explained by magnetization precession of xz plane. We have measured the spin dynamics in 50 nm-5 nanostructures. The mode structure of these nanostructures was confirmed by micro-magnetic simulations, and shows that above a critical size, both center and edge modes are observed. The significant difference in line width between the various diameters is most likely a result of the edge mode being as opposed to a change in damping constant. This result opens strategies for the design of spintronic nano-oscillators in that the magnetization rotation mode allows magnetization dynamics.

ACKNOWLEDGMENT This work was supported in part through the Storage Research Consortium (SRC) and Center of Education and Research for Information Electronics systems of Global COE Program, Japan. REFERENCES [1] J. G. Zhu, X. Zhu, and Y. Tang, IEEE. Trans. Magn., vol. 44, p. 125, 2008. [2] J. M. Shaw, S. E. Russek, T. Thomson, M. J. Donahue, B. D. Terris, O. Hellwig, E. Dobisz, and M. L. Schneider, Phys. Rev. B, vol. 78, p. 024414, 2008. [3] J. P. Park, P. Eames, D. M. Engebretson, J. Berezovsky, and P. A. Crowell, Phys. Rev. Lett., vol. 89, p. 277201, 2002. [4] R. D. McMichael and B. B. Maranville, Phys. Rev. B, vol. 74, p. 024424, 2006. [5] J. M. Shaw, T. J. Silva, M. L. Schneider, and R. D. McMichael, Phys. Rev. B, vol. 79, p. 184404, 2009. [6] G. Counil, J.-V. Kim, T. Devolder, C. Chappert, K. Shigeto, and Y. Otani, J. App. Phys., vol. 95, p. 5646, 2004. [7] C. Kittel, Phys. Rev., vol. 73, p. 155, 1948.