Chapter Introduction Chapter Introduction The use of magnetism and magnetic materials has a long history. Ancient Chinese made use of lodestones as magnetic compasses for navigation. Scientific understanding of magnetism can be traced back to the 17th century with pioneering work done by Gilbert [1]. Further studies were undertaken by for example Coulomb, Oersted, Ampere, and Faraday [2] in the 18th and 19th century. Classical electromagnetism was summarized as Maxwell’s equations [3] at the end of the 19th century. A better understanding of magnetism came with the birth of quantum mechanics at the beginning of the 20th century and the realization that the electron has an intrinsic spin and magnetic moment. Detailed models of the microscopic structure of magnetic materials were then constructed by scientists like Stoner, Weiss and Bloch [4, 5]. Today, the study of magnetism has come to a new stage – nanomagnetism. With the development of nanoscience and nanotechnology, magnetic structures with length scales ranging from a few inter-atomic distances to one micron have attracted intense research interests in the past few decades [6-8]. The scientific and technological importance of magnetic nanostructures is due to three main reasons. Firstly, there is an overwhelming variety of structures with interesting physical properties, ranging from naturally occurring nanomagnets to artificial nanostructures. Secondly, the involvement of nanoscale effects in the explanation and improvement of the properties of advanced Chapter Introduction magnetic materials. Thirdly, the study of magnetic nanostructures has led to completely new research areas like spintronics. Though nanomagnetism started only a few decades ago it has now evolved into a well-established branch of condensed matter physics. A brief review of some magnetic nanostructures as well as their fabrication and characterization techniques is presented in the following sections. 1.1 Magnetic Nanostructures There are a variety of magnetic nanostructures such as thin films, multilayers, dots, stripes, nanowires and nanorings. A comprehensive introduction of these structures goes beyond the scope of this work. Discussed below are the three nanoscale systems studied in this project. 1.1.1 Nanowires Magnetic nanowires are scientifically interesting and have potential applications in many areas of advanced nanotechnology. Early works on nanowires focused on anisotropy and magnetostatic interactions between wires. Perpendicular anisotropy has been observed in cylindrical Co nanowires [9] embedded in porous alumina matrix. The magnetic properties, e.g. coercivity, remanence ratio and activation volumes, of the Co nanowires were found to be strongly dependent on nanowire length, diameter and interwire separation. Particularly, when the nanowire size approaches a certain critical length scale, some interesting physical effects would appear. Recently, Wang et al. [10] discovered that spin waves in Ni nanowires were quantized due to spatial confinement. Chapter Introduction The quantization effect indicated a subtle magnetic interplay between nanowires. Further investigation of this phenomenon should be of great interest. 1.1.2 Nanorings 2-D arrays of nanorings have potential applications in high-density magnetic storage media and miniaturized sensor devices. The high-symmetry ring geometry exhibits a wide range of intriguing magnetostatic and magnetodynamic properties. Much research has been done on magnetic nanorings [11]. Of particular interest is the magnetization reversal mechanism in ring structures. In 2001, Rothman et al. [12] reported a transition from a bi-domain “onion” state to a vortex state using micromagnetic simulations. A later work by Steiner et al. [13] showed that the type of magnetization transition is strongly dependent on the shape of the ring. For narrow rings, a sharp transition from onion to vortex was observed. However, for wide rings, local vortices would appear. These studies provided important information for future applications of ring structure. 1.1.3 Exchange Spring Bilayers Magnetic thin films as well as multilayered structures exhibit a number of interesting properties. One specific example is the exchange coupling in layered structures. For instance, in their study of Fe/Cr/Fe layered structures, Grünberg et al. [14] observed the antiferromagnetic coupling of Fe layers across the Cr interlayer. Exchange spring bilayers made of a hard and a soft phase provide a simplified system for investigating the exchange coupling in layered structures. The spin flipping process in the Chapter Introduction exchange spring system is a well-studied area since spin flip governs the speed and stability of magnetic recording. However, the shape effect, influence of defects and impurities complicate the flipping process. A combined study of domain structure, hysteresis loop, as well as study of spin wave excitation can give an overall picture of the magnetization switching process. In 1999, Grimsditch et al. [15] reported studies of the normal magnetic modes in SmCo/Fe bilayers using Brillouin light scattering (BLS). They have formulated a simple model to analyze exchange coupled structures. The experimental and theoretical results agreed well quantitatively. These studies provided guidance for future development and optimization of high-performance magnetic recording devices based on the exchange spring structure. 1.2 Fabrication Techniques Lithography, e.g. e-beam lithography, X-ray lithography and interference lithography, is widely used to fabricate patterned nanostructures. To achieve accuracy down to nanometer scale, scanning probe microscopy (SPM) and scanning tunneling microscopy (STM) are used to manipulate the lithography process. Molecular beam epitaxy (MBE) is used to grow films or layers since it can control the film thickness to atomic scale and maintain the crystallinity and purity as well. To fabricate ordered arrays of nanostructures, porous alumina templates of high aspect ratio and uniformity are commonly used. The permalloy nanowires used for this study were fabricated using these templates. Detailed information on fabrication using anodic aluminum oxide (AAO) masks will be presented in Chapter 4. Chapter Introduction 1.3 Characterization Techniques Scanning electron microscopy (SEM), atomic force microscopy (AFM), and transmission electron microscopy (TEM) are popular characterization techniques which provide topographic images of different types of nanostructures. Magnetic force microscopy (MFM) is commonly used to image the magnetization states and domain structure of nanomagnets. Superconducting quantum interference device (SQUID) is used for hysteresis measurements. Magneto-optical Kerr effect (MOKE) can image domain wall propagation and provide magnetization responses with spatial resolution of < 200 nm on an ultra-fast time scale. Ferromagnetic resonance (FMR) is a powerful tool for probing fundamental magnetic properties of ferromagnetic particles. BLS is excellent tool for studying spin waves in magnetic nanostructures. Details of this technique will be presented in Chapters and 3. 1. Objectives of Present Study The aim of this study is to investigate the spin dynamics and magnetic properties of three types of nanostructures viz. permalloy nanowires, Ni nanorings and Co/CoPt exchange spring bilayers. 1.4.1 Permalloy Nanowires The aim of this part of the study of the 2-D hexagonal ordered ferromagnetic nanowire arrays is to determine the strength and length scale of interwire interaction as well as the effect of anisotropy. BLS measurements were made in either longitudinal (H0 applied along the wire symmetry axis) or transverse (H0 perpendicular to wire symmetry Chapter Introduction axis) magnetic field H0 to obtain the dependence of spin wave frequency on external magnetic field. The interactions between wires were evaluated by applying the AriasMills theory of collective spin waves in 2-D nanowire array in a longitudinal magnetic field [16]. Spin wave frequencies as well as the magnetic scalar potential in nanowires were calculated to elucidate both exchange interaction and dipole interactions between wires. A Hamiltonian-based microscopic theory was applied to the transverse magnetic field case [17] to explain the appearance of the low-frequency spin wave mode observed. 1.4.2 Ni Nanorings The aim of this part of research is to study the spin wave excitation and magnetization switching process in an array of high-aspect-ratio Ni nanorings. The magnetization distribution, spin wave frequencies as well as the Zeeman, demagnetization and exchange energy contributions to the total energy were determined by micromagnetic simulations using the Object Oriented Micromagnetic Framework (OOMMF) 3-D package [18]. 1.4.3 Co/CoPt Bilayers The aim of this part of the research on the exchange spring Co/CoPt bilayers is to study the magnetization reversal in these coupled soft/hard bilayers. BLS was used to study spin wave frequency variations with external magnetic field. The Brillouin data were analyzed using a semi-classical model formulated by Crew et al. [19, 20]. Based on these results further insight into the magnetization reversal was gained. Chapter Introduction The experimental results could provide useful data for the characterization of dynamic properties of magnetic nanostructures and lead to a better understanding of nanoscale phenomena such as exchange coupling, anisotropy contribution and magnetization switching. The study of permalloy nanowires may give useful information for the possible application of nanowire arrays as perpendicular recording media. The study of Ni nanorings could provide guidance for controlling the magnetization switching and using ring structures as ultra-high density magnetic storage devices. The study of magnetization switching in Co/CoPt exchange spring system could provide guidance for the application of such a structure in high quality magnetoresistive random access memory (MRAM) devices. Since this research uses BLS as the main investigation tool for studying spin waves, the basic theories of Brillouin scattering and of spin waves will be presented in Chapter 2. Chapter Introduction References: 1. G. L. Verschuur, “Hidden attraction: the history and mystery of magnetism”, New York: Oxford University Press, (1993). 2. J. F. Keithley, “The story of electrical and magnetic measurements: from 500 BC to the 1940s”, New York: IEEE Press, (1999). 3. J. C. Maxwell, “A Treatise on Electricity and Magnetism”, New York: Dover Publications (1954). 4. N. Majlis, “The quantum theory of magnetism”, Singapore, River Edge, World Scientific, (2000). 5. M. P. Marder, “Condensed matter physics”, New York: John Wiley, (2000). 6. R. Skomski, J. Phys.: Condens. Matter. 15, R841 (2003). 7. J. I. Martín, J. Nogués, K. Liu, J. L. Vicent, and I. K. Schuller, J. Magn. Magn. Mater. 256, 449 (2003). 8. D. C. Jiles, Acta Mater. 51, 5907 (2003). 9. H. Zheng, M. Zheng, R. Skomski, D. J. Sellmyer, Y. Liu, L. Menon and S. Bandyopadhyay, J. Appl. Phys. 87, 4718 (2000). 10. Z. K. Wang, M. H. Kuok, S. C. Ng, D. J. Lockwood, M. G. Cottam, K. Nielsch, R. B. Wehrspohn, and U. Gösele, Phys. Rev. Lett. 89, 27201 (2002). 11. M. Kläui, C. A. F. Vaz, L Lopez-Diaz and J. A. C. Bland, J. Phys.: Condens. Matter 15, R985 (2003). 12. J. Rothman, M. Kläui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, Phys. Rev. Lett. 86, 1098 (2001). 13. M. Steiner and J. Nitta, Appl. Phys. Lett. 84, 939 (2004). Chapter Introduction 14. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, Phys. Rev. Lett. 55, 2442 (1986). 15. M. Grimsditch, R. Camley, E. E. Fullerton, S. Jiang, S. D. Bader, and C. H. Sowers, J. Appl. Phys. 85, 5901 (1999). 16. H. Y. Liu, Z. K. Wang, H. S. Lim, S. C. Ng, M. H. Kuok, D. J. Lockwood, M. G. Cottam, K. Nielsch, and U. Gösele, J. Appl. Phys. 98, 046103 (2005). 17. T. M. Nguyen, M. G. Cottam, H. Y. Liu, Z. K. Wang, S. C. Ng, M. H. Kuok, D. J. Lockwood, K. Nielsch and U. Gösele, Phys. Rev. B 73, 140402 (R) (2006). 18. 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. Keay, G.D. Lian, and M. B. Johnson, Phys. Rev. Lett. 94, 137208 (2005). 19. D. C. Crew, R. L. Stamps, H. Y. Liu, Z. K. Wang, M. H. Kuok, S. C. Ng, K. Barmak, J. Kim and L. H. Lewis, J. Magn. Magn. Mater. 272-276, 273 (2004). 20. D. C. Crew, R. L. Stamps, H. Y. Liu, Z. K. Wang, M. H. Kuok, S. C. Ng, K. Barmak, J. Kim and L. H. Lewis, J. Magn. Magn. Mater. 290-291, 530 (2005). Chapter Chapter Brillouin Scattering from Spin Waves Brillouin Scattering from Spin Waves 2.1 Introduction Since the 1980’s, Brillouin light scattering (BLS) has proved to be very effective for detecting spin wave excitations [1-3] in magnetic structures, such as thin films, multilayers and magnetic nanoelements. In BLS measurements, a beam of highly monochromatic light is focused on the sample surface under investigation. The scattered light within a solid angle is frequency analyzed using a multi-pass Fabry-Perot (FP) interferometer. From BLS measurements of the spin wave frequency as a function of the direction and magnitude of the external magnetic field, magnetic properties such as anisotropy constant, exchange constant, gyromagnetic ratio and saturation magnetization, can be obtained. BLS is a non-destructive and non-contact technique, with a probing area of the order of π × (25) µm2 (determined by the focusing lens and the diameter of the laser beam). Though BLS is a powerful investigative technique, extracting information on the properties of specimens using it is not straightforward. In order to obtain more than qualitative information it is necessary to employ theoretical models which predict the spin wave frequencies in the magnetic structures. The parameters, such as gyromagnetic ratio, saturation magnetization and exchange constant, of the magnetic system can be obtained from an optimum fit of the experimental data to the predicted values of the 10 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers Crew et al. [3] have studied Co (6.4 nm)/CoPt (25.6 nm) exchange spring bilayers by micromagnetic simulations using the OOMMF software [4]. In their 2-D simulations, the spin wave frequency was found by solving the time-dependent Landau-Lifshitz equation of motion. The local effective field acting on each spin includes Zeeman, exchange, magnetostatic and anisotropy terms. It was found that the exchange coupling effect between the two layers has a great impact on the resonant frequency, shown in Fig. 6.2. The minimum frequencies occur for fields that mark the beginning and end of the spiral formation. The height of the peak between the two minima is sensitive to the out-of-plane anisotropy of the Co layer which suggests the frequency measurements would give valuable information about the anisotropy in the soft layer. Fig. 6.2 Simulated resonant frequency as a function of magnetic field for Co anisotropy equal to the bulk value of 0.43 MJ/m3 (squares) and J/m3 (circles). The arrows represent schematically the magnetic moment orientations in each layer for the three regions of the frequency curve. [After Crew et al. Ref. 3] 92 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers This project aims to investigate the magnetization switching and exchange coupling in the Co/CoPt exchange spring bilayers by probing their spin excitations using Brillouin spectroscopy. 6.2 Sample Description 1.7 T 16.7 nm Co CoPt 55° 25 nm SiO2 Fig. 6.3 Schematics of the Co/CoPt thin film bilayer sample. The CoPt layer has an easy axis 55° to the surface normal. The sample was pre-magnetized in a field of 1.7 T. The sample studied here was provided by David Crew from the University of Western Australia. Figure 6.3 shows the schematics of the thin film bilayers of Co (16.7 nm)/CoPt (25 nm). It was fabricated as follows. First, a single-phase film of CoPt, which is a near equi-atomic mixture, was deposited at room temperature onto thermallyoxidized Si (100) wafer by RF sputtering deposition in ultra-high vacuum [5]. After deposition, the sample was annealed at 700°C to form the chemically ordered L10 phase. The polycrystalline thin film has an average grain size of 45 nm and an easy axis 55° to 93 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers the surface normal. The Co layer, having an hcp fiber texture, was then sputter deposited after the annealing treatment. The sample was pre-magnetized to saturation in an in-plane magnetic field of 1.7 T prior to BLS measurements, as shown in Fig. 6.3. 6.3 BLS Experimental Results Brillouin spectra were recorded at room temperature in the 180°-backscattering geometry. 100 mW of light was used for excitation at an incident angle of 45° to the surface normal of the sample. The magnetic field was applied perpendicular to the surface normal. The spin wave wavevector q and wavevectors of the incident light (ki) and scattered light (ks) are shown in Fig. 6.4. The magnetic field H0 was decreased from + 1.1 T to - 1.1 T, where the positive sign indicates that the magnetic field is aligned along the pre-magnetization direction. All measurements were made in the p-s polarization configuration, with free spectrum ranges (FSR) between 40 to 100 GHz. ks ki 45° H0 q Fig. 6.4 The scattering geometry with the magnetic field applied in the plane of the sample surface and perpendicular to the scattering plane. 94 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers Figure 6.5 shows p-s polarized Brillouin spectra (anti-Stokes portion) recorded at various magnetic fields. Only one peak was observed which appears on both the Stokes and anti-Stokes sides. The peak frequency was found to be independent of the incident angle but strongly dependent on the applied magnetic field. Hence the observed peak was assigned as a spin wave excitation in the exchange spring bilayers. 1.0 T Intensity (arb. units) 0.6 T 0.2 T - 0.2 T - 0.6 T - 1.0 T 10 20 30 40 50 60 Frequency (GHz) 70 80 Fig. 6.5 p-s polarized Brillouin spectra of the spin wave excitations in the Co/CoPt thin film bilayers recorded at different magnetic fields. 95 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers Decreasing Magnetic Field Frequency (GHz) 50 40 30 20 Stokes 10 ≈ -150 mT anti-Stokes -1.0 -0.5 0.0 0.5 1.0 Magnetic Field (T) Fig. 6.6 Dependence on in-plane magnetic field of the spin wave frequency for Co/CoPt bilayers. The Stokes and anti-Stokes frequencies are denoted by filled and open circles respectively. The experimental error is about the size of the symbol. The fitted spin wave frequencies (using Renishaw program as described in Chapter 3) at various magnetic fields are shown in Fig. 6.6. The minimal frequency occurs at a field H ≈ −150 mT , which is close to the reversing field obtained by hysteresis measurements [6], as shown in Fig. 6.7. 96 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers 1.0 M / Ms 0.5 0.0 -0.5 - 150 mT -1.0 -1500 -1000 -500 500 1000 1500 Ma g n e t i c F i e l d (m T) Fig. 6.7 Measured hysteresis loop for the Co/CoPt sample. [After Crew et al. Ref. 6] 97 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers 6.4 Theoretical Analysis of Spin Wave Frequencies Layer Layer … Layer n Fig. 6.8 Schematics of the semi-classical model. The BLS data were analyzed using a semi-classical model in the long wavelength limit [7, 8]. As shown in Fig. 6.8, the thin film is divided into a stack of n layers. Each layer is a square array of point dipoles or spins. Each spin is subjected to an effective field Heff : H eff = H ex + H dip + H ani + H (6.1) where Hex represents the Heisenberg exchange, Hdip the dipolar field, Hani the anisotropy field, and H0 the external magnetic field. In other words, the magnetic system is treated as point dipoles, arranged on a simple cubic lattice, interacting via an Heisenberg exchange interaction: H ex = ∑ J (r − r ') S (r ) ⋅ S (r' ) r ,r ' (6.2) 98 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers where S (r ) is the spin operator at lattice site r and J is the exchange constant written as a function of the distance between lattice sites. The summation is taken over all magnetic lattice sites excluding the terms r = r ' . The dipolar interactions are treated classically by direct summation: ⎡ S (r ) ⋅ S (r' ) [ r ⋅ S (r )][ r '⋅ S (r' )] ⎤ H dip = ( g µ B ) ∑ ⎢ − ⎥ r r' r r' r ,r ' ⎢ ⎥⎦ ⎣ (6.3) where g is the Landé factor and µ B the Bohr magneton. The dipolar effects are longranged interactions and the sum includes all spins in the layered system. The anisotropy and Zeeman effects are also included in the calculation of the spin wave frequency. The spins are relaxed to their equilibrium state as a classical vector by a simulated fully damped precession. Spin wave frequencies are obtained from the solution of the eigenvalue problem of the linearized equations of motion: dSn = γ Sn × H eff dt (6.4) where for each layer spin Sn has a static and a dynamic part, Sn = S static + sn e −iωt . The calculated result based on this model is shown as a solid line in Fig. 6.9, together with the Brillouin data (Stokes frequency only). An average over the distribution of in-plane anisotropy directions of the CoPt layer arising from the fiber texture [5] was included. The parameters used for fitting were J = 28.5 meV , K = 0.43 MJ / m3 , S = 1.31µ B for Co and J = 57.8 meV , K = MJ / m3 , S = 0.748µ B for CoPt. J is the exchange parameter, S the spin dipole moment, and K the uniaxial magnetocrystalline anisotropy of the material. The g factor was assumed to be 2.25 which is appropriate for 99 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers Co. 60 Frequency (GHz) 50 40 30 20 10 ≈ -150 mT -1.5 -1.0 -0.5 0.0 0.5 Magnet i c Fi el d( T) 1.0 1.5 Fig. 6.9 Frequencies of the spin wave (Stokes portion) in the Co/CoPt exchange spring bilayers as a function of magnetic field. The dots represent the experimental data and the solid line represents the theoretical spin wave frequencies. There is an overall agreement between theory and experimental results. To fit the minimum in frequency as shown in Fig. 6.9, an anomalous uniaxial in-plane anisotropy, in addition to the magnetocrystalline anisotropy, was assumed in the Co layers. The fitting procedure yields an in-plane anisotropy value of 0.21 MJ/m3 directed along the in100 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers plane CoPt easy axis. This anomalous anisotropy is too large to be a surface anisotropy alone which is normally below mJ/m2 in Co [9], equivalent in a Co film (16.7nm) to a volume anisotropy of 0.06 MJ/m3. This anomalous anisotropy of 0.21 MJ/m3 in the Co layer is approximately twice the volume magnetoelastic anisotropy obtained from the measurements made by Fritzsche et al. [10] of Co (0 0 1) thin film on W [1 0]. For the Co/W film, the lattice misfit is about 3%, while for the Co/CoPt bilayer it is approximately 6%. Hence, it is reasonable to assume that an increase in film strain might lead to the increase of volume magnetoelastic anisotropy. Therefore, this anomalous anisotropy is tentatively ascribed to a magnetoelastic effect. The agreement between calculated and measured magnon frequencies is not good for low fields below - 0.5 T. This could be due to the fact that, in this field regime, the CoPt layer is reversing (as shown in Fig. 6.9), while this is not simulated well by the simple relaxation mechanism assumed in the model discussed above. Hence, further investigation is needed. 6.5 Conclusion In summary, Brillouin scattering has been used to study the spin wave excitation in an exchange spring Co/CoPt bilayer. A semi-classical model has been used to analyze the experimental results. In this model, the bilayer sample is divided into a stack of layers. Each layer is a square array of spins. Each spin is subjected to an effective field. The spin wave frequencies are obtained from the solution of the eigen value problem of the linearized equations of motion. The calculations were, in general, found to be in good 101 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers agreement with experimental results. However, the field regime below - 0.5 T, in which the CoPt layer is reversing, is not simulated well by the simple relaxation mechanism assumed in this model. Hence further investigation is needed. 102 Chapter Spin Waves in Exchange Spring Co/CoPt Bilayers References: 1. R. Skomski, J. Appl. Phys. 76, 7059 (1994). 2. M. Grimsditch, R. Camley, E. E. Fullerton, S. Jiang, S. D. Bader, and C. H. Sowers, J. Appl. Phys. 85, 5901 (1999). 3. D. C. Crew and R. L. Stamps, J. Appl. Phys. 93, 6483 (2003). 4. The OOMMF package is available at http://math.nist.gov/oommf. 5. J. Kim, K. Barmak, and L. H. Lewis, Acta Mater. 51, 313 (2003). 6. D. C. Crew, R. L. Stamps, H. Y. Liu, Z. K. Wang, M. H. Kuok, S. C. Ng, K. Barmark, J. Kim, and L. H. Lewis, ICM, Rome (2003). 7. D. C. Crew, R. L. Stamps, H. Y. Liu, Z. K. Wang, M. H. Kuok, S. C. Ng, K. Barmark, J. Kim, and L. H. Lewis, J. Magn. Magn. Mater. 272-276, 273 (2004). 8. F. C. Nortemann, R. L. Stamps, and R. E. Camley, Phys. Rev. B 47, 11910 (1993). 9. W. J. M. de Jonge, P. J. H. Bloemen, F. J. A. den Broeder, in: J. A.C. Bland, B. Henrich (Eds.), Ultrathin Magnetic Structures, Vol. I, Springer, Berlin, 1994, p. 65. 10. H. Fritzcche, J. Kohlhepp, U. Gradmann, Phys. Rev. B 51, 15933 (1995). 103 Chapter Conclusion Chapter Conclusion In this PhD research, comprehensive studies have been done on the spin dynamics of three different magnetic nanostructures, viz. permalloy nanowire arrays (refer to Chapter 4), Ni nanorings (refer to Chapter 5) and Co/CoPt exchange spring bilayers (refer to Chapter 6). The longitudinal magnetic field dependence of quantized spin waves in the hexagonal array of permalloy (Ni80Fe20) nanowires (nanowire diameter 35 nm, interwire separation 105 nm, and nanowire length µm) was analyzed successfully in terms of an extension of the application of Arias-Mills theory for the collective spin wave in a periodic linear nanowire array to one appropriate for a periodic 2-D hexagonal nanowire array. Comparing the calculated spin wave frequencies in the nanowire array and those of a single nanowire, it is found that the interwire interaction is negligible in the nanowire sample studied [1]. This suggests that such a permalloy nanowire array can be packed with a higher density of nanowires with negligible cross talk between them, thereby increasing its magnetic storage density. The transverse magnetic field dependence of spin waves in the permalloy nanowire array was interpreted using a Hamiltonian-based microscopic theory that included inhomogeneous magnetization and “easy-plane” surface anisotropy. The result indicates that small easy-plane single-ion anisotropy at the nanowire surface plays an important role in the spin dynamics of the nanowire arrays 104 Chapter Conclusion under a transverse magnetic field [2]. Further study of the surface anisotropy influence on the spin wave excitation should be of great interest. 3-D micromagnetic simulations have been performed on high-aspect-ratio Ni nanorings (inner diameter 65 nm, outer diameter 95 nm, thickness 150 nm) using the OOMMF package. Simulations show that under high magnetic fields, applied along the symmetry axis of the ring, the rings assume a bamboo state with all the spins aligned parallel to the ring axis. When the field is decreased to about 50 mT, the rings switch to a novel twisted bamboo state characterized by the opposite circulation of the spin components in the top and bottom planes of the rings [3]. The simulated spin wave frequencies, obtained from Fourier Transform of the magnetization, agree well with those of Brillouin measurements by Wang et al. [3]. For the transverse case (magnetic field applied perpendicular to the symmetry axis of the ring), simulations show that the ring switches from an onion to a vortex state when field falls below a critical magnetic field. The magnetization transition process is similar to that of flat Co rings observed by Rothman et al. [4]. BLS was used to study the exchange spring Co (16.7nm)/CoPt (25nm) bilayers. The dependence on the in-plane magnetic field of the spin waves frequencies in the bilayers was analyzed using a semi-classical model [5, 6], in which, the bilayer sample is divided into a stack of layers. The spin wave frequencies are obtained from the solution of the eigen-value problem of the linearized equations of motion. There is an overall agreement between experiment and theory. However, for fields below - 0.5 T, the 105 Chapter Conclusion agreement is not so good. This could be due to the reason that when the field is below - 0.5 T, the CoPt layer is reversing which is not simulated well by the simple relaxation mechanism assumed in this model. Further study of the spin spiral state in the exchange coupled structure is necessary. Hence, this PhD research has demonstrated that BLS is a powerful tool for investigating the spin dynamics and magnetic properties of magnetic nanostructures. Findings obtained should be of interest to both nanoscience and nanotechnology. 106 Chapter Conclusion References: 1. H. Y. Liu, Z. K. Wang, H. S. Lim, S. C. Ng, M. H. Kuok, D. J. Lockwood, M. G. Cottam, K. Nielsch, and U. Gösele, J. Appl. Phys. 98, 046103 (2005). 2. T. M. Nguyen, M. G. Cottam, H. Y. Liu, Z. K. Wang, S. C. Ng, M. H. Kuok, D. J. Lockwood, K. Nielsch and U. Gösele, Phys. Rev. B 73, 140402 (R) (2006). 3. 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. Keay, G. D. Lian, and M. B. Johnson, Phys. Rev. Lett. 94, 137208 (2005). 4. J. Rothman, M. Kläui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, Phys. Rev. Lett. 86, 1098 (2001). 5. D. C. Crew, R. L. Stamps, H. Y. Liu, Z. K. Wang, M. H. Kuok, S. C. Ng, K. Barmak, and J. Kim and L. H. Lewis, J. Magn. Magn. Mater. 272-276, 273 (2004). 6. D. C. Crew, R. L. Stamps, H. Y. Liu, Z. K. Wang, M. H. Kuok, S. C. Ng, K. Barmak, and J. Kim and L. H. Lewis, J. Magn. Magn. Mater. 290-291, 530 (2005). 107 [...]... BLS Study of Spin Waves The innovation by Sandercock [11 , 12 ], in 19 71, of a multi-pass FP interferometer made feasible the observation of magnons by the BLS technique The first measurements were of the ferrimagnet yttrium iron garnet (YIG) by Sandercock and Wettling [13 ] in 20 Chapter 2 Brillouin Scattering from Spin Waves 19 73 Figure 2.5 shows a BLS spectrum of YIG containing both magnon and phonon... 11 W Hayes and R Loudon, Scattering of Light by Crystals”, New York: Wiley, (19 78) 12 J R Sandercock, in M Balkanski, Ed., “Light Scattering in Solids”, Paris: Flammarion, (19 71) 13 J R Sandercock, and W Wettling, Solid State Commun 13 , 17 29 (19 73) 14 J R Sandercock, and W Wettling, IEEE Trans Magn 14 , 442 (19 78) 15 J R Sandercock, and W Wettling, J Appl Phys 50, 7784 (19 79) 16 C Mathieu, J Jorzick,... well as coupling between magnetic elements Recently, lateral confinement effects of spin waves in nanoscale magnetic structures have drawn intensive research interests Quantization of spin waves 23 Chapter 2 Brillouin Scattering from Spin Waves due to the confinement of lateral dimension has been reported in 1- D array of permalloy wires, of rectangular cross section, by Mathieu et al [16 ], permalloy... wave in a magnetic film [8], in the absence of exchange, the spin wave frequency is given by Eq (11 ) in Ref 3: ωDE = 2π f = γ { H 0 ( H 0 + 4π M s ) + (2π M s )2 × [1 − exp(−2q d )]} 1/ 2 (2.6) where q is the in- plane wavevector, and d the thickness of the film 14 Chapter 2 Brillouin Scattering from Spin Waves 2.2.2 Quantum Mechanical View of Spin Waves (Magnons) For the simplest model of ferromagnetic... exchange spring bilayers The instrumentation and experimental techniques of BLS will be presented in Chapter 3 24 Chapter 2 Brillouin Scattering from Spin Waves References: 1 A S Borovik-Romanov and N M Kreines, Phys Rep 81, 3 51( 1982) 2 M G Cottam and D J Lockwood, “Light Scattering in Magnetic Solids”, John Willey & Sons, (19 86) 3 S O Demokritov, B Hillebrands, and A N Slavin, Phys Rep 348, 4 41 (20 01) 4... (b) Fig 2.6 (a): Brillouin spectra measured for Fe in a magnetic field of 3 kOe and of Ni in a field of 0.4 kOe; (b): Theoretical and experimental values of surface and bulk magnon frequencies as a function of external magnetic field [After Sandercock et al Ref 15 ] 22 Chapter 2 Brillouin Scattering from Spin Waves (a) (b) Fig 2.7 (a): BLS spectrum of a 1- D array of permalloy wires (w = 1. 8 µm, l = 500... aligned interferometer in 35 Chapter 3 Instrumentation and Experimental Techniques Fig 3.6b Two clear distinct series of peaks are seen (displayed on the oscilloscope) Independently optimizing the alignment of both FP1 and FP2, the minima approach zero, as shown in Fig 3.6c An adjustment of the relative spacing of the two interferometers will bring a pair of peaks into coincidence and the pre-alignment of. .. GHz range In order to separate the weak inelastic component of light from the elastically scattered contribution, a high resolution FP interferometer is used (see 3.2.3) 2.3 .1 Kinematics of Brillouin Light Scattering In a BLS experiment a laser beam of fixed angular frequency and wavevector is incident on the surface of a sample Figure 2.2 shows the scattering geometry with an incident angle of θi to... Z Phys 61, 206 (19 30) 5 M Fallot, Ann Phys (Paris) 6, 305 (19 36) 6 P Weiss, Ext Actes VII Congr Intern Froid 1, 508 (19 37) 7 G Heller and H A Kramers, Proc K Akad Wet 37, 378 (19 34) 8 R W Damon and J R Eshbach, J Phys Chem Solid 19 , 308 (19 61) 9 B Lax, and K J Button, “Microwave Ferrites and Ferromagnetics”, McGraw-Hill, New York (19 62) 10 C Herring, and C Kittel, Phys Rev 81, 869 (19 51) 11 W Hayes... magnons (or phonons) In the usual implementation of BLS, the scattered light is collected in the direction 18 0° from the incident light and thus θi = θ s , an arrangement known as the 18 0°-backscattering geometry 16 Chapter 2 Brillouin Scattering from Spin Waves Scattering Plane ks θs ki θi qS θi′ θs′ ks′ ki′ qB Fig 2.2 Scattering geometry showing: the incident and scattered light wavevectors ki and . 290-2 91, 530 (2005). Chapter 2 Brillouin Scattering from Spin Waves 10 Chapter 2 Brillouin Scattering from Spin Waves 2 .1 Introduction Since the 19 80’s, Brillouin light scattering. The kinematics of the Brillouin scattering process follows k s k i θ s θ i q S q B θ s ′ θ i ′ Scattering Plane k i ′ k s ′ Chapter 2 Brillouin Scattering from Spin Waves 18 directly. 2.3 Kinematics of (a) Stokes and (b) anti-Stokes scattering events occurring in Brillouin scattering from bulk magnon (phonon). 2.3.2 Spin Waves Scattering Mechanism Excitations in a solid