Brillouin scattering study of magnons in magnetic nanostructures 1

Chapter 1 Introduction axis magnetic field H 0 to obtain the dependence of spin wave frequency on external magnetic field.. BLS was used to study spin wave frequency variations with exte

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 1 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

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 1 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

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 2 and 3

1 4 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

Chapter 1 Introduction

axis) magnetic field H 0 to obtain the dependence of spin wave frequency on external magnetic field The interactions between wires were evaluated by applying the Arias-Mills 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

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 1 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)

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 2 Brillouin Scattering from Spin Waves

Chapter 2 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)2 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

model (see Chapters 4, 5, and 6)

2.2 Spin Wave Theory

Spin waves are low-lying excitations that occur in magnetic materials The

characteristics of spin waves in any particular materials depend on the type of magnetic

ordering, e.g ferromagnet, antiferromagnet and ferrimagnet For simplicity, only the

ferromagnetic system will be discussed

2.2.1 Semi-classical Model of Spin Waves

The concept of spin waves, as the low lying magnetic states above the ground

state, was introduced by Bloch [4] in 1930 He envisaged some of the spins as deviating

slightly from their ground states, with these disturbances propagating with a wavelike

behavior through magnetic materials This dynamic effect was ignored in the mean field

theory, where the exchange interactions are replaced by a static effective field Bloch’s

theory predicted that the magnetization of a ferromagnet at low temperatures (T) should

deviate from the zero-T value with a T3/2 dependence, instead of the exponential

dependence given by the mean field theory This was later confirmed by measurements

by Fallot [5] and Weiss [6] The semiclassical theory was further developed by Heller and

Kramers [7] in terms of precessing spins Figure 2.1 shows the schematic view of spin

wave in a ferromagnet For a ferromagnetic material, there is interaction between

neighboring electronic spins, which gives rise to a parallel alignment in the ground state

(Fig 2.1a) With perturbation, the spins will deviate slightly from their orientation in the

ground state (Fig 2.1b), and with this disturbance propagating with a wavelike behavior

Chapter 2 Brillouin Scattering from Spin Waves

(Fig 2.1c) through the material

Fig 2.1 Semiclassical representation of spin wave in a ferromagnet: (a) the ground state

(b) a spin wave of precessing spin vectors (viewed in perspective) and (c) the spin wave

(viewed from above) showing a complete wavelength

Spin waves with wavevector (q) in the range 30 < q < 106 cm-1 are usually called

dipolar magnetostatic spin waves or magnetostatic modes since it is almost entirely

determined by magnetic dipole interaction They were first reported by Damon and

Eshbach [8] in 1961 The frequency of the magnetostatic mode depends on the

orientation of its wavevector relative to that of the static magnetization due to the

anisotropic properties of the magnetic dipole interaction Spin waves with higher values

of wavevector, when the exchange interaction can not be neglected, are called

dipole-exchange spin waves

(a)

(b)

(c)

Spin waves are the dynamic eigen-excitations of a magnetic system They are

used to describe the spatial and temporal evolution of the magnetization distribution of a

magnetic medium under the general assumption that locally the length of the

magnetization vector is constant This assumption is satisfied with two prerequisites:

First the sample temperature is far below the Curie temperature (Tc); and second, no

topological anomalies are present Then the dynamics of the magnetization vector are

described by the Landau-Lifshitz torque equation [9]:

1d eff

dt

γ

− M =M H (2.1) ×

where M is the total magnetization, γ gyromagnetic ratio, t the time, and H the eff

effective magnetic field The total magnetization is given by:

( , )M =M s+m R t (2.2) where M s is vector of the saturation magnetization, and m(R, t) is the variable

magnetization which is dependent on time t and the 3-D radius vector R The effective

magnetic field is calculated as a variational derivative of the total energy function E:

eff 0 demag ( 1 ) ani 2 )

2

where H is the applied magnetic field, 0 H demag the demagnetization field, E ani the

anisotropy energy, M s the saturation magnetization and A the exchange stiffness constant

All the relevant interactions (the Zeeman filedH , the dipole interaction0 H demag, the

anisotropy contribution ∇E ani and the exchange interactionA ) in the magnetic media

have been considered

Chapter 2 Brillouin Scattering from Spin Waves

Since the effective magnetic fieldH depends on the magnetization M, Eq (2.1) eff

is basically nonlinear However, if the amplitude of the variable magnetization m(R, t) is

small compared to the saturation magnetization M s, the variable magnetization m(R, t)

can be expanded as a series of plane waves of magnetization (or spin waves):

( , ) q( ) exp( )

q

m R m q R (2.4)

where q is the 3-D spin wave wavevector and Eq (2.1) can be linearized Such a

linearized equation is used for the description of linear spin waves

Generally, the spectrum of the dipole-exchange spin waves in an unlimited

ferromagnetic medium is given by the Herring-Kittel formula [10]:

where ω is the angular frequency of the spin wave, f the frequency, and θ the angle

between the directions of the spin wave wavevector and the static magnetization

As q → 0, ω has the limiting values: ω γ= H0for q M and & s 1/ 2

0(H B)

ω γ= forq⊥M s, whereB H= 0+4πM s Specifically, for the Damon-Eshbach dipolar surface spin wave in

a magnetic film [8], in the absence of exchange, the spin wave frequency is given by

2.2.2 Quantum Mechanical View of Spin Waves (Magnons)

For the simplest model of ferromagnetic material, the Hamiltonian is given by:

0

,

12

where, S i denotes the spin angular momentum operator associated with the magnetic ion

at the lattice site i, and J is the short-range exchange interaction between sites i and j ij

The second term on the right hand side of Eq (2.7) is the Zeeman energy due to an

applied magnetic field H0, where g is the Landé g-factor and µBis the Bohr magneton

The magnetic field is taken to be in the z direction, which if H0 > 0 is also the direction of

the net spin alignment However, this Hamiltonian only includes exchange and Zeeman

terms For real systems, anisotropy and long-range dipole interaction must be included

Finding the eigenstates of this realistic Hamiltonian is certainly a non-trivial problem To

solve the Schrödinger equation using this approximate Hamiltonian, an excitation

consisting of the flipping of a single spin is considered This is not an eigenstate of the

Hamiltonian but it is possible to construct the eigenstates by a superposition of flipped

spin states These turn out to be harmonic traveling waves Using the method of second

quantization each of these oscillators can be thought of as a particle, known as a magnon

Like any kind of quasi-particles, magnons possess energy and quasi-momentum,

which are related by the theory of spin waves However, spin waves differ from phonons

in the wavevector (q) dependence of their frequencies Due to the linear q-frequency

dependence of phonons near the zone center, BLS measurements at different q normally

yield no new information on the phonon system On the other hand, the exchange

Chapter 2 Brillouin Scattering from Spin Waves

coupling of spins produces a nonlinear q dependence of the spin wave frequency, even

near the zone center, so important information on the strength of the exchange may be

deduced by varying q in the light-scattering measurement Furthermore, values for the

gyromagnetic ratio, magnetization, anisotropy, and magneto-optic interaction may be

obtained

2.3 Brillouin Light Scattering (BLS)

BLS measures spin waves with frequencies usually in the 1 – 200 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 the surface normal Most of the light is specularly reflected or

absorbed However, as a result of thermal excitation (magnon or phonon), a small

fraction of the light is inelastically scattered with a frequency shift depending on the

nature of the scattering process The spectrum of the light inelastically scattered at an

angle θs contains information about surface or bulk (or both) magnons (or phonons) In

the usual implementation of BLS, the scattered light is collected in the direction 180°

from the incident light and thus θ θi = s , an arrangement known as the

180°-backscattering geometry

Fig 2.2 Scattering geometry showing: the incident and scattered light wavevectors k i and

k s ; the surface and bulk magnon (phonon) wavevectors q S and q B θi and θs are the angles

between the out going surface normal and the respective incident and scattered light

(The plane which contains the wavevector of the scattered light and the surface normal of

the sample is defined as the scattering plane.)

From a quantum mechanics point of view, such an inelastic scattering can be

described in terms of the creation and annihilation a magnon (phonon) of wavevector (q)

and angular frequency (ω) The kinematics of the Brillouin scattering process follows

Chapter 2 Brillouin Scattering from Spin Waves

directly from the conservation of angular frequency (energy):

ωs = ω ωi± (2.8) and conservation of the wavevector (momentum):

ks = ki±q (2.9) between the magnon (phonon) and the incident (i) and scattered (s) photons, where ωi,

i

k , ωs, and k s are the frequencies and wavevectors of the incident and scattered light

As shown in Fig 2.3, the “+” sign in Eq (2.8) indicates that the photon absorbs a magnon

(anti-Stokes shift); the “−” sign indicates that the photon emits a magnon (Stokes shift)

Fig 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 can inelastically scatter incident light through the induced

modulation of the optical constants of the medium The mechanics of the scattering from

acoustic phonon is mainly due to either elasto-optic (bulk phonon) or surface ripple

(surface phonon) effect Similarly, the spin waves in the magnetic materials cause a

spatially periodic modulation of the permittivity of the medium, and the light is scattered

by the permittivity fluctuations The mechanism of the scattering from spin waves is

known as the magneto-optic effect It can be understood as the fluctuation of the

transverse polarizability of a medium due to the Lorentz force caused by the precessing

magnetization (spin waves) Since the polarization of the scattered light is perpendicular

to that of the incident light, p-s (p means E component of incident light is in the

scattering plane, while s means H component of the scattered light is in the scattering

plane)polarization is commonly used through this project for the study of spin waves so

as to exclude the signal from phonons which normally appears in p-p polarization

Fig 2.4 Illustration of light scattering geometry

ωi, ki

ωs, ks

Scattering Volume

Polarizer

ei Laser

Detector Analyzer

es

Chapter 2 Brillouin Scattering from Spin Waves

Figure 2.4 shows schematically the experimental situation of BLS

Monochromatic light of angular frequency ωi is incident on the scattering medium The

electric field vector Ei is polarized in the direction of unit vector ei, and the direction of

the incident light beam is parallel to the wavevector ki in the medium The magnitude ki

=

k (2.10)

where λ0 is the wavelength of the incident light and ni is the refractive index of the

medium The incident electric field will induce a polarization P in the medium, with

Cartesian components given by:

0( , ) ( , ) i ( , )

νε

r χ r E r (2.11)

where χ is the susceptibility tensor, ε0 is the permittivity of free space, and µ and ν

denote x, y, or z The effect of excitations is to modulate χ and hence produce a

fluctuation term in the polarization P This in turn will give rise to a scattered

electromagnetic wave whose electric field strength Es and frequency ωs can be calculated

from Maxwell’s equations The scattering process will be inelastic when the incident

photon of energy = either takes energy from or gives energy to the excitation in the ωi

medium and produce the scattered photon of energy=ωs

2.3.3 BLS Study of Spin Waves

The innovation by Sandercock [11, 12], in 1971, 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

1973 Figure 2.5 shows a BLS spectrum of YIG containing both magnon and phonon

peaks recorded with a 5-pass FP interferometer The intensity and frequency shift of the

magnon peaks as a function of applied magnetic field and incident light wavelength have

been investigated

Fig 2.5 Brillouin spectrum of YIG showing magnon (M) and phonon (LA mode) peaks

recorded with a 5-pass FP interferometer The unmarked peaks are the neighboring

interference orders [After Sandercock et al Ref 13]

In 1978 [14] and 1979 [15], Sandercock and Wettling reported BLS studies of

magnons in thin polycrystalline Fe and Ni slabs with thickness of 50-100 µm Both bulk

and surface magnons were observed, as shown in Fig 2.6 The sharp peak, with a higher

frequency, appeared only on the Stokes side and was assigned as the surface

magnetostatic mode predicted by Damon and Eshbach [8] The experimental results agree

well with the theoretical calculations in which both exchange and dipolar effects are

λ0=6328Å M

Chapter 2 Brillouin Scattering from Spin Waves

considered For bulk spin waves, the frequency is given by:

= and D′ ≈ 2D)

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]

Fig 2.7 (a): BLS spectrum of a 1-D array of permalloy wires (w = 1.8 µm, l = 500 µm,

and d = 20 nm); (b): Frequency dispersion with in-plane wavevector (comparing with a

continuous thin film of the same thickness) [After Mathieu et al Ref 16]

Lately, BLS has proven to be a powerful method for studying the dynamic

properties of micro- and nano-scale patterned magnetic structures From spin wave

measurements, information can be extracted on the magnetic properties, such as magnetic

anisotropy contributions, homogeneity of internal fields, as 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

(a) (b)

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 dots by Jorzick et al

[17], and 2-D arrays of cylindrical Ni nanowires by Wang et al [18] Figure 2.7 shows

the quantization of surface spin waves in periodical arrays of permalloy wires with a wire

width (w) of 1.8 µm, length (l) of 500 µm, and thickness (d) of 20 nm [16] The surface

spin waves were observed as several discrete modes given by Eq (2.6), with quantized

wavevectors q&,n given by:

,

2

n n

by assuming a standing lateral wave pattern for the spin wave modes with wavelength λn,

where the mode index n = 0, 1, 2… For larger wavevectors, the spin wave dispersion

resembles closely that of the continuous film with the same thickness of 20 nm [see Fig

2.7 (b)]

In this research, BLS was used to study spin wave excitations in hexagonal arrays

of permalloy nanowires and Co/CoPt exchange spring bilayers The instrumentation and

experimental techniques of BLS will be presented in Chapter 3

References:

1 A S Borovik-Romanov and N M Kreines, Phys Rep 81, 351(1982)

2 M G Cottam and D J Lockwood, “Light Scattering in Magnetic Solids”, John

Willey & Sons, (1986)

3 S O Demokritov, B Hillebrands, and A N Slavin, Phys Rep 348, 441 (2001)

4 F Bloch, Z Phys 61, 206 (1930)

5 M Fallot, Ann Phys (Paris) 6, 305 (1936)

6 P Weiss, Ext Actes VII Congr Intern Froid 1, 508 (1937)

7 G Heller and H A Kramers, Proc K Akad Wet 37, 378 (1934)

8 R W Damon and J R Eshbach, J Phys Chem Solid 19, 308 (1961)

9 B Lax, and K J Button, “Microwave Ferrites and Ferromagnetics”,

McGraw-Hill, New York (1962)

10 C Herring, and C Kittel, Phys Rev 81, 869 (1951)

11 W Hayes and R Loudon, “Scattering of Light by Crystals”, New York: Wiley,

(1978)

12 J R Sandercock, in M Balkanski, Ed., “Light Scattering in Solids”, Paris:

Flammarion, (1971)

13 J R Sandercock, and W Wettling, Solid State Commun 13, 1729 (1973)

14 J R Sandercock, and W Wettling, IEEE Trans Magn 14, 442 (1978)

15 J R Sandercock, and W Wettling, J Appl Phys 50, 7784 (1979).

16 C Mathieu, J Jorzick, A Frank, S O Demokritov, A N Slavin, and B

Hillebrands, Phys Rev Lett 81, 3968 (1998).

17 J Jorzick, S O Demokritov, B Hillerbrands, B Bartenlian, C Chappert, D

Chapter 2 Brillouin Scattering from Spin Waves

Decanini, F Rousseaux, and E Cambril, Appl Phys Lett 75, 3859 (1999).

18 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)

Chapter 3 Instrumentation and Experimental Techniques

The components of the experimental set-up used for BLS are a single-mode laser,

an optical system for focusing and collection of light, a Fabry-Perot (FP) interferometer and its control unit, and a photon detector The whole system sits on a steel plate which is bolted onto sturdy wooden tables The optical components, sample holder, and the FP interferometer are mounted on an optical bench system All optical components are mounted on X-Y-Z translators, thus their positions can be adjusted with ease and precision along the X-Y-Z axes

Chapter 3 Instrumentation and Experimental Techniques stream of pure argon gas is directed at the irradiated spot on the specimen to cool it and to keep air away from it For the study of spin waves (magnons) a computer-controlled electromagnet with maximum field of 1.2 T is used to generate the static magnetic field

A special sample holder was designed so as to place the sample into the small gap between the poles of the electromagnet The scattered light is collected by the collection lens and focused onto the pinhole of the input shutter of the FP interferometer To minimize aberration, achromatic lenses are used For polarization studies, a polarizer is

inserted between the tiny mirror and focusing lens so that only p-polarized or s-polarized

light passes through A polarization rotator can be screwed onto the laser head to obtain

s-polarized incident light

Fig 3.1 Experimental set-up for BLS in the 180°-backscattering geometry

Sample

Filter Beam Splitter

Oscilloscope

Detector

Control Unit

A JRS Scientific Instrument (3+3)-pass tandem FP interferometer with its control units, a silicon avalanche diode single photon detector (rated at 9 dark counts per second),

an oscilloscope (used for alignment checking of the optics of the interferometer), and a computer interfaced with the control unit, is used to record the Brillouin spectra

3.2 Instrumentations

3.2.1 Laser

For Brillouin scattering studies, laser light of single frequency and single mode is essential A Spectra Physics Model BeamLok 2080-15S Argon ion laser [1] equipped with a Z-Lok accessory package is used in this project to meet these requirements The laser emits a light beam with diameter of about 1.9 mm at 1/e2 points, and beam divergence of about 0.45 mrad The 514.5 nm radiation was used in all Brillouin measurements The laser system is extremely reliable and stable with high power stability and beam pointing stability

1 Laser Head

The Laser head is made up of a mechanical resonator, the plasma tube, the magnet and the BeamLok beam-positioning module The three-bar resonator is temperature compensated and is extremely rigid and stable The resonator and plasma tube combine to provide excellent beam pointing stability BeamLok is an active beam positioning system and consists of a mirror actuator, detector, system electronics and a Model 2474 BeamLok remote control module When engaged, the output beam is locked onto a fixed reference point beyond the cavity If the beam moves, the output mirror will respond to

Chapter 3 Instrumentation and Experimental Techniques restore the beam position For the model BeamLok 2080 Argon ion laser, the beam position offset is < 0.5 µm/°C and angular offset is < 0.5 µrad/°C

2 Z-Lok Package

The Model 587 Z-Lok system, consisting of an etalon assembly, electronics module, and a wavelength selective mirror, provides automated single-frequency operation with stable output power When combined with the BeamLok, it controls the laser cavity length to stabilize both frequency and beam motion to prevent mode hops and ensure automatic etalon alignment of optimum power

The light modulator, shown in Fig 3.2, is a double shutter system mounted directly behind the entrance pinhole of the FP The device operating with a reference beam is able to modulate the light intensity reaching the photomultiplier and protect the detector from the strong elastic scattering from the sample For scanning of the Brillouin signal from the sample, shutter 1 is open and shutter 2 is closed The experimental signal enters from Pinhole P1 While scanning the strong elastic scattering, shutter 1 is closed to block the elastic signal At the meantime, shutter 2 is open A suitable light signal is thus introduced for stabilization purpose via the Pinhole P1′

3.2.3 Multi-pass Tandem FP Interferometer

Chapter 3 Instrumentation and Experimental Techniques

1 Properties of FP Interferometer

A typical FP interferometer [2] consists of two partially reflecting plane

fused-silica mirrors mounted accurately parallel to one another at a distance (L) Light can be transmitted only if L is equal to a multiple of half of its wavelength (λ0):

02

GHz mm2

c f

∆ = = ⋅ (3.2)

This interorder spacing is called the free spectra range (FSR) of the interferometer The

finesse (F) of the FP interferometer is related to the linewidth δλ of a given transmission peak by:

where T0 (<1) is the maximum transmission determined by the system

The contrast for an n-pass interferometer [3] is the nth power of that of a

single-pass one For example, a five-single-pass interferometer can achieve a contrast of at least five or six orders of magnitude greater than that of a single-pass interferometer.At the same time the peak transmission (~50%) and finesse (50 -100) stay comparable [4]

2 Tandem FP Interferometer

The layout of the tandem FP interferometer system is shown in Fig 3.4 The first interferometer FP1 lies in the direction of the translation stage movement One mirror sits

on the translation stages, and the other on a separate angular orientation device The

second interferometer FP2 lies with its axis at an angle θ to the scan direction One mirror

is mounted on the translation stage in proximity to the mirror of FP1, the second mirror

on an angular orientation device The changes in FP1 δL 1 and in FP2 δL 2 satisfy the synchronization condition:

δL1/δL2 =L L1/ 2 (3.5)

Fig 3.4 The translation stage allowing automatic synchronization scans of the tandem

interferometer

Translation Stage

Chapter 3 Instrumentation and Experimental Techniques

For the JRS (3+3)-pass tandem FP interferometer, the two interferometers are arranged by a novel parallelogram construction which can achieve both statically and dynamically stable synchronization The advantage of the tandem FP interferometer includes tilt-free scan, high linear scan, continuous change and measurement of mirror spacing, ability to change the mirror spacing moderately without losing alignment, higher contrast and larger effective FSR (5 GHz to 300GHz)

3 Operation of The (3+3)-pass Tandem FP Interferometer

Fig 3.5 Optical system for pre-alignment of the FP interferometer

Before measurement, a pre-alignment of the two FPs is required to set the correct relative spacing between them Figure 3.5 shows the optical system for pre-alignment The collected light passes through a beam splitter onto FP1 The reflected light passes via

a second beam splitter onto FP2 whence the doubly reflected beam is directed to the photon detector

Fig 3.6 Principle of the pre-alignment of the FP interferometer

The pre-alignment method is based on the fact that when an interferometer is transmitting, the reflected intensity tends to zero Hence a minimum value will be obtained when the interferometer is optimally aligned Scanning the interferometer, the photon detector signal will show a background intensity punctuated by minima whenever either FP1 or FP2 transmits This is shown for a poorly aligned interferometer in

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 the tandem FP is completed Switching on the optical system to the multi-pass measurement configuration, transmission will be observed with minor adjustments necessary to optimize the transmission

Fig 3.7 Optical system for (3+3)-pass tandem operation

On switching to the tandem mode, it is ready for measurement Figure 3.7 shows the optical setup for the (3+3)-pass tandem FP interferometer The scattered light enters the system at the adjustable pinhole P1 The aperture A1 defines the cone of the light accepted Mirror M1 reflects the light towards the lens L1 where it is collimated and directed via mirror M2 to FP1 Here it passes through aperture 1 of the mask A2 and is directed via mirror M3 to FP2

After transmission through FP2 the light strikes the 90° prism PR1 where it is reflected downwards and returned parallel to itself towards FP2 It continues through the aperture 2 of A2 to FP1 After transmission through FP1 it passes through lens L1, underneath mirror M1, and is focused onto mirror M4 This mirror returns the light through lens L1 where it is again collimated and directed through FP1

The combination of lens L1 and mirror M4 lying at its focus is known as a eye It is optically equivalent to a corner-cube but has the advantage that is also acts as a spatial filter that filters out unwanted beams such as the beams reflected from the rear surface of the interferometer mirrors

cats-After the final pass through the interferometers, through the aperture 3 of A2, the light strikes the mirror M5 where it is directed to the prism PR2 This prism, in combination with the lens L2 and the output pinhole P2, forms a band-pass filter with a width determined by the size of the pinhole The mirror M6 sends the light to the output pinhole and will have to be adjusted whenever the laser wavelength is changed

Chapter 3 Instrumentation and Experimental Techniques

The optical system has low cross talk and stray reflection which enables a very high contrast to be achieved (typically 1011 for interferometer mirror reflectivity of 92-94%) The system is designed using a minimum number of components and thereby reduces the optical losses to a minimum

3.2.4 Detector

Detectors with high signal-to-noise ratio and low dark count are required for BLS study since the Brillouin signal is generally weak A single photon counting module SPCM-AQ is used, which is currently the most efficient detector for Brillouin scattering Its quantum efficiency (QE) is about 60% at 500 nm The high QE means that weak signals can be measured far more quickly than with normal photomultiplier tubes (typically QE 10-15%)

The SPCM-AQ is a photon counting system producing TTL pulses There is a dead time of about 50 ns between pulses The solid-state detector utilizes a unique silicon avalanche photo-diode that has a circular active area with a diameter of 200 µm The photo-diode is both thermoelectricity cooled and temperature controlled, ensuring stabilized performance despite changes in the ambient temperature The SPCM-AQ requires a +5 volt power supply A 50 Ω TTL pulse, 2 volts high and ∼30 ns wide, is output at the rear BNC connector as each photon is detected The photon pulses are collected and displayed as spectrum on the computer The maximum dark count is 9 cps

An f/1.5 lens, with diameter of 18 mm, is positioned in front of the silicon avalanche diode

3.2.5 Electromagnet

A computer-controlled GMW 3470 electromagnet [5] is used to generate a static magnetic field of up to 1.2 T The pole gap can be varied between 0 to 75 mm When the pole gap is changed, a recalibration is needed Figure 3.8 shows a typical calibration curve for a pole gap of 15 mm Controlled by the calibration program, the electric current

is varied between - 1.8 A and + 1.8 A A digital teslameter is placed in the middle of the pole gap to measure the generated magnetic field and feed back to the computer For a pole gap of 15 mm, a maximum field of 0.9 T is achieved when a current of 1.4 A is applied For higher magnetic fields, smaller pole gaps are needed

Fig 3.8 Calibration plot of the electromagnet for a pole gap of 15 mm

Chapter 3 Instrumentation and Experimental Techniques

When using the electromagnet, the magnetic field is set by keying in the magnetic field value in the “Field Setpoint in Tesla” box in the control program (see Fig 3.9) The program automatically determines the current required for the magnetic field according to

the recorded calibration curve Clean, cool (16°C - 20°C) water at 1 l / min at 0.3 bar is required to cool the magnet

Fig 3.9 Control panel of the electromagnet with the field set at 0.6 T

3.3 Analysis of Brillouin Spectrum

The Brillouin data are recorded by a PC equipped with the Multi-Channel Scalar (MCS) software in binary file The frequencies of the Brillouin peaks in the measured