P L A S M O N I C E X C I TAT I O N A N D T- M O K E E F F E C T
by
jorge nicolás hayek valencia code: 201113534
jorge nicolás hayek
Presented to Universidad de los Andes, to aim for the Undergraduate degree in Physics November 2015
Jorge Nicolás Hayek:Plasmonic Excitation and T-MOKE effect,Presented to Universidad de los Andes, to aim for the Undergraduate degree in Physics, © November 2015
This document is concerned with the optical properties of a set of Ag thin films, and the magneto optical properties of a set of Au/Co/Au trilayers, vari-ating by the thickness of each layer. The Ag films have been produced by Vapor Deposition Technique, and the trilayers were grown back in the ex-periment conducted by Cesar Herreño and Edgar Patiño in Ref. [9] using the Electron Beam Physical Vapor Deposition.
The Optical properties were principally investigated by inciding a laser beam of known wavelength onto one of the mentioned samples, where the photons excite conduction electrons on the sample surface, through the em-ployment of the Kretschmann configuration and fulfilling an angle condi-tion, into a collective oscillation of electrons propagating through a dielectric-metallic interface, known as Surface Plasmon Polaritons.
On the other hand, the magnetic properties were described by using the magneto-optical Kerr effect in a transversal configuration. The magnetic properties are acquired by using two methods: A phase sensitive method, and a method that involves taking hysteresis measurements for a set of an-gles and acquiring the difference in the remanence. These measurements were made using equipment from Ref. [9] and a few data processing ele-ments constructed during the course of this present work.
A B S T R AC T
Este documento se enfoca en la obtención de propiedades ópticas de un set de películas delgadas de Ag, y la obtención de las propiedades magneto ópticas de un set de tricapas de Au/Co/Au, variando el espesor de cada capa según la muestra. las películas delgadas de Ag son producidas usando la técnica de deposición química de vapor, mientras que las tricapas fueron crecidas en un trabajo previo de Cesar Herreño y Edgar Patiño [9] , donde usaron la técnica de deposición química de vapor con haz de electrones para el crecimiento de las muestras.
Las propiedades ópticas fueron principalmente investigadas al incidir un láser de longitud de onda conocida en una de las muestras mencionadas, donde los fotones excitan los electrones de conducción en la superficie de la muestra que pasan a ser una oscilación colectiva de electrones propagándose a través de la interfaz metal-dieléctrico, mediante el uso de la configuración Kretschmann y al satisfacer una condición en el angulo de incidencia, Esta oscilación de electrones bajo las mencionadas condiciones es también cono-cido como Plasmon Polariton de Superficie.
Por otro lado, las propiedades magneto ópticas son descritas al usar el efecto magneto óptico Kerr en una configuración transversal. Estas propie-dades se pueden obtener al usar dos métodos: El primero es sensible a la fase, y el segundo involucra la obtención de curvas de histéresis para un set de ángulos de incidencia, donde se obtiene la diferencia en remanencia. Estas medidas son realizadas usando equipo de la referencia [9] y algunos elemen-tos de procesamiento de señales construidos en el proceso de el presente trabajo.
AC K N O W L E D G M E N T S
I want to express my gratitude towards Universidad de los Andes for the academic formation which was provided through the undergraduate studies of Physics. To my professors through the career whom I hope to have ful-filled their expectations. To my adviser Edgar Patiño and to Cesar Herreño, who shared the information of their works, provided insight and guidance through the course of this work, by way of which this thesis could have not been finished. And to Jhony O. Turizo, David Guzman, Luis C. Gómez and Cesar Talero for providing expertise that greatly assisted this work.
Many thanks to everyone who gave me all their support, specially to my family and friends, who have supported me throughout the entire career and life.
i introduction 1
1 theoretical framework 3
1.1 Surface Plasmons (SPs) 3
1.1.1 Dispersion Relation 4
1.1.2 Excitation by Light 6
1.2 Magneto-Optic Kerr Effect (MOKE) 8
2 A u/C o/A uexperiments 13
ii methodology 14
3 experimental set-up 15
3.1 Sample preparation 15
3.2 Setup and Sample characterization 16
3.3 Data acquisition Equipment 20
3.4 Data Acquisition Software 22
iii results 27
4 acqired data 28
4.1 Optical characterization for Ag and Au/Co/Au samples 29
4.2 MO characterization for the A u/C o/A u sample with a phase sensitive method 32
4.3 MO characterization using Hysteresis loops for theA u/C o/A u
sample 34
iv analysis of results and discussion 36
5 analysis of results and discussion 37
v conclusions 41
6 conclusion 42
vi appendix 43
a wiring and experimental set-up schematics 44
b dispersion relation of sps on a surface of a semi-infinite solid 47
c example of a common wiring error 49
bibliography 51
L I S T O F F I G U R E S
Figure 1 Schematic for oscillating charges and the EM field propagating on a surface. 5
Figure 2 Configurations for SPs Interfaces 7
Figure 3 Scheme of the Kretschmann configuration 7
Figure 4 Schematic for S- and P- Polarization 9
Figure 5 MOKE Spatial Configurations 10
Figure 6 Vapor Deposition Machine 15
Figure 7 3D model for the distribution of the Optical
mount-ings 17
Figure 8 Distribution of the SPR and MOKE setup 18
Figure 9 Optical Characterization - flow diagram 19
Figure 10 Flow diagram for the MO Characterization, Phase sensitive method 19
Figure 11 Flow diagram for the MO Characterization, Hys-teresis loops method 20
Figure 12 Data acquisition Equipment 21
Figure 13 Laser Alignment Software 23
Figure 14 KEPCO Current Source Controller 23
Figure 15 SPR Main Program 24
Figure 16 T-MOKE Experiment Program 26
Figure 17 Theoretical model of the optical characterization in a thin film of Ag. 29
Figure 18 Graph of the SPR angular characterization for the S1 and S2 samples 30
Figure 19 Graph of the SPR angular characterization for the S1 and S2 samples 31
Figure 20 SPR angular characterization after realignment of the S2 sample 31
Figure 21 Magnetic Field characterization 32
Figure 22 Graph of the MO characterization for the 21B and 28B samples 33
Figure 23 MO characterization after realignment of the Au(11,6)/Co(10,2)/Au(3,0)
sample 33
Figure 24 Hysteresis loop for the 21B sample at 50° 34
Figure 25 Hysteresis loops for the 21B sample at different
an-gles 35
Figure 26 Graph for the Delta R for all the hysteresis loops
taken 35
Figure 27 Comparison between MO characterization methods 38
Figure 28 Optical characterization and model for the S1 and S2 samples 39
Figure 29 Optical characterization and model for the S2 sam-ple after realignment. 40
Figure 30 MO characterization for the 28B, 21 and Au(11,6)/Co(10,2)/Au(3,0) samples. 40
Figure 31 Schematics for the Experimental Set-Up 44
Figure 32 Schematic of the wiring for reflectivity spectra char-acterization and phase sensitive MO
characteriza-tion 45
Figure 33 Schematic of the wiring for the Magneto-Optic Char-acterization by acquiring Hysteresis loops. 46
Figure 34 Hysteresis loop recorded- Wiring Error 49
Figure 35 Hysteresis loop recorded - FT 50
L I S T O F TA B L E S
Table 1 List of the material thickness for the samples in the work of Cesar Herreño and Edgar Patiño 13
Table 2 Synthesizer (Reference Signal) Operation
Parame-ters 24
Table 3 Lock-In Operation Parameters 25
Table 4 LABVIEW Program Operation Parameters 25
Table 5 Low-Noise Preamplifier (Filter) Operation
Parame-ters 25
Part I
Plasmonic Excitation and T-MOKE effect
The plasmonics forms a major part of the nanophotonics field, which is based on interaction processes between electromagnetic radiation and conduction electrons at metallic interfaces and explores how electromagnetic fields can be confined to dimensions of the order, or less, than its wavelength [16]. The experiment will be based on superficial plasmonic excitation, which involves incident transversal polarized waves that interacts with the electrons from the conduction band on the surface of the metal.
The excitation, or collective oscillation of conduction electrons known as surface plasmon polaritons (SPPs), propagates at the interface of a dielectric and a conductor, in this case the material where the incident radiation is directed are a set of Au/Co/Au thin films [9]. SPPs propagating at the flat in-terface between a conductor and a dielectric are essentially two-dimensional electromagnetic waves. The effect can be detected by recognizing that the production of plasmonic excitation implies that the electromagnetic radia-tion will not be reflected. In this case, the transverse magneto-optical (MO) Kerr effect (T-MOKE) will be studied on the samples, which is defined as a change of reflected intensity of polarized light when the direction of the external static field is changed from the saturated state+Msto−Msbeing
Msthe saturation magnetization [17].
The study of magneto-optic and plasmonic functionalities has been under development to take advantage of features from both fields. A well known application is MO recording, which uses the MOKE effect to read data from a magnetic disc [30].
Motivated by the works of Cesar Herreño and Edgar Patiño, on a previous characterization of the T-MOKE effect on Au/Co/Au structures using green light source, we focus our interest on the enhancement of the set up by intro-ducing and relocating optical devices, and the acquirement of the magneto optical characterization data by using two techniques; a phase sensitive, and by acquiring the remanence from hysteresis loops.
1
T H E O R E T I C A L F R A M E WO R KThe term of Nanophotonics is defined as nano-scale optical science and tech-nology, and the field that studies the interaction between light and matter on wavelength and sub-wavelength scale of radiation, as well as the design of structured optical materials and devices and the development of nano-characterization tools.
In the sub-field of nanophotonics is developed the so-called plasmonics, whom together with magnetic functionalities became an active topic of re-search named magneto-plasmonics. Here, the magnetic functionality al-lows the control of the plasmonic properties by an external magnetic field, and the plasmonic structures affect significantly the magneto-optic (MO) properties[5,8]. This association is of great interest in applications such as ’active plasmonics’, term related to the MO devices, which includes tech-niques for controlling propagation of guided surface plasmon polariton signals[15].
In this chapter the general concepts concerning this monography will be presented. First of all, a slight introduction of the general features of Surface Plasmons Polaritons will be described. It will be followed by the general aspects of the MO Kerr effect, emphasizing the transversal configuration. Then, the Kretschmann configuration is described, which is required to im-plement in order to acquire the signal from both the plasmonic excitation and the Transversal MO Kerr effect.
1.1 surface plasmons (sps)
The Plasmonics is the study of the interaction between electromagnetic field and free electrons in a metal. The plasmonics also include the development of miniaturized optical devices exploiting surface plasmon effects, such as the confinement of electromagnetic field by localized plasmon coupling[23].
The collective oscillation of conduction electrons is known as a Plasmon. The electromagnetic wave coupled to a plasmon (The polariton) at the inter-face between materials having positive and negative permittivities, typically a metal and a dielectric, is known as the quasi-particles Surface Plasmon Po-laritons (SPPs)[9,11,19]. They can take various forms, such as propagating electron density waves along metal surfaces, or localized electron oscilla-tions on metal nanoparticles [13]. In the case of propagating electron density waves, and the incidence of light in a metal, the electric component of the light can excite the free electrons in order to acquire a collective oscillation that matches with the light in its energy(¯hω)and linear momentum
¯ h~k [6,9,13,21,29].
In the plasma concept, the free electrons of a metal are considered as an electron liquid of high density ∼1023cm−3
. This concept is used as one type of approach to describe the electronic properties of the solid state, such that longitudinal density fluctuations, or plasma oscillations, will propagate through the volume of the metal. The quanta of these “Volume plasmons” have an energy of ¯hωp = h¯
p
4πne2/m0, wheren is the electron density, of the order of10eV[22].
Research in Surface Plasmon Resonance (SPR) has became a major inter-est in different sensing applications. This phenomenon has been found to enable a wide range of practical applications such as light guiding and manip-ulation at the nanoscale, enhancement of sensing capabilities of biosensors like biodetection at the single molecule level and applications in medical di-agnostics, enhanced optical transmission through subwavelength apertures, and high resolution optical imaging below the diffraction limit [9,13,19]. The SPR phenomenon is represented as a dip of curve which exhibits the minimum reflectance. However, it is important to differentiate between the existence of SPR and destructive interference, where both lead to an absorp-tion dip in the reflectance funcabsorp-tion [19].
1.1.1 Dispersion Relation
The propagating SPs frequencyωis related with its wave vector
−→
k through the dispersion relation ω(k) which describes a significant part of its
be-haviour.
These charge fluctuations in the SPs are accompanied by a mixed transver-sal and longitudinal EM field which disappears at|z| →∞, and has a maxi-mum in the surfacez=0, which is typical for surface waves. This explains their sensitivity to surface properties. As a consequence of this, the field is described by the solution of a plane wave:
E=E0±exp[+i(kxx±kzz−ωt)] (1)
with+ for z ≥ 0, − for z ≤ 0, and imaginary kz, which causes the
exponential decay of the field Ez(Fig.1) [22]. Also,kx lies parallel to the x
direction and |kx| = 2π/λp withλpbeing the wavelength of the plasma
1.1 surface plasmons (sps) 5
Figure 1.: Schematic for oscillating charges and the associated electromagnetic field of a SP propagating on a surface in the xdirection. The 3D model was designed in Blender software[7]. The exponential dependence of the field Ezis seen below. The applied magnetic fieldHyis shown in they
direc-tion of the p-polarized wave.
In order to specify the dispersion relation, it is useful to consider the case of propagation of the electromagnetic field from SPs on a surface in the x direction at the interface between two semi-infinite media, a dielectric with a real refraction index (na =
√
e2) and a metal with a complex dielectric function(em =e1=e01+ie001). This is the same consideration made when
a p-polarized wave propagates in the xdirection, thus there is noy depen-dence. The dielectric media is defined as the semispace where z > 0, and the metalic media as the region wherez <0(Fig.1) [22].
From Maxwell’s equations it can be obtained the retarded dispersion rela-tion for the plane interface:
kz1
e1
+ kz2 e2
=0 (2)
eik20 =k2x+k2zi (3)
withk0 = ω/c. In order to meet the requirement for kz > 0, due to
represent a physical wave,e1ande2must have opposite signs, which is the case for the interface between a metal and a dielectric.
Hence, the dispersion relation can be written as (The full derivation can be seen at AppendixB) :
kx =k0
e1e2
e1+e2
1/2
Besides, if is considered a realωande2such thate002 <|e01|, it is obtained
a complexkx=k0x+ik00x with:
k0x =k0
e10e2
e10 +e2
1/2
(5)
k00x =k0
e10e2
e10 +e2
3/2 e001
2 e012
(6)
Wherek00x determines the internal absorption and defines the propagation length of the SPs, which is assigned as the lengthLi where the intensity of
the propagating SPs decreases to 1/e. This intensity decreases as e−2k00xx,
thus we obtain the length asLi = (2k00x)−1.
As mentioned above, with bothkz1andkz2being imaginary,kzidecay
ex-ponentially ase−|kzi||z|, normal to the surface. The skin depth or penetration
distance at wich the field becomes1/e, becomes
z=1/|kzi| (7)
or, depending on whether the medium is the dielectric (e2) or the metal (e1), the skin depth will be respectively:
z2=
λ 2π
e01+e2
e21
1/2
z1 =
λ 2π
e01+e2
e012
1/2
(8)
1.1.2 Excitation by Light
A wide variety of optical techniques have been developed for exciting Sur-face Plasmons (SPs). It is possible to excite localized SPs on nanowires and nanoparticles by inciding a light beam on their surfaces. On the other hand, it is not as simple to excite nonradiative SPs on planar surfaces that do not directly couple with the incident light because the energy and momentum of an incident photon cannot be matched with the SP. In order to overcome this difficulty, many approaches have been used, such as using Attenuated Total Reflection (ATR) via prism coupling [24]. In pursuance of coupling the photon into a SPs, it is required to increase the wavevector of a given photon (of energyh¯ω) by a∆kx= kSP−kphoton.
The ATR method considers the case where light is reflected at a metal surface covered with a dielectric medium (e0 > 1) e.g., with a quartz half cylinder, and its momentum becomes(¯hk0)
√
e0instead of¯hk0.
kx = √
e0k0sinθ0 (9)
Another way to understand the formation of SPs in this device: The SPs occurs in the interface quartz/metal, an evanescent light wave with a phase
1.1 surface plasmons (sps) 7
velocityv = ω/kx = c/( √
e0sinθ0)propagates in the interface. The con-dition of resonance for SPs is:
ω/k0x= c s
e1+1
e1
= c/(√e0sinθ0) (10)
There are two possible configurations (Fig.2): a)the metal surface is sep-arated by air or dielectric slit at a distance of about λ from the medium e0(glass or quartz). The evanescent field couples with the SP on the 1-2 in-terface. Orb)the metal filme1is in contact with the mediume0. Here, the EM field decreases exponentially in the film and excites the SPs on the 1 - 2 interface. The experiment described in this document is made with theb) device (Kretschmann-Raether configuration).
Figure 2.: Configurations for SPs Interfaces.
A popular configuration for SP excitation is the “Kretschmann configura-tion” or “Kretschmann-Raether configuraconfigura-tion” (Fig.3). The light is incident through a prism in this configuration, but in contrast with the Otto config-uration (Another well-known configconfig-uration), it has a thin metal film at the bottom surface of the prism. Here, at the appropiate angle of incidence, the energy and momentum of the incident photon is efficiently transferred to the SP, and there is a substantial reduction in the reflected light intensity [9,19,24].
Figure 3.: Scheme of the Kretschmann configuration.
The quantitave description of the minimum of reflected intensityRcan be given by Fresnel’s equations for the system [0-1-2]: 0 as the dielectric medium (d); 1 as the metal film (m) of thicknesst; 2 as air (a). The reflectivity
Rfor p-polarized light, withE0the incoming field and Er as the reflected
[22].
R=r
p dma 2 =
Erp
E0p 2 =
rdmp +rmap exp(2ikz1t)
1+rpdmrmap exp(2ikz1t)
2 (11)
rikp =
kzi
ei −kzk
ek / kzi ei
+ kzk ek
(12)
1.2 magneto-optic kerr effect (moke)
The study of magneto-optic and plasmonic functionalities, referred as mag-netoplasmonics, has been under development to take advantage of features in both fields. The Magneto-Optical (MO) effect in magnetic materials arise due to the optical anisotropy of the materials. Such optical anisotropy de-rives from the magnetisation within the surface domains which can be influ-enced by external forces like magnetic fields. The optical anisotropy changes the state of linearly polarized light reflected from magnetic materials [4].
Magneto Optical Kerr (MOKE) effects can be described by the dielectric tensor theory[32], or the effects can also be described microscopically, where the electric field of the light and the magnetic field coupling occurs by the spin-orbit interaction. These effects can also be described by using the idea of Lorentz force [4]. In order to become familiar with the MOKE effect, it is required to understand the terminologies associated with the effect, suchlike the dependence of the state of polarization of reflected light upon the initial polarization and the magneto optical geometrical configuration.
Light is a transverse EM wave which can be manipullated optically into plane, circularly or elliptically polarized light. For the case of plane polarized light, the component of the electric field can be parallel to the plane made by the propagation direction and the normal of the plane (P-polarized) or
perpendicular to the named plane (S-polarized).* *For fact, the P from P-Polarization comes from the German Parallel, and the S from S-Polarization comes from the german Senkrecht, which means perpendicular.
1.2 magneto-optic kerr effect (moke) 9
Figure 4.: Schematic for a S- and P- Polarizated wave.
The MOKE is the study of the change of polarization state of light reflected from magnetized media. This reflection can produce several effects, includ-ing the rotation of the direction of polarization, introduction of ellipticity in the reflected in the reflected beam and a change in the intensity of the reflected beam [1,14,20]. These changes depend on the orientation of the magnetic field respect to the plane of incidence and the surface of the mate-rial. Therefore, three spatial configurations for MOKE experiments can be defined; Polar, Longitudinal and Transversal.
In the Polar MOKE (P-MOKE) the magnetic vector is parallel to the plane of incidence and normal to the reflecting surface (Fig.5, P-MOKE). On the other hand, the configuration for the Longitudinal MOKE (L-MOKE) varies on the direction of the magnetic vector, which is parallel to both, the plane of incidence and the reflecting surface (Fig.5, L-MOKE). In both Polar and Longitudinal cases, occurs a rotation on the plane of polarization.
When incident light is either p- or s-polarized, then the reflected light will still be plane polarized after reflection. This is because the reflecting surface is a plane of symmetry of the system. With a magnetic surface, this sym-metry is destroyed upon reflection for plane polarized light. In other words, when p-polarized light is reflected off a magnetic surface, the reflected light has a p-component and in addition has a small s-component appearing in the beam. this causes the light to become elliptically polarized, with its ma-jor axis rotated from the initial incident polarization plane. A similar effect occurs to s-polarized light. These two effects are known as Kerr ellipticity and Kerr rotation. The changes in the Kerr angle are described as:
withθkas the rotation of the polarization plane, andek as the ellipticity
[4].
For the case of the Transversal MOKE (T-MOKE) configuration,the mag-netic vector is parallel to the plane of incidence and normal to the reflecting surface (Fig.5, T-MOKE).
Figure 5.: Spatial configuration for the L-, P-, and T- MOKE experiments. Each one are differentiated by the direction of the magnetic field.
For the T-MOKE configuration, there are two cases of incident polariza-tion that has to be considered, whether the incident light is P- or S- polarized. Here, only the P-polarization shows an effect which is quite different from the other configurations. A small kerr vector is generated, which is parallel to the reflected polarization. The increase and decrease of the polarization amplitude depends on the direction of the magnetic field [20]. The Kerr sen-sitivity is defined as the difference in the intensity for a sample magnetised in opposite directions and normalized to the maximum intensity [4].
IKerr = ∆
I I =
Imax−Imin
Imax (14)
As mentioned earlier, the MO effects are described using dielectric tensor theory. In the theory, the plane polarized light is viewed as a superposition of two circular components, L and R-circularly polarized light, and the mag-netic medium has different refractive indices for these two polarized modes. Thus, these modes travel with different velocities [5,4,31]. The dielectric
1.2 magneto-optic kerr effect (moke) 11
tensor of a material, under the presence of a magnetic field, adopts the non-diagonal form:
exx −iMz iMy
iMz eyy −iMx
−iMy iMx ezz
=e (15)
where the components Mi are the Voigt MO constants of the material
(eMO). This Voigt term covers the first order proportional to the magnetism
of the material, containing the components of the applied magnetic field for paramagnetic and diamagnetic materials, and the magnetization for ferro-magnetic materials. On the other hand, if the material is optically isotropic,
exx=eyy =ezz[5].
For example, if the P-MOKE configuration is present, assuming the sample plane as XY and the magnetization aligned perpendicular to the same plane, the dielectric tensor will be:
exx −iMz 0
−iMz eyy 0
0 0 ezz
=e
Thus the X and Y components of the EM field are coupled, therefore in-ducing changes in the state of polarization of the light and proin-ducing Kerr ellipticity. In other words, the nondiagonal Fresnel coefficients accouting for polarization depend linearly with Mz. A similar effect is observed with
L-MOKE, where the non-diagonal, and non-zero components will beaMx.
Finally, with the T-MOKE configuration, the MO component couples com-ponents of the EM field that are on the incidence plane, i.e. only p-component of the light will be affected by the applied magnetic field, whilst the s-component is unaffected. This configuration involves no change in polarization but a change in the reflected intensity of the p-polarized light [5,31].
exx 0 −iMy
0 eyy 0
−iMy 0 ezz
=e
The Kerr Fresnel coefficients summarizes the behaviour of reflected light at the surface of magnetic films, which has been obtained from applying the Maxwell boundary conditions at these magnetic films [4,31,32]. The coefficients for T and L-MOKE are:
rtpp =
nβ−β0
nβ+β0 1+
in2Msin2θ n2(n2cos2θ−1) +sin2θ
(16)
rtss= β−nβ 0
β+nβ0
rlpp = nβ−β 0
nβ+β0
rlss= β−nβ 0
β+nβ0
rlps= −rlsp= βin
2Msinθ
n2β0(n
β+β0) (β+nβ0)
Whereθis the angle of incidence,nis the index of refraction of the film,
β = cosθ, andβ0 = h
1− sin2θ
n2 i1/2
. Besides, the termrsprepresents the
2
A u/C o/A u E X P E R I M E N T SThe focus of the work of Cesar Herreño and Edgar Patiño (Ref.[9]) was to maximize the T-MOKE effect of an Au/Co/Au structure. In order to reach this objective, a numerical method to obtain the optimum thickness values for each layer was proposed. At the end of this numerical method stage, the pre-dicted optimized structure was Au(1 4 . 1n m)/Co(1 0 . 2n m)/Au(0 . 5n m). Then these results were ratified by growing a set of Au/Co/Au trilayers (Ta-ble ) and performing the optical and MO characterization using the Kretschmann configuration.
Au/Co/Au Thickness (n m) Au/Co/Au Thickness (n m) 3 0 / 4 / 0 . 5 1 4 . 1 / 1 0 . 2 / 0 . 2
3 0 / 1 0 . 2 / 0 . 5 2 4 / 1 0 . 2 / 0 . 5 3 0 / 2 4 / 0 . 5 1 4 . 1 / 1 0 . 2 / 5
4 / 1 0 . 2 / 0 . 5
Table 1.: List of the material thickness for the presented samples in the work of Cesar Herreño and Edgar Patiño[9].
The optical and MO characterization were made by angular spectral reflec-tivity and T-MOKE signal respectively. The procedure consisted on inciding a 533 nm p-polarized green laser beam on a sample through a cylindrical lens, then the reflected beam is focused through a set of lens and the inten-sity of this reflected beam is sensed in a photodiode, which sends the signal to a lock-in amplifier. The sample is positioned on a base with two degrees of freedom, controlled by a servo motor, which allows to align the beam and to perform an angle sweep for the optical and MO characterization. A coil is set to apply a field following the T-MOKE configuration, located above the incidence point with a distance of approximately one centimeter. A periodic magnetization is experienced in the sample by using an AC signal for the current varying by a square signal with frequency of 3Hz. (Ref.[9])
The obtained experimental results and the theoretical predictions of the T-MOKE signal match fairly well the theoretical prediction for all the cases for varying thickness of Co and the Au layers.
With this in mind, we focus on the use of the experimental set-up and some of the samples from this work, and the introduction and rearrange-ment of some optical devices and data acquisition equiprearrange-ment in order to acquire complementary data for the optical and MO characterization. An-other center of attention is the relationship of the different hysteresis loops obtained at multiple angles, in contrast to the behavior of the phase sensitive method to characterize the MO properties of the samples.
3
E X P E R I M E N TA L S E T- U PThe following chapter describes a general idea for the fabrication of the sam-ples, and the sample characterization techniques used for this study. This includes the experimental equipment and software.
3.1 sample preparation
In order to obtain a sample for the experiment, it was used a substrate where the metallic thin film, which can be Au, Co, or Ag, was deposited by using ei-ther the Vapor Deposition Technique or the Electron Beam - Physical Vapor Deposition (EB-PVD) technique, which can be used in the Sala Semi-limpia from the department of physics at the Universidad de los Andes.
Figure 6.: Vapor Deposition Machine. a)The first image is the outside of the
vac-uum chamber for the system. b)The second image is the insides of the
chamber, focusing on the tungsten crucible holding a melted pellet of cop-per.
Thin film evaporation
The samples are evaporated over a glass substrate. In this case, the glass substrate is a cover-slip, a thin flat and fragile piece of glass with of about 22×22mmand a thickness in the range of0.13−0.17mm.
The thin metallic films are obtained by using a Vapor Deposition machine1 , which requires a Ultra High Vacuum (UHV) system in order to reduce impu-rities and increasing the mean free path for the particles. The UHV system helps to evacuate the air inside the machine and reduce the pressure until 10−7mbarare reached. The regime of very low pressures is required in order to deposit uniformly the material layer, which is evaporated using tungsten as crucible of the material of interest (Fig. 6 b)), by using very high
elec-1 The use of the Vapor Deposition Machine, and therefore grew the Ag samples in the course of this work, was conducted by Cesar Talero, Coordinator of the Investigation Laboratories from the department of physics at the Universidad de los Andes.
tric currents, then transferring heat to the material until its fusion point is reached. Then, the material is condensed onto the substrate.
Another way to obtain thin metallic films is by using EB-PVD2, which is also a low pressure process, similar to the thermal evaporation in the sense of words that the source material is heated above its boiling or sub-limation temperature, and the vapor forms a film on a surface. An advan-tage of this method over the thermal evaporation is the possibility to add a larger amount of energy into the source material. Another advantage is that a lower degree of contamination from the crucible will be present compared to the thermal method, because the electron beam only heats the source ma-terial and not the entire crucible. The process consists on drawing electrons from a filament by applying a large voltage, and focusing as a beam on the source material by using bending magnets. The beam is swept along the surface of the source material in order to heat all the material. [2]
Quartz crystal micro-balance
Taking into consideration the requirement of knowing the thickness of the material layer deposited, the Vapor Deposition Technique counts with a Quartz Crystal micro balance, which is a simple high-resolution mass sens-ing technique based upon the piezoelectric effect.
The effect consists on applying an alternating electric field across the quartz crystal through upper and lower metal electrodes covering the quartz surface and producing a mechanical oscillation of characteristic frequency f on the crystal. Then, an increase in the mass bound to the quartz surface causes the oscillation frequency to decrease. Then, for pure elastic mass added to the surface, the linear Sauerbray equation[18] can be used to quan-tify the change in mass added to the surface.
∆f =−2∆m f2/A(µρq)0.5 =−Cf∆m (17)
With ∆f as the resonant frequency decrease, f as the intrinsic crystal frequency,Athe electrode area,ρqthe density of the quartz, andµthe shear
modulus. Then, together with the density of the deposited material and the electrode area, the thickness of the deposited material can be known.
3.2 setup and sample characterization
The plasmon excitation experiment requires a setup that allows the acquisi-tion of data at different angles in order to acquire the Reflectance Angular Spectra (optical characterization), reason of which the Kretschmann config-uration has been used. On the other hand, the setup requires a magnetic field source, a series of filters and amplifiers in order to obtain the T-MOKE signal (MO characterization) which has a very low magnitude (in the order of micro-volts, same as the noise).
The Optical and the MO characterization techniques use the same distri-bution for the optical devices, varying from technique to technique on the parameters used for the reference signal for the external magnetic field, and the parameters and equipment used for the signal processing.
2 On the other hand, the growth of the last Au/Co/Au sample through the course of this work, by using the EB-PVD technique, was conducted by the Edgar Patiño, Professor at the Uni-versidad de los Andes, and Member of the PhD and Masters Committee.
3.2 setup and sample characterization 17
The optical mounting was arranged while taking a few considerations: The power of the laser was too high for the sensors used; The experiment required to polarize a laser beam, then incide it to a cylindrical lens where the sample will be located following the Kretschmann configuration, and detect the signal with a sensor; It was considered to vary the incident angle, so the sample and the reflected beam sensor had to be allowed to rotate; A magnetic coil had to be localized following the Transversal-MOKE configuration.
Figure 7.: 3D model for the distribution of the Optical mountings designed using the software Blender[7]. The model shows the location of the different optical equipment and how the beam passes through each one.
According to these specifications, the laser was passed through a filter in order to reduce the power of the laser, then the laser beam was aligned to a polarizer using a set of mirrors, thus obtaining a polarized beam. Later it passes through a lens and a beam splitter (BS), where the lens focuses the beam onto the sample and the BS allows to have a reference for the incident beam by inciding it onto one sensor. In contrast with the previous set up from Ref.[9], the lens and the beam splitter step was introduced, and the lens focusing the reflected beam were removed, so the intensity loses from the referece measurement are caused by merely the Kretschmann set up and the properties of the photodiode. After passing through the Kretschmann configuration, the reflected beam is recorded at a second sensor (as seen at the Fig.7and8). The Kretschmann mounting and the second sensor are located onto a motorized goniometer3where the angles, for the sample with respect the incident beam and the second sensor, can be controlled externally. Additionally, a magnetic coil is located following the T-MOKE configuration
3 The goniometer was designed and assembled at the Mechanics Laboratory from the depart-ment of physics at the Universidad de los Andes. Then the controlling programs were de-signed and programed at the Electronics Laboratory.
(A schematic of the location of the optical devices can be seen at Appendix
AFig.31).
Figure 8.: Distribution of the SPR and MOKE setup.
In order to acquire both types of characterization (Optical and MO), two se-tups were operated. The first apparatus, used in the work of Cesar Herreño[9], was able to acquire the optical characterization from the samples, and a phase sensitive method to obtain the MO characterization (Phase sensitive method), based on the use of a Lock-In Amplifier. The second setup was con-structed in the Electronics Laboratory from the department of physics at the Universidad de los Andes with the purpose of acquiring a MO characteriza-tion of the samples by obtaining hysteresis loops from applying a magnetic field over a sample and observing the effects on the intensity of the reflected beam, following the T-MOKE configuration.
SPR Characterization
The Surface Plasmonic Resonance (SPR) characterization consists on per-forming a measurement of the reflected beam obtained from the experimen-tal set-up with a variating incident angle ranging from 35° to 65°. After the laser is reflected from the sample and measured on a photodiode, the
cap-3.2 setup and sample characterization 19
tured intensity signal is directed to a Lock-In (acting as a voltmeter) and stored in an array of data together with the angle recorded from the go-niometer (Fig.9). This variating signal shows the angle at which the total reflection is reached, followed by the angle where the plasmonic excitation is obtained.
Figure 9.: Optical Characterization - flow diagram.
MO Characterization
Phase sensitive Method
Another way to measure this MO effect consists on obtaining the Intensity of the reflected beam in the same way that the SPR Characterization does, with the difference that the sample is being affected by a periodically changing external magnetic field with frequency fB, and the voltmeter acquires only
the data that is in phase with this magnetic field (Fig.10), eliminating the offset component, and noise from other sources. Through this way, only the maximum value for the inphase reflected signal is obtained, and can be compared with different readings for each angle.
Figure 10.: Flow diagram for the MO Characterization, Phase sensitive method.
Hysteresis loop Method
A way to obtain the Magneto-Optic effect is by measuring the saturation remanence from a graph of reflected Intensity vs External magnetic field, which becomes a Hysteresis loop. The intensity changes are on the same order of the noise, hence the frequencies bigger than one order of magnitude greater than the frequency of the external magnetic field are filtered, and
the rest is amplified. Finally, the obtained signal is a composite of a DC signal from the SPR and the AC signal from the MO effect, which can be written asIMeasured = IAC+IDC. Then, thisIDCis taken away by applying
a differential amplifier from a DC source (Fig.11), followed by the use of this IAC together with the magnetic field to obtain the mentioned Hysteresis
loops, and therefore the difference in saturation remanence can be acquired. These steps must be followed for each angle of interest, and the behavior of the delta of remanence depending on the angle leads to the same behavior from the phase sensitive MO method.
Figure 11.: Flow diagram for the MO Characterization, Hysteresis loops method.
3.3 data acqisition eqipment
The studied signal was generated from a CL-2000 Diode Pumped Crystal Laser Power Supply and the respective Crystal Laser. On the other hand, both reference and reflected signals were acquired through a set of Si-Based photodiodes from THORLABS which can detect an incident light with a range of wavelength from400to1100nm.After the acquirement of the re-flected and reference signal, it was required to use a set of filters, sources, ref-erences and signal operators in order to cleanse the signal of interest. (Fig.12. See AppendixAfor wiring schematics).
3.3 data acqisition eqipment 21
Figure 12.: Data acquisition Equipment used for the reflectivity angular spectra characterization and both methods for MO characterization. See Ap-pendixAfor wiring schematics.
Model SR830 DSP Lock-In Amplifier
In experimental physics, some measurements involve the detection of an electrical quantity. Quantities such as temperatures, pressure displacement or light intensity can be converted to electrical quantity by using a sensor. Perversely, this electrical quantity, or signal, will be accompanied by noise. There exists any techniques that recover the signal of interest from the com-posite of signal and noise, and one of them is the phase sensitive (Lock-In) de-tection (PSD). Lock-In amplifiers are used to detect and measure very small AC signals, all the way down to nanovolts. Basically, a PSD rectifies an in-coming signal and then filters it. In order to rectify the signal, the PSD is composed of a synchronous switch with upper and lower positions, in the upper position it passes the incoming signal unaltered, and in the lower po-sition it passes the signal inverted. The switch is designed so that it spends an equal amount of time in each position corresponding to the period of a reference signal, and to single out the component of the signal at a specific reference frequency and phase. Noise signals, at frequencies other than the reference, are rejected and do not affect the measurement.[25]
Bipolar Operational Power Supply/Amplifier (BOP)
BOPs are high speed power operational amplifiers that has two bipolar con-trol channels (Voltage or Current), selectable and individually concon-trollable either by their front panel, or by remote signals, and can provide dynami-cally agile voltage and current outputs for test and simulation. It can be also controlled via BIT plug-in cards for remote digital control.[3,12]
Model SR560 Low-Noise Preamplifier
The instrument provides DC-coupled low-noise amplification of input sig-nals at gains of 1 to 50.000. It also counts with two configurable R-C filters to selective condition signals in the frequency range from DC to 1MHz [26].
8904A Multifunction Synthesizer DC-600 kHz
The HP 8904A is a Multifunction Frequency Synthesizer that produces com-plex signals from six fundamental waveforms. The available waveforms are: dc, sine wave, ramp, triangle, square wave and noise. It counts with an option to add up to three more identical internal synthesizers which can modulate the synthesizer or be summed to the output. the equipment also counts with an option to fast hop between different phase, frequency, and amplitude settings [10].
Low Signal Differential Amplifier
The instrument was designed at Universidad de los Andes and is capable of the amplification of low amplitude signals from 100X to 2500X with a saturation at 10V. It counts with two input channels, A and B, and two output signals, A and A-B [28].
For the hysteresis curves method, the signal is amplified by the Differen-tial Amplifier 200 times .
DC Voltage Compensator
The instrument produces a DC signal ranging between 0 and 6 V with no noise level. It is powered with an internal battery that guarantees zero noise level [27].
3.4 data acqisition software
LabView (Laboratory Virtual Instruments Engineering Workbench) is a plat-form and a development environment from National Instruments (NI), de-signed for linking different data acquisition equipment through a DAQ card (data acquisition card), and the programming of the acquirement, process-ing and the interface for data visualization. This software worked as a basis for the data acquisition of the different experiments and calibrations. The following programs were developed on the LabView platform at the Elec-tronics Laboratory of the Department of Physics at the Universidad de los Andes.
Servo-Motor Controller
This program allows the control and automation of the motorized goniome-ter, which can rotate both the sample and one of the photodiodes in order to change the incident angle and capture the reflected light beam. This pro-gram can set the starting angle for the experiments that require an angle sweep.
3.4 data acqisition software 23
Figure 13.: Laser Alignment Software. The interface allows to visualize the current angle for each motor of the goniometer and to set the starting angle for the SPR Main Program.
KEPCO Current Source Controller
This program communicates with the KEPCO power supply and allows to control the current flowing through the coil as a constant function in order to permit measurement of the magnetic field with a Hall effect sensor. Then it shows a reading of both the current and voltage for further calibrations of the equipment and the readings from other programs.
Figure 14.: KEPCO Current Source Controller.
SPR Main Program
This program allows to characterize the Surface Plasmonic Response by do-ing an angle discrete sweep and a readdo-ing of the reflected light beam onto the photodiode for each change in the angle. Here, the Voltage of both the photo-diode 1 and photophoto-diode 2 are read in order to obtain a reference for the inci-dent beam and correct the reflected reading. The program writes a file with the readings of: the magnitude of the Voltage for both photodiodes; current;
the sign for the voltage; a calculation of normalization for the first photodi-ode readings following thatVnorm =V1/VIncident Beam=V1/(V2/C)with
Vias the reading for each photodiode, andCas the constant that relates the
reference reading and the incident beam separated by a beam splitter, such asVIncidentC=Vre f.
On the other hand, it counts with a mode for T-MOKE characterization. It takes advantage of a the external square signal that defines the behavior of the magnetic field from the T-MOKE configuration, and calculates the maximum and minimum reflectance for each angle for the incident beam in order to calculate theKerrSensitivity = ∆II, write a file, and plot the value with
respect the angle. This method is phase sensitive, and filters out information that is out phase.
Figure 15.: SPR Main Program.
In pursuance of the Surface Plasmonic characterization mode or the T-MOKE characterization using either the Phase senssitive or the hysteresis loops method, it is required to set different parameters for the Lock-In, the Synthesizer and the program (Tables2,3,4and5).
DC Mode AC Mode Hysteresis loops Mode
Amplitude 1V 1V 1V
Frequency 1kHz 3Hz 3Hz
Waveform Sine Square Sine
Phase 0 0 0
3.4 data acqisition software 25
DC Mode
(Optical Characterization)
AC Mode (MO Characterization)
Time Constant 10µs 3s
Signal Input A−DC−GRD A−AC−GRD
Sensitivity 1V 5mV
Reserve NORMAL NORMAL
Filters LINE LINE
Channel One R-DISPLAY R-DISPLAY
Channel Two Y noise-DISPLAY R-DISPLAY
Reference SINE-EXTERNAL SINE-EXTERNAL
Table 3.: Lock-In Operation Parameters
DC Mode AC Mode
Step Waiting (ms) 1000 15000
Step Delay (ms) 0 20000
STEPS-MOTOR 1 15 15
Direction-MOTOR 1 CW CW
STEPS-MOTOR 2 30 30
Direction-MOTOR 2 CW CW
PARAMETRO T Ciclos Ciclos
Frequency (Hz) 0 0
B Offset 1.5133 1.5133
Tiempo (s) 1 1
# Ciclos 1 1
Start Angle 35 35
Stop Angle 65 65
Cte 18.31 18.31
Table 4.: LABVIEW Program Operation Parameters
DC Mode AC Mode Hysteresis loops Mode
Filter Cutoff 10Hz 10Hz 10Hz
Coupling DC DC DC
Source A A A
Invert O f f O f f O f f
Gain Mode Low Low Low
Gain 1X 1X 10X
T-MOKE Experiment Program
The T-MOKE Experiment allows to visualize and write a file with indefinite cycles of hysteresis loops. These cycles can be processed by taking advan-tage of the number of samples per Channel and by taking a mean of the reading for the number of sample for each cycle.
Part III
4
AC Q U I R E D D ATAThe samples
The samples object of this thesis, are a set of Au/Co/Au continuous multi-layer samples and thin films of Ag. The thickness of the Au/Co/Au and the Ag samples can be seen at the Table 6. The Au/Co/Au samples were used for the experiment in Ref. [9], where only the 21B and the 28B samples were chosen because they were in good condition.
Sample Material Thickness(nm) Sample Material Total
Thickness (nm)
21B Au/Co/Au 27.3/7.8/3.5 S1 Ag 47.3
28B Au/Co/Au 14.1/10.2/5.0 S2 Ag 48.6
01M Au/Co/Au 11.6/10.2/3.0 S3 Ag 47.8
Table 6.: List of the thickness of the material layers in the samples. The sample 01M was grown on the course of the experiment by Edgar Patiño.
The samples, Au/Co/Au and Ag, were characterized under SPR while the Au/Co/Au [21B] was characterized for both the methods presented to ob-tain the T-MOKE characterization. The non-labeled Au/Co/Au sample was characterized under the phase sensitive method for the T-MOKE characteri-zation.
The sampleS1was deposited 117 days before the data final measurement day, displayed in this work, while theS2sample was grown 50 days before the final measurement day, and the sampleS3was grown the same day that it was optically characterized.
model for optical characterization
A model that follows the eq.11, programmed in the work of Cesar Herreño[9], shows the theoretical behavior of the optical characterization for a single material deposited as a thin film over a substrate. The model considers dif-ferent parameters of wavelength of the inciding beam, type of material (Au, Ag, Cu) and thickness of the deposited material (Fig.17).
4.1 optical characterization for ag and au/co/au samples 29
Figure 17.: Graph for the theoretical model of the optical characterization in a thin film of Ag. a) shows the behavior under an inciding green laser of wave-length 532nm, and b) shows the graph for a red laser of wavewave-length of 732nm.
4.1 optical characterization for ag and au/co/au samples
The angular SPR characterization technique was applied to the samples at the plasmonic set-up located at the superconductivity laboratory at the Uni-versidad de los Andes. Here, as mentioned in previous chapters, the angle where the total reflection and the plasmonic excitation are reached, can be observed.
First of all, the measurement were made on the S1 and the S2 samples (Fig.18). As mentioned before, these samples contain a thin film of Ag, thus
the data obtained can be compared with the model made back at Sec.(1.1). The obtained data shows the mentioned normalized reflectance, which for convenience is denoted re-iteratively as Rnorm = R1/C·R2, where R1 is the measured reflectance,Cis the ratio between the incident beam andR2, which is the reference measurement.
After that, the technique was applied to the samples 21B and 28B, which are the Au/Co/Au trilayers (Fig.19).
Figure 18.: Graph of the SPR angular characterization for the S1, S2 (a) and S3 (b) samples. The S1 and S2 samples have 47.3nm and 48.6nm of thickness of Ag material respectively. The sample S3 has 47.8nm of thickness of Ag.
4.1 optical characterization for ag and au/co/au samples 31
Figure 19.: Graph of the SPR angular characterization for the 21B and 28B samples.
Posterior to this, a realignment of the inciding beam was done and the sample S2 was again characterized. This realignment led to a change in the angle of plasmonic excitation and the angle for total internal reflection (Fig.20).
Figure 20.: Graph of the SPR angular characterization after realignment of the S2 sample
magnetic field characterization
The coil used for the MO characterization was previously described by us-ing a teslameter positioned under the center of the iron nucleus at a static distance of2.5mm±0.5mm, same as the distance of the incident plane to the same iron nucleus. Then, a current sweep test ranging from0to2Awas performed in order to identify the behavior of the magnetic field related to the current.
Figure 21.: Graph of the magnetic field associated to multiple values of current ap-plied to the coil. With the apap-plied current, the voltage was measured in order to determine the variation of the resistance of the coil by changes of temperature, which led to consider a linear dependence.
4.2 mo characterization for the A u/C o/A u sample with a phase sensitive method
As previously stated, the T-MOKE characterization consists on obtaining the intensity of the reflected beam in Transversal configuration for the MOKE experiment. The data obtained indicates the phase-sensitive changes in this measured intensity using the Lock-In Amplifier with, as phase reference, the frequency of the changing magnetic field. The results manifest a change of intensity depending on the incident angle (Fig.22).
4.2 mo characterization for the A u/C o/A usample with a phase sensitive method 33
Figure 22.: Graph of the MO characterization for the 21B and 28B samples, using the phase sensitive method through a Lock-In Amplifier.
After a realignment, the phase sensible T-MOKE characterization tech-nique was applied to a grown sample of Au/Co/Au with thickness of 11.6/10.2/3.0nmrespectively (Fig.23).
Figure 23.: MO characterization after realignment of the Au(11,6nm)/Co(10,2nm)/Au(3,0nm) sample.
4.3 mo characterization using hysteresis loops for theA u/C o/A u sample
Another way to obtain the MO characterization is by acquiring the inten-sity change of the reflected beam from the hysteresis loop produced at the remanence of the magnetic field over the sample.
When the signal is captured from the set-up, it was filtered and then am-plified 2000 times in order to be able to observe the changes and manipulate the signal. Then, after processing, this amplification can be taken into con-sideration and reduced from the obtained data.
As mentioned before, the acquired data is a composition of IMeasured = IAC+IDC, where IDCmust be eliminated from the total signal by using a
compensator and differential amplifier. This DC or offset from the compen-sator is manually controlled and its difficult to reduce the observed DC signal to 0V, then, in order to reduce this offset, the maximum and the minimum values from the remanence were obtained and the mean between them was acquired and subtracted from the array of data.
Figure 24.: Hysteresis loop for the 21B sample at 50 Degrees before (a) and after (b) piling the multiple cycles of data.
The obtained data reflects various cycles of 1000 data points each , which are distributed through the periodic signal used as reference for the magnetic field, measurement made for different angles. In order to reduce these points, one can take the mean per position of each one of the 1000 data points, i.e. piling the data to a single cycle composed of the means for each of the 1000 data positions between all the cycles (Fig.24). By this, a single cycle is ob-tained, where the maximum and minimum values for the remanence can be subtracted and therefore the∆Rcan be acquired for each angle, which can be compared with the phase sensitive method.
4.3 mo characterization using hysteresis loops for the A u/C o/A usample 35
Figure 25.: Hysteresis loops for the 21B sample taken from different angles.
5
A N A LY S I S O F R E S U L T S A N D D I S C U S S I O NThe studied samples are a set of Au/Co/Au trilayers and Ag thin films, de-posited on cover slip. The dede-posited material thickness varies from sample to sample, which allows to retrieve different outcomes when the optical and MO characterization techniques are applied. From the set of Au/Co/Au sam-ples grown in the work of Cesar Herreño[9], only a few were avaiable for using in this experiment, either because of poor handling or a degradation of the sample.
First of all, the changes in the experimental set-up allowed to take an intensity reference at any time, in order to normalize the data with the in-troduced beam splitter and photodiode. This change enabled to measure and normalize data without requiring to obtain an intensity reference in a different time than the acquirement of the experimental data. Another in-troduced optical device was the lens, which allowed to focus the laser beam before taking a reference and passing through the Kretschmann configura-tion, whilst the previous configuration had a set of lens after passing through the Kretschmann configuration, which could produce a drop of reflected in-tensity, resulting in the record and normalization of information that not only was affected by the experiment but the set of lens.
The optical characterization allowed to observe the angle at which the total internal reflection and the SPP excitation is reached for a certain set of materials in a configuration of layers. Initially, the technique was applied to thin films of Ag, grown at different dates with different thickness from one sample to another. The sampleS1was deposited 117 days before the data final measurement day, displayed in this work, while the S2 sample was grown 50 days before the final measurement day. The handling through this lapse of time could produce a degradation of the sample, which could explain the change in the maximum value recorded for each sample and the difference in the plasmonic excitation angle seen in Fig. 18. The sample S3was characterized on the same day that was grown, but it is noticeable that the normalization was not well applied. From the18, the effects of the degradation of the samples through the time is noticeable, the angle where the plasmonic excitation is reached is displaced to a longer angular distance through the time. On the other hand, the lecture in the reference photodiode varies irregularly, which produces an error to the lectures.
The optical characterization technique was applied to the 21B and 28B samples. Here, the total internal reflection and the plasmonic excitation were also manifested. In contrast with the single layer of Ag, the trilayer of Au/Co/Au takes a wider angle to reach a small percentage of the initial reflectance. This difference reflects the effect that an interface with various materials produce in the plasmonic excitation, leading to the known sensi-tivity of the technique to the materials, which is basis of some bio-sensors.
Subsequently, the MO characterization technique gave evidence of con-trolling the intensity of the reflected beam, which is the basis for reading data from a magnetic disc in a MO recording device. The changes depending on the incidence angle on the sample can be recorded by using two meth-ods, a phase sensitive method and by recording the difference of reflected
intensity in the remanence of the hysteresis curves. The first method allows to obtain a reading of the maximum AC value coinciding with the refer-ence phase, which was the same as the used for the magnetic field, while the second method records the changes in the hysteresis curve produced by plotting the reference signal and the MO behavior of the material, which follows a sine and square-like signal respectively. A difference in reflected intensity from the saturation points in the hysteresis curves would be more close to the value obtained from the phase sensitive, however, the second method is vulnerable to containing components with a different frequency, thus the pre-processed signal has to be filtered (An example for this can be recognized from appendixC).
Figure 27.: Comparison between MO characterization methods for the 21B sample, which are the phase sensitive method and the delta remanence acquisi-tion from hysteresis curves method.
The second method (∆Racquirement from hysteresis curves) has the same behavior than the first method (phase sensitive), which leaves as factible the possibility to scale the second method in order to acquire the data from the first method.
Offset at the Optical and MO characterization techniques
The data obtained by the optical characterization technique can be compared with a model that follows the eq.11, programmed in the work of Cesar Her-reño, which can be used for continous layers of material such as the Ag layer in the present experiment. By doing the comparison, a possible attribute to consider in the samples is that the alignment of the laser beam and the sam-ple can produce an offset in the angle of incidence, which can be appreciated by comparing the angle at which the total reflection is reached. This offset appears in the angle of all the techniques.
analysis of results and discussion 39
Figure 28.: Optical characterization and model for the S1 and S2 samples. Then again, the S1 and S2 samples have 47.3nm and 48.6nm of thickness of Ag material respectively. In the graph below, take into consideration that each pair of curves (result - model) is separated by an offset.
This offset, manifested in the angle, led to a realignment of the incident beam and the posterior data acquisition of the S2 sample from the optical characterization. After acquiring this data, the angle of total internal reflec-tion and the angle of plasmonic excitareflec-tion are translated, which allows to consider to take this translation as the mentioned offset and redo the re-alignment process until the angle of total internal reflection matches with the theory (Fig.29). However, the behavior of the curves, before and after the realignment, is the same. The curves shows that the plasmonic excitation is reached after the Total internal reflection is obtained, separated by around 5 degrees, and different from the model by recognizing that the sample takes a wider angle to enter and exit the plasmonic excitation.
Figure 29.: Optical characterization and model for the S2 sample.
After the process of realignment, a measurement using the phase sensible MO characterization technique over a grown sample of Au(11,6)/Co(10,2)/Au(3,0) was done and compared with the MO characterization data from the B21 and B28 samples, acquired before alignment.
Figure 30.: MO characterization for the 28B, 21 and Au(11,6)/Co(10,2)/Au(3,0) sam-ples. Data acquirement of the samples 21B and 28B before realignment, while the Au(11,6)/Co(10,2)/Au(3,0) was acquired after realignment.
Part V
6
C O N C L U S I O NFirst of all, the changes of the experimental set-up from the experiment per-formed by Cesar Herreño and Edgar Patiño [9], allowed to normalize the reflected intensity and allowed to focus the incident beam and the reflected beam onto the sample in the Kretschmann configuration and onto the sensor respectively, without the possible effects that can produce an optical device located in the reflected beam path.
The optical characterization allowed to recognize the angle where the plasmonic excitation is reached by using as reference the total internal reflec-tion. It was also recognized that the degradation of the samples (in the case of the set of Ag samples) produced an angular displacement, i.e. a longer lapse of time between the growing event and the measurement, produced a bigger angular displacement. A better estimation of the angles where the total internal reflection and the plasmonic excitation are reached could be ac-quired by performing a realignment that reduce significantly the mentioned angle offset. After reducing this offset, it is found that the plasmonic excita-tion is reached in a Ag monolayer below 48 degrees and above 40 degrees. In the case of the Au/Co/Au monolayer, the angle varies depending on the thickness of each layer and the quality of the samples, leading to an angle for plasmonic excitation ranging between 47 and 55 degrees for the studied trilayers. After reaching the plasmonic excitation, the monolayers retrieve a significant percentage of the maximum intensity for the reflected beam in a smaller angular displacement than in the case of the trilayers.
In both, the Ag monolayer and the Au/Co/Au trilayer cases, a poor han-dling and the degradation of the samples affects significantly the characteri-zation, until the point that the sample could not be useable. The degradation effect on the characterization techniques is encouraged to describe in further experiments.
For the T-MOKE experiment, tha characterization can be done by using either the phase sensitive method, or the∆Rcalculation from the remanence in the hysteresis loops method. Both techniques lead to the same behavior in a curve, curve dependant of the incident angle and parameters of the applied magnetic field.
Part VI
A
W I R I N G A N D E X P E R I M E N TA L S E T- U P S C H E M AT I C SFigure 31.: Schematics for the Experimental Set-Up
wiring and experimental set-up schematics 45
Figure 32.: fig:Schematic of the wiring for reflectivity spectra characterization and phase sensitive MO characterization.
Figure 33.: Schematic of the wiring for the Magneto-Optic Characterization by ac-quiring Hysteresis loops.
B
D I S P E R S I O N R E L AT I O N O F S P S O N A S U R FAC E O F AS E M I - I N F I N I T E S O L I D
The layer system has an interface(1|2), on which a p-polarized wave prop-agates in thexdirection, thus noydependence. The fields in the media(1), (2)are described as:
z>0,H2= (0,Hy2, 0)exp i(kx2x+kz2z−ωt) (18)
E2= (Ex2, 0,Ez2)exp i(kx2x+kz2z−ωt)
z<0,H1= (0,Hy1, 0)exp i(kx1x−kz1z−ωt) (19)
E1= (Ex1, 0,Ez1)exp i(kx1x−kz1z−ωt)
Fields that have to satisfy the Maxwell equations.
∇ ×Hi =ei
1 c
∂
∂tEi (20)
∇ ×Ei =−
1 c
∂
∂tHi (21)
∇ ·(eiEi) =0 (22)
∇ ·Hi =0 (23)
and by fulfilling the continuity relations,
Ex1 =Ex2 (24)
Hy1 = Hy2 (25)
e1Ez1 =e2Ez2 (26) which leads to obtain from the fields that:
kx1=kx2 =kx (27)
The Maxwell eq. gives:
∂Hy
∂z =− e c
∂Ex
∂t
∂Hy
∂x = e c
∂Ez
∂t
1 c
∂
∂tHy =− ∂Ex
∂z + ∂Ez
∂x
that causes that:
kziHyi=∓eiExi
ω
c (28)
kxHyi=−eiEz
ω
c (29)
ω
c Hyi =∓Exkzi−Ezkx (30) and using the continuity relations:
Ex
Hy
ω c =−
kz1
e1
= kz2 e2
kz2
e2
+ kz1 e1
=0 (31)
which is the dispersion relation of the SPs propagating in a interface be-tween two media. On the other hand, we obtain:
ω c
2
=∓ Ex
Hyi
ω ckzi−
Ez
Hyi
ω ckx
ei
ω c
2
=k2zi+k2x (32)
and with the dispersion relation, the following equation can be obtained:
kz2
e2
+ kz1 e1
= s
ω2 c2e 1
−k2x
e21 +
s ω2 c2e 2
− k2x
e22 =0
ω c
21
e1
− 1
e2
=k2x
1
e21
− 1
e22
ω c
2 e
2e1
e1+e2
=k2x (33)
we can assume the mediume2 = 1(air) and e1 < 0(metal),|e1| > 1, thenkx > ω/candkzi becomes complex. The fields have their maximum
in the surface at z = 0 and decay exponentially in both directions, as is characteristic for plane waves.