1. X-Ray Resonant Reflectivities
at FEL Sources
Masterarbeit
zur Erlangung des akademischen Grades
Master of Science
(M.Sc.)
der Universit¨at Siegen
Department Physik
vorgelegt von
Billal Pervaz
Juli 2016
4. ABSTRACT
Our idea is to study magnetic properties and spin diffusion in a magnteic
tri-layer system. We measured resonant magnetic reflectivities by using ex-
treme ultraviolet (XUV) radiation. We used femtosecond pulses of x-ray free
electron laser (FEL) for the first time to measure magnetic reflectivities em-
ploying the x-ray magnetic circular dichroism (XMCD) effect. We performed
the experiment at FERMI seeded FEL, Trieste, Italy. Despite the challenges
of the fluctuating machine parameters, we were able to record first ever mag-
netic reflectivities at M edges. The measured asymmetries also hint the effect
of the high fluence of x-rays on the absorption of the material.
5. Motivation
The ultrafast magnetisation dynamics arised as a new research field with
the discovery of the magnetization dynamics on femtosecond (fs) timescale
dating back to 1996 by Beaurepaire et al. [1]. They showed a decrease of
the magnetization of a thin Ni film to almost 50% of its actual value during
the first picosecond (ps) after excitation with a 60 fs laser pulse. They used
Magneto-optical Kerr effect (MOKE) for measuring the magnetization in this
all-optical pump-probe experiment. The ultrafast demagnetization process
via the optical means is faster (which occurs at time scale of 100s of fs) than
the conventional magnetic means (which occurs at time scale of nanosecond
(ns)). The optical demagnetization being faster, makes it important for the
memory storage. The complete understanding of the phenomenon could play
a vital role in improving the speed of future data storage devices. Therefore,
the study of ultra fast demagnetization has been the part of many scattering
experiments since its discovery.
The detailed understanding of the phenomenon at ultrafast timescales needs
ultrafast probes. Ideally it is possible to measure ultrafast magnetization dy-
namics on the timescale of fs. Therefore, research in magnetization dynamics
steped forward with the advancement in instrumental development and new
experimental methods. Ultrafast demagnetization of a ferromagnetic sample
on a sub-ps timescale, could be best studied after fs pulsed lasers became
available, and the timescale of the observed effect was not faster than the
time resolution of the probe anymore. FEL is the most advanced source with
ultra short pulses to study the ultrafast magnetisation dynamics. It allows
the pump probe experiments with delay time in the range of fs.
The diffusion of spins is an important aspect to understand ultrafast mag-
netisation dynamics. Studies of spin transport as a mechnism of ultrafast de-
magnetisation was published by M. Battiato et al.[2]. They gave the theory
for spin diffusion which is explains the 50% of the ultrafast demagnetisation
on femtosecond timescale. Ultrafast spin transport is considered as the main
candidate of femtosecond demagnetization [2-4]. The change of magnetic do-
mains by pumping and the underling spin transfer mechanism was published
by B. Pfau et al.[5]. They used the Battiato’s spin theory to explain their
results.
6. Other interesting phenonmenon link with ultrafast demagnetisation includes
magnetization enhancement by super diffusive spin currents in try-layer sys-
tem published by Rudolf et al.[6]. They reported optically induced demag-
netisation in the top layer of the trilayer (Ni/Ru/Fe) system produces en-
hancement in the magnetisation of the bottom layer (Fe).
Recently Boris Vodungbo et al. published about the indirect excitation of
ultrafast demagnetisation[7]. They explain the ultrafast demagnetization
without the direct influence of pumping photons on magnetic layer.
Most of the scattering studies for ultrafast demagnetisation has been per-
formed in transmission geometry and with simple mono or multilayer sam-
ples including the affect of spin orbit interaction[8-12]. We selected reflection
geometry to further explore the aspects of magnetic dynamics including the
spin dynamics and effect of ultrafast magnetic roughness. we want to explore
the spatial information and phenomenon occurring at the interfaces of layers.
Magnetic reflectivty at the resonant edges contains the spatial information
of the sample. This information is important to understand the phenomenon
of ultrafast magnetism.
7. 1. X-RAY REFLECTIVITY
X-ray reflectivity is one of the standard non-destructive methods to investi-
gate surfaces and interfaces. It gives information of charge density profiles
with sub-nanometer resolution.
1.1 Fundamentals of Reflectivity
The Helmholz equation can be used to represent the propagation of a plane
electromagnetic wave E(r) = E0exp(ik · r) in a medium of refractive index
n(r)
∆E(r) + k2
n2
(r)E(r) = 0 . (1.1.1)
With the assumption of electron act as harmonic oscillators with resonance
frequencies ωj, the index of refraction n(r) for a crystal of N atoms per unit
volume is expressed as
n2
(r) = 1 + N
e2
om
N
j=1
fj
ω2
j − ω2 − 2iωηj
, (1.1.2)
where ηj is the damping factor, ω represents the frequency of the incident
waves and fj represents the forced oscillation strength of electrons for each
electron. In general, fj is complex and requires absorption and dispersion
corrections
fj = fo
j + fj(E) + ifj (E) . (1.1.3)
For X-rays with frequencies ω >> ωj, eq 1.1.2 can be replaced by
n(r) = 1 − δ(r) + iβ(r) . (1.1.4)
The dispersion δ(r) and absorption terms β(r) are given by
8. Master Thesis 1. X-RAY REFLECTIVITY
δ(r) =
λ2
2π
reρ(r)
N
j=1
fo
j + fj(E)
Z
, (1.1.5)
β(r) =
λ2
2π
reρ(r)
N
j=1
fj (E)
Z
=
λ
4π
µ(r) , (1.1.6)
where re represents the classical electron radius re = e2
/(4π omc2
) = 2.814×
10−5˚A.
1.2 Reflection and Refraction
Fig. 1.1: Reflection and refraction of a plane wave with incident wave vector ki at
a flat surface. kf and kt represent the wave vectors for the reflected and
transmitted wave respectively [13].
Figure 1.1. represents a plane electromagnetic wave with wavevector ki strik-
ing a surface at a grazing angle αi. The wave is partially reflected (Er, αf =
5
9. Master Thesis 1. X-RAY REFLECTIVITY
αi) and transmitted as a refracted wave (Et) under the angle αt. αf and αt
stands for angle of reflected and transmitted waves respectively. The wave
amplitudes can be written as
E(r, t) = Eoei(ki·r−ωt)
, (1.2.1)
Er(r, t) = Erei(kf ·r−ωt)
, (1.2.2)
Et(r, t) = Etei(kt·r−ωt)
. (1.2.3)
The frequency and the wave vectors are related via
k =
2π
λ
=
ω
co
. (1.2.4)
Snell’s law, well known from optics is also valid for X-rays. During passing
from a medium with refractive index n1 to a medium with refractive index
n2, the angles of incidence and transmission are related through
n1 cos αi = n2 cos αt . (1.2.5)
For incidence angles below the critical angle αc total external reflection oc-
curs (αt = 0). Taking the first medium as air (n1=1) and the second with
refractive index (n2= 1 - δ) into the Snell’s law with (αt = 0) and using Tay-
lor series expansion for cosine, one can deduce the important relationship for
the critical angle
αc =
√
4πρero
k
=
√
2δ , (1.2.6)
with ρe is the electron density. For Cu-Kα radiation and silicon one obtains
a value of delta in the order of 10−6
and thus the critical angle αc is about
0.23◦
. Exponentially damped evanescent waves are generated below the sur-
face for incidence angles below the critical angle. This evanescent wave has
the penetration depth of the order sub-Angstrom.
For angles above αc, the transmitted wave enters the medium and is at-
tenuated by absorption with the medium. The penetration depth can be
expressed as
Λ =
1
2kIm(αt)
. (1.2.7)
6
10. Master Thesis 1. X-RAY REFLECTIVITY
Wave vector transfer ’Q’ is the parameter generally used in the discussion of
reflectivity and diffraction. Mathematically it is given as
Q = 2k sin αi . (1.2.8)
Mostly calculations and results in reflection geometry involve ’Q’ dependence.
1.3 Fresnel-reflectivity of a smooth surface
The Fresnel equations can be used to formalise the reflectivity from an ide-
ally smooth surface. We obtain the relation of the Fresnel reflection and
transmission coefficients for small angles
rF (αi) =
Er
Ei
=
(kiz − ktz)
(kiz + ktz)
=
αi − αt
αi + αt
, (1.3.1)
tF (αi) =
Et
Ei
=
2kiz
(kiz + ktz)
=
2αi
αi + αt
, (1.3.2)
where rF and tF represents the amplitude reflectivity and transmittivity re-
spectively. One gets the appropriate coefficients R and T for the reflected
and transmitted intensity via
RF (α) =
Ir
Ii
=| rF |2
, (1.3.3)
TF (α) =
It
Ii
=| tF |2
. (1.3.4)
Interfaces with roughness displays weaker intensities of reflected and trans-
mitted waves because off-specular reflection occurs. Here Fresnel reflection
and transmission coefficients can be replaced by
r = rF e−2kizktzσ2
, (1.3.5)
t = tF e(kiz−ktz)σ2/2
. (1.3.6)
7
11. Master Thesis 1. X-RAY REFLECTIVITY
1.4 Parratts recursive method
The Parratt formalism is a standard and exact calculation for reflection from
multilayer interfaces. L.G. Parratt introduced it to calculate the reflectivity
of multilayer system [14]. However, it can also be used to treat arbitrary
dispersion profiles.
Figure 1.2 shows the case of a system of N layers with the (N+1)th
layer
as substrate. i = 1 denotes the semi-infinite material through which the
incident wave is propagating. The wave field is transmitted through N layers
of thickness di until it is reflected from the substrate of infinite thickness i =
N + 1. At each interface i between the layers i and i+1, the transmitted wave
Ti separates into the reflected wave Ri, propagating through the layer i and
the transmitted wave Ti+1, propagating through the layer i+1. In addition,
the wave Ri+1, reflected from the interface i+1, interferes with those waves.
An electromagnetic wave of amplitude T1 = 1 impinges at the multilayer
structure. At each interface it is split into a transmitted wave Ti+1 and a
reflected wave Ri that interfere with the waves coming from the top (Ti) and
bottom (Ri+1) layer. Parratts recursive method links the reflectivity and
transmittivity coefficients, for the layer j to the coefficients of the layer j+1
below
Xj =
Rj
Tj
= e−2ikz,jzj
rj,j+1 + Xj+1 · e2ikz,j+1zj
1 + rj,j+1Xj+1 · e2ikz,jzj
. (1.4.1)
The reflectivity coefficients are calculated employing the change in the z-
component of the wave vector (kz,i = ki · ez)
rj,j+1 =
kz,j − kz,j+1
kz,j + kz,j+1
. (1.4.2)
Since the substrate has an infinite thickness there is no incoming reflected
wave RN+1. It follows that XN+1 = 0. With this starting point Eq. 1.4.1
can be applied recursively to retrieve all the coefficients Xi until the total
reflectivity of the multilayer can be calculated after N iterations
R = |R1|2
, (1.4.3)
since T1 = 1.
8
12. Master Thesis 1. X-RAY REFLECTIVITY
So far the calculated reflectivity is exact only for a multilayer system with
perfect interfaces. It does not include roughness. For a small roughness
(roughness d,) the effect of the roughness of the interfaces can be ap-
proximated by multiplying the reflectivity coefficients of each interface with
an exponential damping factor
rj,j+1 ≈ rj,j+1 · e−q2
zσ2
. (1.4.4)
The Parratt formalism can be used to solve an arbitrary dispersion profile
δ(z) by slicing it into small slabs of thickness dz. The dispersion of the slab
i at depth zi is δ(zi). Then this multilayer of small, but perfect slabs is
recursively solved.
9
13. Master Thesis 1. X-RAY REFLECTIVITY
Fig. 1.2: Reflection from N interfaces. At each interface a transmitted wave and
a reflected wave are created. These wave fields interfere with the incom-
ing waves, transmitted from the interface above and reflected from the
interface below [15].
10
14. 2. RESONANT SCATTERING AND XMCD
2.1 Introduction
The dispersion correction terms of the atomic form factor depends upon
photon energy. At the absorption edges these terms are called resonant
scattering terms. Recalling equation 1.1.3 as given below
f(Q, ω) = fo
(Q) + f (ω) + if (ω) ,
where the first term represents the charge scattering. It depends on the
scattering wave vector ’Q’. The resonant scattering discussed here is elastic
in nature. The electron changes its state by absorbing the photon and release
back the photon of same energy via an intermediate process.
The second term in the equation represents the real part of dispersion correc-
tions while the third term represents the imaginary part corresponding to the
absorption processes. One way to understand the resonant scattering is to
consider electrons as harmonic oscillators and the forced harmonic oscillator
shows resonance when the driving force is tuned to the frequency near the
resonance frequency.
2.2 The Oscillator model
Consider an electron as a single oscillator which is under the influce of an
electric field of electromagnetic waves with linearly polarisation along the
x-axis. The equation of the motion for the electron can be written as
¨x + Γ ˙x + ω2
s x = −(
eEo
m
)e−iwt
, (2.2.1)
where Γ ˙x represents the damping term.
15. Master Thesis 2. RESONANT SCATTERING AND XMCD
By using the above equation we can can end up with the following expression
for the disperion correction
χ(ω) = fs + fs =
ω2
s
ω2 − ω2
s + iωΓ
, (2.2.2)
where ωs represents the resonant frequency for the single electron, while
fs + fs corresponds the dispersion and absorption corrections respectively
for a single electron.
The plot for the dispersion correction is shown in the figure 2.1. we notice
there is a rapid change in the dispersion and absorption at the point where
the driving force corresponds the resonance frequency of the electrons. In-
dividually the real and imaginary part of the dispersion correction can be
given by the following expressions
fs =
ω2
s (ω2
− ω2
s )
(ω2 − ω2
s )2 + (ωΓ)2
, (2.2.3)
fs = −
ω2
s ωΓ
(ω2 − ω2
s )2 + (ωΓ)2
. (2.2.4)
This rapid change is important for the study of properties of material. The
change is also element specific.
2.3 X-ray Magnetic Circular Dichroism (XMCD)
2.3.1 X-ray Polarisation
X-rays are electromagnetic waves. The direction of the electric field deter-
mines the polarisation. Figure 2.2 represents circularly polarised X-rays.
There are two types for the circularly polarisation for X-rays. If the electric
field vector is changing its direction clock wise with respect to wave vector k,
it’s termed as right circularly polarised (RCP) X-rays. While if the direction
of the electric field is anti-clock wise it’s termed as left circularly polarised
(LCP) X-rays. In the figure red line represents the wave vector and the blue
stair case represents the electric field.
12
16. Master Thesis 2. RESONANT SCATTERING AND XMCD
Fig. 2.1: The real and imaginary part of the dispersion correction is plotted against
the ratio of driving frequency to single electron resonant frequency [16].
2.3.2 XMCD
X-ray Magnetic Circular Dichroism (XMCD) is a property of ferromagnetic
substances when they are studied by circularly polarised X-rays. It is basi-
cally the difference in the absorption of two circularly polarised X-ray waves.
The signal from XMCD experiments is proportional to change in absorption
which is used to study the magnetisation of the material. The circularly po-
larised waves consists of photons with certain Jz eigenvalue. RCP and LCP
has Jz values + and - respectively. This fact invokes selection rules for the
transition of electrons to ensure the conservation of angular momentum.
For the understanding of the selection rule in the XMCD effect we start
with a simple model of eight electrons. A possible transition from 1s to 2p
is restricted by the dipole selection rules (∆l=±1) and (∆m=+1) for RCP
while (∆m=-1) for LCP. ’l’ and ’m’ represent the angular quantum number
and the magnetic quantum number, respectively.
13
17. Master Thesis 2. RESONANT SCATTERING AND XMCD
Fig. 2.2: Schematic of the circularly polarised X-rays [16].
Fig 2.3 represents the simplified model for the eight electrons. The electronic
configuration is 1s2
, 2s2
, 2p4
. This means that two empty states are available
in 2p level. When the system is illuminated with RCP the transition of
electron from |0, 0> to |1, 1> is allowed for RCP(left) while the transition
from |0, 0> to |1, -1> with ∆m = -1 is not possible as all states are filled.
Therefore LCP has low absorption probability for the given model and the
photon with right polarisation has high probability to get absorbed. The
difference in the absorption between right and left gives rise to the XMCD
effect.
The sample which are used for the experiments are discussed in details in
chapter 5 (subsection 5.1.1). Iron is the ferromagnet which has been used
in the sample. Iron has configuration 1s2
, 2s2
, 2p6
, 3s2
, 3p6
, 4s2
, 3d6
. The
transition from 3p to 3d contributes to the M2,3 edges with ∆m = 1.
14
18. Master Thesis 2. RESONANT SCATTERING AND XMCD
Fig. 2.3: Simple electron model for 8 electron[16].
2.4 Magnetic Resonant Scattering
The experiment at FERMI was performed at the M edge of iron which is
sensitive to magnetic moment. Magnetic scattering away from the edges is
order of magnitude lower than the corresponding charge scattering signal. At
resonance conditions the scattering amplitude is much higher and is given by
fres
n = (ˆk · ˆk)f(o)
n − i(ˆk × ˆk) · ˆmnf(1)
n + (ˆk · ˆmn)(ˆk · ˆmn)f(2)
n , (2.4.1)
where ˆk and ˆk are the unit vectors of the E-field.(’) notation is used for the
scattered wave. ˆmn represents the the unit vector for the magnetic moments.
The first term in equation 2.4.1 depends on the charge distribution with
no effect from the magnetisation. The second term has contribution from
magnetism and gives rise to the XMCD. The third term represents the X-ray
linear dichorism (XMLD) effect. Moreover, the third term is quadratic in ˆmn
and is not dependent on the direction of magnetisation. The XMLD effect
is much weaker then the XMCD effect and is not considered in the following
section.
15
19. Master Thesis 2. RESONANT SCATTERING AND XMCD
2.5 XMCD for Reflectivity
In the reflectivity geomentry the XMCD effect is measured in terms of the
asymmetery(A) which is
A =
I+ − I−
I+ + I−
∗ 100 , (2.5.1)
where I+ and I− represent the reflected intensities and the subscript’+’ and
’-’ represents RCP and LCP respectively.
The reflected intensity is proportional to the square of the form factor and
if we are taking resonance into account then the following expreession would
evolve
I± = |fc ± fm|2
, (2.5.2)
I± = |f2
c + f2
m ± 2fc · fm| . (2.5.3)
If we use the values 2.5.3 in equation 2.5.1 then we can deduce that A ≈
fcfm. Alternatevely we can say that the asymmetry is the charge-magnetic
interference term.
The second term of equation 2.4.1 for circularly polarised light gives the
following results
( ˆk± × ˆk±) · ˆmn = ±
i
2
(ˆk + ˆk) · ˆmn +
1
2
(ˆk × ˆk) · ˆmn . (2.5.4)
If we use equation 2.4.1, 2.5.1-4 then we can deduce the following result for
the asymmetry
A ∝ |(ˆk + ˆk) · ˆmn|2
. (2.5.5)
k’ and k in the figure 2.4 represents the unit wave vector of reflected and
incident wave respectively. Equation 2.5.5 suggests that the magnetisation
vector should be in ’y’ direction to have the maximum A as k+k’ would yield
a vector prallel to ’y’ axis.
16
20. Master Thesis 2. RESONANT SCATTERING AND XMCD
Fig. 2.4: Coordinate system for magnetic moments.
17
21. 3. ULTRAFAST DEMAGNETIZATION
3.1 Discovery
The discovery of ultrafast demagnetisation process by Beaurepaire et al. in
1996 [1] ignited the debate of its mechanism. They studied the relaxation
process of electrons and spin systems in Nickel after the absorption of fs laser
pulses. Ferromagnets experience demagnetisation via optical means at ultra-
fast timescales generally in order of fs. Before Beaurepaire’s experiment there
has not been much attention to magnetic effects occuring on fs timescale.
Fig. 3.1: (a) Experimental pump-probe setup allowing dynamic longitudinal Kerr
effect and transient transitivity or reflectivity measurements. (b) Typical
Kerr loops obtained on a 22 nm thick Ni sample in the absence of pump
beam and for a delay ∆t = 2.3 ps between the pump and probe pulses.
The pump fluence is 7 mJ cm−2.[1].
Optical pulse of fs length can produce a nonequilibrium electron gas which
subsequently thermalizes to Fermi distribution via electron-electron interac-
tions. This process takles place within about 500 fs[19,20]. Electron-phonon
interaction is the next process in the range of 1-10 ps which helps electron
22. Master Thesis 3. ULTRAFAST DEMAGNETIZATION
gas to release its energy to lattice. These time-scales are slower than the
magnetic effects occurring on the femtosecond time scales.
Time resolved magneto-optical Kerr effect (MOKE) configuration was used to
measure the spin dynamics. Fig. 3.1(a) represnets the longitudinal MOKE
setup and (b) represents the hyterisis loop for non-pumped and pumped
sample. Figure 3.2 shows the complete magnetisation dynamics for a laser
fluence of 7mJ/cm2
. There is a rapid decrease in the magnetisation in first
two ps.
Fig. 3.2: Transient remnant longitudinal MOKE signal of a Ni(20 nm)/MgF2(100
nm) film for 7 mJ cm−2 pump fluence. The signal is normalized to the
signal measured in the absence of pump beam. [1].
In conclusion they reported fast sub-ps demagnetization in metallic nickel
films can be induced using fs optical pulses. The sharp demagnetization is
followed by long relaxation state. Laser-induced demagnetization reveals in-
teresting path for magnetic memory storage with unprecedented speeds [17].
However, despite the technological attraction the phenomenon underlying
the concept is still highly disputed.
19
23. Master Thesis 3. ULTRAFAST DEMAGNETIZATION
3.2 Door to new scientific research
The discovery of ultrafast demagnetisation pave the path for theories and new
experiments to explain the phenonmenon. The underneath scientific quest is
how a laser pulse can change the magnetic moment [8, 9, 18, 19].The existence
of an ultra-fast channel for the conserving of spin angular momentum has
been part of many studies [20-24]. Various such mechanisms which discuss
electron spin-flip in a ferromagnetic metal are being investigated. The highly
debated mechanisms for a fast spin-flip process are a Stoner excitation, an in-
elastic magnon scattering, an Elliott-Yafet-type of phonon scattering [20,21],
spin-flip Coulomb scattering [22], laser-induced spin flips [23,25], or relativis-
tic quantum electrodynamic processes [24]. Spin-polarized transport of laser
excited hot electrons is relatively new investigated phenomenon in the ultra-
fast-magnetism theory, it is considered to have a little role in spin transport.
The ideas of ultra fast quenching of ferro-magnetism has been discussed by
J. Wang et al.[26].
During ultrafast demagnetization of a ferromagnet, angular momentum must
be transferred between the electrons and phonons in the system on femto-
and picosecond timescales in order to follow the conservation law. Battiato
et al [2] shows calculation for spin-dependent transport of laser-excited elec-
trons provides a considerable contribution to the ultrafast demagnetization
process and can even completely explain it. They developed a model that
explains laser driven fs demagnetization on the basis of spin angular momen-
tum conserving super diffusive transport. They showed that approximately
50% of ultrafast demagnetization is created within 200 fs without invoking
the spin-flip channels. They showed that the super diffusive spin transport
plays a major role in first few hundred femto-second. B. Pfau et al. [5]
reported the experimental evidence of ultra fast spin transport.
3.3 Spatial Resolution
So far the focus for scattering studies of ultrafast demagnetisation studies
remained on homogeneous samples and transmission geometry experiments
to understand the demagnetization on ultrafast timescales. There has not
been much emphasis on spatial resolution. Femtosecond X-ray free laser
sources provides the ultrafast time resolution, the magnetic sensitivity and
the short wavelength radiation to probe interfaces and in-depth profiles.
20
24. Master Thesis 3. ULTRAFAST DEMAGNETIZATION
At the resonant edges the information regarding the magnetic structure can
be obtained by tuning the beam energy to the energies of resonant edges.
The reflectivity at the resonant edges with circularly polarised light allows
to deduce the XMCD signal which depends upon the magnetic absoption.
Magnetic reflectivity yields information about surface averaged spin-profiles
perpendicular to the sample surface and overall roughness parameters.
From magnetic reflectivity experiments, quantities such as the interlayer
roughness (magnetic and chemical) can be deduced. Thus the results of
ultrafast magnetic reflectivity experiments can bring information of spin dif-
fusion and transport processes perpendicular to interface structures.
21
25. 4. FREE ELECTRON LASER
4.1 Introduction
Free Electron Laser (FEL) is most advanced X-ray source which produces
X-rays with unprecented coherence, ultra-high brilliance and time structure.
This capability makes FEL a source of new studies. Holographic and lensless
imaging in materials science and biology requires coherrent sources e.g. ul-
trafast intense coherrent pulses made the meausurement of protein molecular
structure possible under native conditions and without radiation damage to
cells has been achieved via FEL pulses. The high intensity FEL beam with
ultra-shot pulse also used in pump-probe experiment to investigate optically
disturbed systems on ultra short timescale.
Fig. 4.1: Simulation of a temporal (left) and energy (right) FEL Profile [27].
An important characteristic of radiation sources is the pulse duration. Ultra
short, sub-picosecond radiation pulses are needed to perform investigations
26. Master Thesis 4. FREE ELECTRON LASER
in the field of ultrafast magnetism covering not only the structure of a sample
but also its dynamics during irradiation. Free Electron Lasers (FEL) have
the potential to produce light pulses with sub-picosecond pulse lengths. Fig
4.1 shows a simulation of temporal (in sub pico-second range) and energy
(narrow peak at 124 eV) profiles of FEL. The short pulses of some hundreds
of femtosecond are necessary to probe the magnetisation processes which
occurs at ultrafast timescale.
4.2 FEL Working Principle
G. Margaritondo and Primoz Rebernik Ribic published a simplified descrip-
tion of X-ray free-electron lasers [28]. Electron bunches travelling close to
the speed of light experiences optical amplification inside a linear accelerator
(LINAC). These bunches in the undulator emit radiation while going through
a periodic path deviation as shown in fig 4.2 (a) and (b). The magnetic field
of the undulator is responsible for the slight undulation of the electrons.
Electrons at relativistic speed with these oscillations and the corresponding
acceleration emit electromagnetic waves.
Assume that a given electron, after entering the undulator, emits a wave. The
velocity of electron and the B-field of the emitted wave produces a Lorentz
force which pushes the electrons to form micro bunches with a periodicity
equal to the emitted wavelength as shown in fig 4.2 (c) and (d). Micro-
bunches have electrons which oscillate all together under the magnetic field
of the undulator.
This fact has its consequences, firstly the wave intensity is proportional to
the square of the E-field, the total emitted intensity is proportional to N2
(N
is the number of electron in a bunch) rather than to N. Secondly the net wave
intensity is exponentially amplified along the undulator. Note that the start-
ing wave subsequently amplified could be an external electromagnet beam
injected along with the electron beam (a seed) rather than the spontaneous
initial emission of the electrons, this process is called seeding [29].
The amplification of the radiation takes place by energy transfer from the
electrons to the previously emitted wave. This is done via a negative work of
the force caused by the wave E-field. The time rate of energy transfer for one
23
27. Master Thesis 4. FREE ELECTRON LASER
electron is proportional to the product of the wave E-field magnitude times
the electron transverse velocity[28].
Fig. 4.2: Mechanism of a free-electron laser for X-rays. (a) The optical amplifica-
tion is produced by relativistic electrons in an accelerator and is activated
by a periodic array of magnets (undulator). (b) The first waves emitted
by the electrons trigger the formation of microbunches. (c) and (d) Con-
trary to non-microbunched electrons (c), the emission of electrons in mi-
crobunches (d) separated from each other by one wavelength is correlated
[28].
Microbunching is caused by the interaction between the electrons oscillating
in the transverse direction and the transverse B-field of the previously emitted
waves. The transverse velocity and the B-field produce a longitudinal Lorentz
force that pushes the electrons to form microbunches. The microbunching
24
28. Master Thesis 4. FREE ELECTRON LASER
Lorentz force is proportional to the transverse electron velocity and to the
wave B-field strength [28].
Relativity explains how the emitted wavelength are in the X-ray range. The
electron speed is close to speed of light c, when it enters the undulator. The
undulator transverse B-field in the electron reference frame fig 4.3(a), after
a Lorentz transformation, becomes the combination of a transverse B-field
plus a transverse E-field fig 4.3(b), traveling together at a speed close to c
[28]. This combination resembles with electromagnet waves. The wavelength
of this wave is given by the undulator period corrected for the relativis-
tic Lorentz contraction in the electron reference frame. In the longitudinal
direction the contracted length is L/γ, where γ is the relativistic γ-factor,
defined by the equation 1/γ2
= (1 − u2
/c2
) and proportional to the electron
energy γm0c2
(m0 = electron rest mass).
The electrons view the undulator as the electromagnet wave as shown in Fig
4.3(c). This wave causes the electron to oscillate and to emit waves of equal
wavelength L/γ (in electron’s frame of reference). The correction for Doppler
effect is required to get the wavelength in laboratory frame. Therfore, the
wavelength in the laboratory becomes L/2γ2
as shown in Fig 4.3(d).
Lorentz force on electrons forces them to form microbunches while travelling
inside the undulator. Assume that at a certain time (Fig. 4.4, top) the B-field
of the already existing wave and the electron transverse velocity vT create a
Lorentz force f pushing the electron towards a wave node. The electron and
the wave do not travel with the same velocity. The (u-c)difference creates
precisely the conditions for the microbunching to continue. In fact (Fig. 3,
bottom), as the wave travels over a distance L/2 in a time L/(2c), the electron
travels over a smaller distance Lu/(2c). This shift is approximately half of
wavelength of the existing waves[28].Thus, after one-half undulator period
both the electron transverse velocity and the wave B-field are reversed, the
Lorentz force keeps the same direction and microbunching continues.
25
29. Master Thesis 4. FREE ELECTRON LASER
Fig. 4.3: (a) The relativistic electron approaches the periodic B-field of the un-
dulator. (b) In the electron reference frame the undulator period L is
Lorentz-contracted to L/γ and the B-field is accompanied by a trans-
verse E-field perpendicular to it: the two fields resemble an electromag-
netic wave. (c) This wave stimulates the electron to oscillate and emit
waves of equal wavelength. (d) The (relativistic) Doppler effect further
reduces the wavelength in the laboratory frame, bringing it to the X-ray
range [28].
26
30. Master Thesis 4. FREE ELECTRON LASER
Fig. 4.4: The speed difference (c-u) between waves and electrons makes mi-
crobunching possible. Top: in this situation the longitudinal Lorentz
forces caused by the wave B-field BW and to the electron transverse ve-
locity vT push the electrons towards microbunching. Bottom: after the
electron travels over one-half undulator period, its transverse velocity is
reversed. The wave travels ahead of the electron by one-half wavelength:
its B-field is also reversed, the Lorentz force keeps its direction and mi-
crobunching continues [28].
4.3 FERMI
The experiments were performed at the Diffraction and Projection Imaging
(DiProI) beam line at FERMI, the Elettra free-electron laser. The beam
line is designed to perform vearious types of experiment including static
and dynamic scattering experiments. The various schemes for time-resolved
experiments can be employed with both soft X-ray FEL and seed laser IR
radiation. There is a possibility of reflection geometry scattering experiments
27
31. Master Thesis 4. FREE ELECTRON LASER
which gives possibility for both high lateral and depth resolution.
Fig. 4.5: Layout of the FERMI-FEL and IR laser beam lines delivering FEL and
IR light to the DiProI end-station[30].
The experiment chamber of DiProI receives the FEL beam which is controlled
and monitored via gas chamber and beamline optics. It also hosts a dedicated
IR beam line for laser-seeded experiments as shown in fig 4.5. The beam
line has two sources FEL-1 and FEL-2. Both operates in different energy
ranges (FEL-1: 20-100 nm and FEL-2: 4-20 nm). The IR Laser can be
synchronised with FEL according to the need of the experiment. The beam
line has gas cells to change the intensity of the beam as per the requirement of
the experiment. The KB system is used to deviate the beam in the direction
of the sample and for focusing.
28
32. Master Thesis 4. FREE ELECTRON LASER
4.4 Undulator
Fig. 4.6: Undulator arrays adjustment for vertical polarised X-rays[31].
FERMI has the capability to produce the radiation with linear and circular
polariation. It uses APPLE II type helical undulator. APPLE stands for
Advanced Planar Polarized Light Emitter. It consists of 4 magnetic arrays
of magnetic structure which generate an oscillating B field depending on the
distance between upper and lower arrays and on the longitudinal position of
the opposite arrays. By moving two opposing magnet arrays with respect
to the other two longitudinally, the strengths of the vertical and horizontal
magnetic field components can be varied, and hence the polarisation of the
radiation produced. The benefit of such a device is that the radiation can
be polarised vertically, horizontally, and circularly by moving arrays. These
arrays provide a horizontal field, as well as a vertical one depending on the
position of magnet blocks above and below the electron beam. Fig 4.6-8
shows the position of magnetic arrays for different polarisations.
4.5 Reflectometer
The experimental chamber has been equipped with our reflectometer. The
detector arm in the reflectometer gives the possibility to mount both detec-
29
34. Master Thesis 4. FREE ELECTRON LASER
tors (photo-diode and CCD) at the same time. Therefore the setup allows to
take the 2-D scattering measurements on CCD and classical reflectivity scans
via photo-diode without opening the chamber for changing the detector. The
reflectormeter allows to take measurements for incident angle from 0◦
-55◦
.
The sample stage can be moved linearly in coordinate axes (x, y and z).
4.5.1 Set-up
Fig. 4.9: Sample holder with electromagnet.
For the magnetic reflectivity experiments we also used an electromagnet
which is shown in figure 4.9 and 4.10. Because of the electromagnet the
range for the θ − 2θ configuration reduces from 0-55 deg to 20-50 deg. This
reduction in the range of incident angle does not pose a problem for the our
experiment as expected XMCD effect accordring to our calculation (discussed
in chapter 6) is evident above 20 deg.
The electromagnet is controlled by an external power supply which is not
shown in the figure. The current in the coil can be switched from -5A to 5A.
The coil is strong enough to produce the magnetic field (± 150 mT ) which
is sufficient for the saturation of our sample.
31
35. Master Thesis 4. FREE ELECTRON LASER
Fig. 4.10: Sample holder with electromagnet.
The use of an electromagnet is also a source of an unwanted stray field
inside the chamber. There are motors and other steel components around
the sample which either produce magnetic field itself or get magnetised by
the electromagnet.
32
36. 5. SAMPLE CHARACTERISATION
5.1 Hard x-ray measurements
In this chapter we present the hard x-ray reflectivity experiments of the
samples used. we deduce parameters such as electron density profiles, layer
thichness and roughness etc. The chapter also includes the comparision of
the estimated profile and experimental results.
5.1.1 Samples
Fig. 5.1: General configuration of the samples. The trilayer system consists of two
ferromagnet layers sandwiching a non-ferromagnet layer. The topmost
layer of ferromagnet is protected by capping.
The ultimate goal of the project is to understand the diffusion of spins in
ferromagnets, therefore we used trilayer samples with general configuration
as shown in the above figure 5.1.The sample has a capping layer of aluminum
37. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.2: Sample 5 and 6 has permalloy as ferromagnet layers with Tantalum
and Magneium Oxide as non-ferromagnet layer, respectively. Sample
7 and 8 has alloy (Co70Fe30) as ferromagnet layers with similar as non-
ferromagnet layer as Sample 5 and 6.
to save the topmost layer of ferromagnet from oxidation. The next layer con-
sists of non-ferromagnet material which is preceeded by another ferromagnet
layer. The idea behind using a non-ferromagnetic material in between the two
ferromagnetic layers is to probe the diffusion of spins through ferromagnet
and non ferromagnet layers.
Figure 5.2 shows all four samples. We used ’Permalloy(Py)’ as the sandwich-
ing layers for non-ferromagnet layer of Tantalum (Ta) and Magnesium Oxide
(MgO) in sample 5 and 6, respectively. In Sample 7 and 8 the layer of Permal-
loy (Py) is replaced by an alloy of Co and Fe with configuration (Co70Fe30).
MgO and Ta are insulator and metal, respectively. The idea behind the use
34
38. Master Thesis 5. SAMPLE CHARACTERISATION
these two material with different nature with respect to conductivity is to
study the difference in spin diffusion from the upper ferromagnetic layer to
the metal (Ta) or insulator(MgO).
5.1.2 Reflectivities at 8 KeV
We performed X-ray reflectivity experiment at the at home lab in the uni-
versity of Siegen. The measured reflectivities for all four sample were fitted
by using softwares for the Parrot algorithm. Figure 5.3 - 5.10 represents
the reflectivity measuements and their corresponding charge profiles. Figure
5.13 shows the summary of fitting results. In all samples we noticed that the
capping layer is oxidized and has scattering length density close to aluminum
oxide. The surface roughness of the aluminum is found between 7-10 ˚A, along
with the thickness of 33-37 ˚A. The ferromagnetic layers in sample 5 and 6
have thickness around 90 ˚A, with roughness varrying between 3-8 ˚A. While
in sample 7 and 8 the thickness is around 100 ˚A, with roughness of 3-6 ˚A.
MgO has a thickness of ca. 75 ˚A, which is less than the value expected from
sample growth of 100 ˚A.
35
39. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.3: Hard x-ray reflectivity of sample 5 at 8 KeV. Experimental data (dots)
and fit (blue line).
36
40. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.4: Profiles for sample 5 at 8 KeV. Values from Henkel Tables (dots) and fit
(blue line).
37
41. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.5: Hard x-ray reflectivity of sample 6 at 8 KeV. Experimental data (dots)
and fit (blue line).
38
42. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.6: Profiles for sample 6 at 8 KeV. Values from Henkel Tables (dots) and fit
(blue line).
39
43. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.7: Hard x-ray reflectivity of sample 7 at 8 KeV. Experimental data (dots)
and fit (blue line).
40
44. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.8: Profiles for sample 7 at 8 KeV. Values from Henkel Tables (dots) and fit
(blue line).
41
45. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.9: Hard x-ray reflectivity of sample 8 at 8 KeV. Experimental data (dots)
and fit (blue line).
42
46. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.10: Profiles for sample 8 at 8 KeV. Experimental data (dots) and fit (blue
line).
43
47. Master Thesis 5. SAMPLE CHARACTERISATION
Fig. 5.11: The results from the analysis.
44
48. 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
6.1 ReMagX
This chapter represents the pre-experimental calculations for magnetic reflec-
tivities based on the ’ReMagX’, additional parameters like magnetic absorp-
tion and dispersion are required to calculate magnetic reflectivities apart from
conventional parameters of reflectivity softwares. The standard absorption
and dispersion of material at their edges requires the following corrections[32].
β = βo βM [sin θ cos φM − cos θ sin φM sin θM ] (6.1.1)
δ = δo ± δM [sin θ cos φM − cos θ sin φM sin θM ] (6.1.2)
where θ represents the incidence angle of the x-rays, while θM and φM are
the spherical coordinates of magnetisation vector. Figure 2.4 in chapter 2
gives the reference for the coordinate of the magnetization.
In equation 6.1.1 and 6.1.2 δM and βM represent the magnetic contribution
to the dispersion and absorption.
The magnetic absorption relate with the XMCD signal strength as
βM =
∆µ
4ko[sin θ cos φM − cos θ sin φM sin θM ]
. (6.1.3)
The magnetic contribution to the absorption is directly proportional to the
XMCD signal ’∆µ’ or the asymmetry as shown in equation 6.1.3[32].
6.2 Dependence of Magnetic Reflectivity on the Direction of
Magnetization Vector
Calculated magnetic reflectivities for sample 5 with right circular (R+) and
left circular (R−) x-rays are shown in fig 6.1 - 6.6. We change the orienta-
tion of magnetisation in the xy-plane for these calculation. The change in
49. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
reflectivities can be observed in each plot as the direction of magnetization
vector is different for each plot. The corresponding asymmetries are shown
in fig 6.7 with values varying around 0-12%. We notice the highest asym-
metry between 30 to 50 degree (Q = 0.039 ˚A−1
) of incident angle. We used
the thickness and roughness values extracted from hard x-ray analysis (see
table in fig 6.8). We change the values of absorption from the tabulated as
the absorption values for ferromagnet are higher at edges than tabulated[33].
For the magnetic optical constants we used the same values as the charge
optical constants but one order small.
The discussion regarding the importance of direction of magnetisation is
given in section 2.4 and 2.5 of chapter 2. At φM = 90 deg we have maxi-
mum calculated asymmetry as the magnetisation vector is parallel to k+k’
(see figure 2.4). The asymmetry vanishes when the magnetisation vector is
perpendicular to (k+k’).
46
50. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Recalling the coordinate system for magnetic moments. The figure has been dis-
cribed in chapter 2 (Figure 2.4).
47
51. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.1: Calculated magnetic reflectivity with φM = 0. Reflected circular right
x-ray (blue) and circular left x-ray (red) overlap as the magnetisation
contribution is zero in resonant scattering factor. In this case there is no
difference in the calculated reflectivities.
48
52. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.2: Calculated magnetic reflectivity with φM = 15 deg. Reflected circular
right x-ray (blue) and circular left x-ray (red) starts separating as the
magnetisation contribution shows the effect in the resonant scattering
factor in this case.
49
53. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.3: Calculated magnetic reflectivity with φM = 30 deg. The separation of
calculated magnetic reflectivities becomes more wider as the magnetisa-
tion contribution increases in the resonant scattering factor.
50
54. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.4: Calculated magnetic reflectivity with φM = 45 deg. The separation of
calculated magnetic reflectivities widens more as the magnetisation con-
tribution keeps increasing in the resonant scattering factor.
51
55. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.5: Calculated magnetic reflectivity with φM = 60 deg. The same increasing
effect is observed in the separation of the reflectivities.
52
56. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.6: Calculated magnetic reflectivity with φM = 90 deg. The magnetic con-
tribution is maximum in this case as the magnetisation vector is parallel
to (k + k’).
53
57. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.7: Calculated asymmetries with φM varying between 0-90 deg. Asymme-
try increases as the magnetic contribution is increasing in the resonant
scattering factor (see equation 2.4.1).
54
58. Master Thesis 6. CALCULATIONS OF MAGNETIC REFLECTIVITIES
Fig. 6.8: Values used for the calculations. Charge Optical contants are used
from the Henkel Tables (except the absortption values of Py). For the
magneto-optical constants we used the same values as charge constants
with one order small.
55
59. 7. FERMI FEL MEASUREMENTS
7.1 Sample Absorption
This chapter includes transmission and absorption calculations along with
the measured magnetic reflectivities, asymmetries and discussions. We per-
formed calculations for the absorption of XUV as we planned experiments
at the M-edges. Figure 7.1 represents the absorption calculations for the
sample 5. We noticed that at angles below 40 degree, more than 50 % XUV
get absorbed by permalloy and aluminium. We used the Henke tables for
the calculation of transmission. At resonant edges the values of absorption
for ferromagnet differ from tabulated ones [30]. Therefore, we consider these
calculation as a guide. In almost all cases (20-50 deg) the XUV seems to get
absorbed more than 80% after tantalum (the sandwiched layer).
We used the trilayer system with the thickness of 10 nm for each layer. In
order to reduce the absorption and achieve information of larger Q space, one
can reduce the thickness but the experiment has been performed at resonant
edges (M edges) which restricts the maximum accecible Q-range. Reflectivity
measurements at higher angles is a solution for our experiment to get infor-
mation of larger Q-space but our current setup restricts the measurements
between 20◦
to 50◦
.
7.2 Pointing Stability
The pointing stability of FEL is also a matter of concern for experiments.
Pointing stability is the source of inherrent asymmetry in the intensities of
incident beams of two polarisations. This means on changing the polarisation
from left to right one measures some inherent asymmetry in intensity because
of the change of the intensity of the incident beams on the sample. The
pointing stability of FERMI is in the range of some micro-radians. The
beam size is of 100s of microns. This means if the pointing stability is
60. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.1: Calculated absorption for sample 5. The vertical dotted black lines repre-
sents the interface boundaries. Starting with Al with 3nm then permalloy
10nm which is followed by tantalum and permalloy of same thickness of
10 nm each.
not controlled, the beams of different polarisation have different foot-prints
on the sample which affects the reflectivity. This problem along with the
intensity fluctuation could pose hurdles for the asymmetry measurements.
The expectation of asymmetry according to calculation was around 10-14%
for our sample. Therefore, it is necessary to have minimum possible intensity
fluctuation and higher possible pointing stability.
Fig. 7.2 displays the direct beam measurments as a function of FEL energy
density. Picoampermeter values are directly proportional to intensity of the
beam. Circular left (red squares) and circular right (blue diamonds) are
57
61. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.2: The direct beam measurement without sample. Blue dashed line rep-
resents the fit of Circular left beam measurements (red squares). Red
dashed line represents the fit of Circular right beam measurements (blue
diamonds).
away from each other. This is one of the worst case. The asymmetry in
direct beams is around 30%. This differnce in intensities appears because of
the lack of pointing stability. To measure the asymmetry of 10-14% in the
magnetic reflectivities, one must get rid of this inherrent asymmetry before
taking the measurements of physical worth. The improvement of pointing
stability is done by changing machine parameters and operating conditions.
Fig 7.3 shows the direct beam results after the pointing stabilty achieved
agian. Circular left (red squares) and circular left (blue diamonds) overlaps
each other.
58
62. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.3: The direct beam measurement without sample after recovering pointing
stability. Blue dashed line represents the fit of Circular left beam mea-
surements (red squares). Red dashed line represents the fit of Circular
right beam measurements (blue diamonds).
59
63. Master Thesis 7. FERMI FEL MEASUREMENTS
7.3 Magnetic Reflectivities and Asymmeteries
Fig. 7.4: Magnetic Reflectivity of the trilayer sample with permalloy as ferromag-
net and tantalum as spacer. The change in reflectivity is clearly visible
after Q = 0.03 ˚A−1.
The magnetic reflectivities were measured at the M edge of iron which is at
52.7 eV. Figure 7.4 and 7.5 shows magnetic reflectivity and the correspond-
ing asymmetry measurements respectiviely. The measurements were carried
out without applied magnetic field. In fig 7.4, the difference between the
reflectivity of circular right (blue) and circular left (red) is clearly visible
after Q=0.03 ˚A−1
. Each point in the reflectivity consists of the mean value
of the 200 shots. In fig 7.5, the corresponding asymmetry displays the max-
imum value of 14 % around Q=0.035 ˚A−1
. The calculation of the error bar
60
64. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.5: Corresponding asymmetry of the trilayer sample with permalloy as fer-
romagnet and tantalum as spacer without applied magnetic field.
for asymmetry (A) is done by the following equation using standard error
propagation.
∆A = A ∗
σLCP
ILCP
2
+
σRCP
IRCP
2
(7.3.1)
where ’σ’ is the standard deviation and ’I’ represents the intensity of the
incident beam. Equation 7.3.1 shows that the standard deviation should be
minimum to have small error bars. Therefore, it is necessary to have less
intensity fluctuations. Intensity fluctuations of FERMI seeded FEL arises
from shot-to-shot fluctuations in the electron-beam and seed parameters [45].
Figure 7.6 (left) represents these 200 shots of different intensity for an incident
angle. The black line shows the mean value of intensity of 200 shots. Fig 7.6
61
65. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.6: Intensity variation of 200 shots of FEL radiation (left). Each point in the
magnetic reflectivity represents the mean of these 200 shots. Variation
shot occurence (right) around the mean value of intensity.
(right) shows occurrence of shots around mean intensity of 200 shots.
We also measured asymmetry with the applied magnetic field. We found the
mean asymmetry with maximum value of 12%. Fig 7.7 and 7.8 represent
the magnetic reflectivity and corresponding asymmetry measured under the
influence of applied magnetic field. The values of the asymmetry is less in
terms of mean amplitude if we compare it to the case of no magnetic field
but the error bars touches the 14 % mark. The larger error bars reflects the
higher intensity fluctuations in the shots.
62
66. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.7: Magnetic Reflectivity of the trilayer sample with sample Permalloy as
ferromagnet and Tantalum as spacer with the applied magnetic field.
As discussed in chapter 6, the magnetic reflectivities varies with the change in
the magnetization vector. The setup consists of reflectometer. It has various
components which has steel and ferromagnet. So on the application of the
external magnetic field, there has been a possibility for these components to
get magnetized. Consequently the presence of stray field inside the chamber
is inevitable. This net stray field has the ability to change the magnetic
moments inside our samples.
7.4 MOKE Measurements
MOKE is a standard experimental procedure which is used to study the
magnetic properties of magnetic materials via reflection of the polarized light.
63
67. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.8: Asymmetry of the trilayer system with the applied magnetic field.
The polarized light on the interaction with the magnetic sample changes its
polarization. This change has the information about the magnetization of
the sample.
These samples were prepared in Johannes Guttenberg University of Mainz
by the group of Prof. Dr. Mathias Kl¨aui. Prof. Dr. Hartmut Zabel of the
same institue is also in collaboration of these experiments. He shared the
results of MOKE experiment which he performed on sample 5 in his lab in
Mainz. Figure 7.9 represents the results which shows the sample is very soft
in terms of magnetisation. This makes us to propose more firmly that stray
field might be a possible reason to produce change in magnetisation inside
sample.
64
68. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.9: Hysteresis curve measured via MOKE setup for the Sample. The general
view suggest that the sample is very soft in terms of magnetisation
Figure 7.10 shows rescaled Hysteresis curve. The curve shows the field require
to saturate the the sample is very small. Moreover this also indicates that
even the small stray field can effect our sample.
Actually the value of the measured coercive field is very small (0.5 Oe which
is equivalent to 50 µT). Even if we compare it to earths magnetic field which
ranges from 25 to 65 microtesla on Earth surface.
65
69. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.10: Enlarged Hysteresis curve measured via MOKE setup for the Sample.
66
70. Master Thesis 7. FERMI FEL MEASUREMENTS
7.5 Asymmetry Deviation from Calculations
We tried to fit one of the measured asymetry by using software ReMagX as
shown in fig 7.11. The calculated asymetry (red) using the optical constants
from the Henke tables does not fit well with the measured asymetry. Whereas
the calcuated asymetry with reduced optical constants is a better fit to the
measured asymmetry.
Beer-Lambert law describes the absorption of X-rays in materials. However
St¨ohr et al. presented an analytical expression for the modified polarization-
dependent Beer-Lambert law for the case of resonant core-to-valence elec-
tronic transitions [34]. They predicted that the resonant absorption and
dichroic constants are found to vanish with increasing x-ray intensity.
They applied the theory for the case of 3d transition metal samples whose po-
larization dependent transmission exhibits both a charge and spin response,
the latter through the x-ray magnetic circular dichroism (XMCD) effect [34].
They reported for Co L3 absorption resonance at 778 eV (wavelength of
1.6 nm), the sample becomes increasingly transparent with the spin-based
XMCD contrast disappearing sooner than the charge-based absorption con-
trast at higher intensities.
Considering the prediction of St¨ohr et al. [34], the calculation of the asym-
metry employing the FEL high fluence effect (blue curve in fig 7.11) displays
more closer curve to the measured curve. The absorption constant has smaller
values in comparision to the tabulated values. Similarly the dispersion also
get reduced for the first ferromagnet layer. The dispersion is directly pro-
portional to the electron density. The depletion of both constants hints the
infleunce of the high fluence of FEL. The parameters used for fitting after
experiment ae tabulates in fig 7.12.
67
71. Master Thesis 7. FERMI FEL MEASUREMENTS
Fig. 7.11: Measured asymmetry vs the calculation. On reduction of absoption
values, the peak position in the calculation comes closer to the measured
data. This also hints about the high fluence effect in which most electron
attains higher states and the absorption decreases.
Fig. 7.12: The parameters used for the recalculation of asymmetry.
68
72. 8. CONCLUSION AND OUTLOOK
Within the domain of the thesis we were able to measure XMCD effect at
M-edges with FEL short pulses. Although the magnetic reflectivities via
soft x-rays have been measured for depth resolution [35, 36, 37] but the
magnetic reflectivity measurement at M edges with ultra shot pulses is first
ever measurement of its kind. We found asymmetry in the intensity of the
polarised (RCP and LCP) reflected beams around 14% for trilayer sample.
The surface and interface chracterisation was done by hard X-ray reflectivity
measurements. These measurements helped us to learn about the interface
roughness and oxidisation of the capping layer. The roughness at the inter-
faces of the sample ranges from 3-10 ˚A. The thickness for Magnesium Oxide
is (around 25˚A) less than the value expected from sample growth of 100 ˚A.
FEL is considered a chaotic source. The limited control over the beam pa-
rameters results in intensity fluctuations and pointing instability which pose
a challenge for experiments. Specially in the reflection geometry for XMCD
studies, it becomes more crucial to have the parameters in desired limits to
get the signals of the physical worth.
Despite the challenges of the fluctuating parameters, we were able to record
magnetic reflectivities at M edges. We deduced XMCD effect from magnetic
reflectivites which are near to the calculations. The asymmetry which cor-
responds to XMCD in the reflectivity geometry has small error-bars in best
data sets.
There are steel components, motors and parts of set-up inside the chamber
which could produce a net stray field. We used the electromagnets for pro-
ducing the magnetic field to align the magnetic moments inside the sample.
The electromagnet could also be a cause of inducing magnetisation in the
components of the chamber.
73. Master Thesis 8. CONCLUSION AND OUTLOOK
The stray field can be avoided by using non magnetic steel. The problem
is there are motors and other components which are standard components.
The motors with non-magnetic material is not possible and the other cus-
tomise components with non-magnetic material would increase the cost of
experiments
The other possibility is to use the hard materials for the experiments which
can hold their remanance against the stray field. The MOKE measurements
also showed that the material is soft enough to get disturbed even by the
Earth’s magnetic field.
The next step is to pump out the magnetisation and to see the effect in
the reflectivity and consequently in asymmetry. The time evolution of the
asymmetry would help us to understand the diffusion of spins at the interfaces
and magnetic roughness.
The measured asymmetries signals also hints the effect of the high fluence
X-rays on the absorption of the material. The theory for high fluence effect
was published by J. St¨ohr and A. Scherz [34]. The experimental proof of
the theory has already been published recently by B. Wu et al., [38]. In our
results, the fitting of asymmetry after the experiment suggests that the reso-
nant absorption start vanishing. Customised fluence dependent experiments
is the next step to support this theory.
70
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Appendix
Pointing Stability Precision Measurements
1. The difference in the circular right intensity in up and down quadrant of photo
diode (top). The difference in the intensity of left and right quadrant (bottom).
Photodiaode is divided into four quadrants. Fig 1(top). shows direct beam
measurements for circular right. Blue circles shows sum of intensities mea-
sured in the top two qudrants of the photdiaode. While red squred shows sum
of intensities measured in the bottom two quadrants. Similarly Fig 1(bot-
tom) also shows direct beam measurements for circular right. Blue circles
represents the sum of intensities measured in the right two qudrants of the
picoammeter. While red squred shows sum of intensities measured in the left
two quadrants. Fig 2 represents the same measurements for circular left.
76
80. Master Thesis Bibliography
2. The difference in the circular left intensity in up and down quadrant of photo
diode (top). The difference in the intensity of left and right quadrant (bottom).
77
81. Acknowledgments
Firstly I would like to thank my supervisor Prof. Dr. Christian Gutt for
allowing me to work in his group and specially for his encouragement in
difficult times during my Master Studies. I belive without his continuous
supervision it would be difficult for me to work on such topic. His assistance
during the experiments on FERMI FEL has been crucial to understand and
interpret the results. Lastly, I also feel obliged to my supervisor for the fact
that he overlooked my complete ignorance of football and Bayern Munich
football history.
I would also like to thank Dr. Tushar Sant for his valuable assistance during
my time in the group for my Master thesis. He is the one who always available
for my queries. He also helped me to learn the matlab as my skill for matlab
was just plotting of simple graph at the start of the thesis. He also helped me
to work with fitting softwares. His assistance in understanding the research
papers were also contribute alot for me.
Special Thanks to:
Prof. Dr. Ullrich Pietsch and Dr. Dmitry Ksenzov for their support during
the experiments and analysis of experimental data.
Beamline scientist Flavio Capotondi, Emanuele Pedersoli and Maya Petrova
Kiskinova for their support during the planning, preparation and execution
of the experiment.
Prof. Dr. Mathias Klui and Prof. Hartmut Zabel for their collaboration and
assistance.
Lastly I would like to dedicate my thesis to my brother who supported me
throughout my life despite my unorthodox decisions.
82. DECLARATION/ERKL ¨ARUNG
Hiermit erkl¨are ich, dass ich die vorliegende Masterarbeit selbstst¨andig ver-
fasst und keine anderen als die angegebenen Quellen und Hilfmittel benutzt
sowie Zitate und ergebnisse Andere kenntlich gemacht habe.
(Place/Ort) (Date/Datum) (Signature/Unterschrift)
