I
NSTITUTO DEF´
ISICA“G
LEBW
ATAGHIN”
EDUARDO HENRIQUE DE TOLEDO POLDI
X-RAY MAGNETIC DICHROISM INSTRUMENTATION
TO INVESTIGATE ELECTRONIC AND MAGNETIC
PROPERTIES UNDER EXTREME CONDITIONS
INSTRUMENTAC
¸ ˜
AO DE DICRO´ISMO MAGN ´
ETICO DE
RAIOS X PARA INVESTIGAR PROPRIEDADES
ELETR ˆ
ONICAS E MAGN ´
ETICAS EM CONDIC
¸ ˜
OES
EXTREMAS
X-RAY MAGNETIC DICHROISM INSTRUMENTATION TO INVESTIGATE ELECTRONIC AND MAGNETIC PROPERTIES UNDER EXTREME CONDITIONS
INSTRUMENTAC¸ ˜AO DE DICRO´ISMO MAGN ´ETICO DE RAIOS X PARA INVESTIGAR PROPRIEDADES ELETR ˆONICAS E MAGN ´ETICAS
EM CONDIC¸ ˜OES EXTREMAS
Dissertation presented to the Institute of Physics Gleb Wataghin of the University of Campinas in partial ful-fillment of the requirements for the degree of Master in Physics, in the area of Physics.
Dissertac¸˜ao apresentada ao Instituto de F´ısica Gleb Wataghin da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obtenc¸˜ao do t´ıtulo de Mestre em F´ısica, na ´Area de F´ısica.
Supervisor/Orientador: Dr. Narcizo Marques de Souza Neto
Co-supervisor/Coorientador: Prof. Dr. Fl´avio C´esar Guimar˜aes Gandra
ESTE EXEMPLAR CORRESPONDE `A VERS ˜AO FINAL DA
DISSERTAC¸ ˜AO DEFENDIDA PELO ALUNO EDUARDO
HEN-RIQUE DE TOLEDO POLDI, ORIENTADO PELO DR. NARCIZO MARQUES DE SOUZA NETO.
Biblioteca do Instituto de Física Gleb Wataghin Lucimeire de Oliveira Silva da Rocha - CRB 8/9174 Poldi, Eduardo Henrique de Toledo,
P757x PolX-ray magnetic dichroism instrumentation to investigate electronic and magnetic properties under extreme conditions / Eduardo Henrique de Toledo Poldi. – Campinas, SP : [s.n.], 2020.
PolOrientador: Narcizo Marques de Souza Neto. PolCoorientador: Flávio César Guimarães Gandra.
PolDissertação (mestrado) – Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin.
Pol1. Magnetismo. 2. Radiação sincrotrônica. 3. Experimentos de altas pressões. 4. Instrumentação científica. I. Souza Neto, Narcizo Marques de, 1978-. II. Gandra, Flávio César Guimarães, 1954-. III. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. IV. Título.
Informações para Biblioteca Digital
Título em outro idioma: Instrumentação de dicroísmo magnético de raios X para investigar
propriedades eletrônicas e magnéticas em condições extremas
Palavras-chave em inglês:
Magnetism
Synchrotron radiation High pressure experiments Scientific instrumentation
Área de concentração: Física Titulação: Mestre em Física Banca examinadora:
Narcizo Marques de Souza Neto [Orientador] Abner de Siervo
Flávio Garcia
Data de defesa: 28-08-2020
Programa de Pós-Graduação: Física Identificação e informações acadêmicas do(a) aluno(a)
- ORCID do autor: https://orcid.org/0000-0002-8738-5956 - Currículo Lattes do autor: http://lattes.cnpq.br/6445546285503177
MEMBROS DA COMISSÃO JULGADORA DA DISSERTAÇÃO DE MESTRADO DE
EDUARDO HENRIQUE DE TOLEDO POLDI – RA 155216 APRESENTADA E
APROVADA AO INSTITUTO DE FÍSICA “GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 28 / 08 / 2020.
COMISSÃO JULGADORA:
- Prof. Dr. Narcizo Marques de Souza Neto – Orientador – CNPEM - Prof. Dr. Flávio Garcia – CBPF
- Prof. Dr. Abner de Siervo – DFA/IFGW/UNICAMP
OBS.: Ata da defesa com as respectivas assinaturas dos membros encontra-se no
SIGA/Sistema de Fluxo de Dissertação/Tese e na Secretaria do Programa da Unidade.
CAMPINAS 2020
Aos meus pais, Carolina e Lu´ıs, ao meu irm˜ao, Victor, e a minha fam´ılia e amigos em Limeira: s˜ao impag´aveis anos de conv´ıvio, tornando esta jornada acadˆemica imposs´ıvel sem seu amor e apoio. A saudade ser´a imensa.
`
A minha namorada, J´ulia, que me aturou e apoiou durante uma graduac¸˜ao e um mestrado inteiros, um quarto da minha vida. N˜ao consigo imaginar toda essa viagem (e as futuras) sem sua companhia e suporte.
Aos moradores e ex-moradores da Rep´ublica do Barril, minha casa, com quem tive a oportunidade de compartilhar ´otimos momentos: Ac¸´ucar, Baliza, Binho, Bob, Burpee, Canh˜ao, Chera, Chuveiro, Fashion, Fil´e, Ganso, Hinode, Indi˜ao, Jon, Maguila, Marquito, Mentira, Moeda, Pau, Pirelli, Poldinho, Ran-dandan, Segredo, Takeda, Tamans´a, Testa, Ti˜ao, Toninho, Totti, Tropec¸o, Tutu e Wando. Com vocˆes e com os maravilhosos agregados da rep, esses ´ultimos 4.5 anos de UNICAMP foram infinitamente melhores.
Aos membros do ex-grupo XDS: B´arbara, Carlos, Danusa, Gustavo, Gu´ercio, Leonardo, Lucas, Jairo, Jud´a, Marcos e Ulisses. Um abrac¸o extra para os que sofreram calados em several beamtimes comigo. Agradec¸o tamb´em aos outros
pr´oximo: Camila, Joel, Lucas, Marina e Vanessa. Um agradecimento especial ao Ricardo por promover o in´ıcio dessa caminhada, em que discutimos desde propagac¸˜ao de erros at´e magnetismo em geral, and several other subjects, in English, for mutual conversation enhancement.
Finalmente, aos meus orientadores, Narcizo e Gandra, por todos os momen-tos de esclarecimento, conselhos e risos, tanto na graduac¸˜ao quanto na p´os. Um abrac¸o especial ao Narcizo que est´a presente nessa jornada desde 2014, propor-cionando crescimento tanto pessoal quanto profissional. Guardo comigo v´arias de nossas discuss˜oes, indo desde como escrever um e-mail claro e objetivo, at´e suas ideias ambiciosas e coment´arios sempre pertinentes.
Agradec¸o `as agˆencias de fomento CNPq (136119/2018-2) e FAPESP (2013/ 22436-5) pelo suporte financeiro a este projeto.
Uma das maneiras de estudar propriedades magn´eticas dos materiais ´e uti-lizando a t´ecnica de dicro´ısmo circular magn´etico de raios X (XMCD). Esta ´e uma t´ecnica bem estabelecida em s´ıncrotrons, com sua principal caracter´ıstica sendo a seletividade ao elemento qu´ımico e ao orbital atˆomico. Sinais de XMCD variam em intensidade, sendo em geral de 1 a 4 ordens de grandeza menores do que o salto de absorc¸˜ao da amostra. Ent˜ao, em diversos casos cient´ıficos, ´e necess´aria muita estat´ıstica e, consequentemente, tempo de medida para se obter um espectro de XMCD com boa relac¸˜ao sinal ru´ıdo. Portanto, neste projeto,
desenvolvi uma instrumentac¸˜ao baseada em lˆamina de 1/4 de onda e aquisic¸˜ao
s´ıncrona otimizada para experimentos de XMCD, podendo ser utilizada tanto em linhas de luz de ´optica monocrom´atica quanto policrom´atica. Ainda, a instrumentac¸˜ao ´e compat´ıvel com experimentos em altas press˜oes, baixas tem-peraturas e altos campos magn´eticos, e foi utilizada para medir XMCD na borda
L3 do Gd em um composto de GdCo2 em func¸˜ao de P e T.
Palavras-chave: Magnetismo, radiac¸˜ao s´ıncrotron, altas press˜oes, instrumentac¸˜ao cient´ıfica.
One way to study magnetic properties of materials is using the X-ray mag-netic circular dichroism (XMCD) technique. This is a well-established tech-nique in synchrotron facilities, and its main characteristic is selectivity to the chemical element and to the atomic orbital. XMCD signals vary in intensity, usually being from 1 to 4 orders of magnitude smaller than the sample ab-sorption jump. In many scientific cases, the amount of statistics necessary is high, consequently requiring a large period of time to obtain an XMCD sig-nal with reasonable sigsig-nal-noise ratio. Therefore, in this project I developed an instrumentation based on quarter wave plate and synchronous acquisition optimized for XMCD experiments, with the possibility to be applied in both monochromatic and polychromatic beamlines. Besides, this instrumentation is also compatible with high pressure and low temperature experiments, as well as with high magnetic fields. It was utilized to measure the dichroic signal at Gd
L3-edge in a GdCo2 compound as function of P and T.
Keywords: Magnetism, synchrotron radiation, high pressure, scientific instru-mentation.
1 Introduction 11
2 Scientific Background 16
2.1 Synchrotron Radiation . . . 16
2.2 Core Level Spectroscopy . . . 21
2.2.1 X-ray Absorption Spectroscopy . . . 21
2.2.2 X-ray Magnetic Circular Dichroism . . . 29
2.3 X-ray Diffraction and Birefringence . . . 32
3 Instrumentation Development 39 3.1 Bragg Transmission Phase Retarder in Monochromatic X-ray Optics . . . 42
3.1.1 Dispersive Polychromatic X-ray Optics . . . 48
3.2 Synchronous Acquisition . . . 54
4 GdCo2 Under Extreme Conditions 60 4.1 Sample Growth by Arc Melting . . . 61
4.3 X-ray Magnetic Circular Dichroism Experiments . . . 66
4.4 X-ray Diffraction Experiments . . . 70
4.5 Ab Initio Calculations of XAS and XMCD . . . 73
5 Conclusion and Perspectives 80
Bibliography 84
Appendix A - Calculation of Offset for Maximum PC 93
Chapter 1
Introduction
Magnetic materials have been studied by distinct civilizations for millennia, since the discovery of its interesting properties: from the most basic for macro-scopic objects, like attraction, repulsion and alignment with magnetic forces; to the capability of generating electricity by varying magnetic fields with respect to a given area. Moreover, this discovery also brought several possible appli-cations, from the compass, centuries ago, to speakers and synchrotron facili-ties. With the recent exponential technological progress, a huge necessity has emerged in order to understand the phenomena responsible for these proper-ties. Taking hard disk drives as an example, in the last few decades technology allowed to storage, read and erase information in relative alignment of ferro-magnetic domains. Then, finding materials each time more suitable for this role than its predecessor, in matters of cost, speed and size, requires a clear un-derstanding of the variables that control every compound magnetic properties.
Beyond that, for direct applications in modern society, it is often required the ability to control the magnetism according to specific necessities. As magnetism in materials arises from two electronic properties (angular and spin momenta), and strongly depends on these properties interaction among ions, to change a compound magnetism we can interfere in this interaction by tuning the lattice, using thermodynamic variables such as pressure and temperature to change the distance between atoms, and to increase or decrease the system disorder.
The lanthanide family is a series of chemical elements that have been largely studied because its magnetic properties are given mainly due to an screened, well-localized 4f electronic state, with maximum ionic magnetic moment for seven unpaired electrons in gadolinium. Macroscopic techniques to measure magnetization, e.g. using a SQUID magnetometer, can easily probe this mo-ment; but extreme conditions of pressure and temperature, concomitantly, are difficult to be obtained due to the small sample space. In that sense, microscopic techniques that give a magnetic response are an advantage, because extreme P and T are easily to achieve in confined spaces. Besides, in many occasions we are interested in the magnetic contributions of each chemical element that com-poses an alloy. Summing up these needs, X-ray magnetic circular dichroism (XMCD) [1, 2] is an ideal microscopic element selective technique to probe magnetism in extreme conditions. An XMCD measurement is obtained from the difference between two absorption spectra, performed with X-ray of
oppo-site helicities. Either the sample must have a magnetization component in the X-ray beam direction, or a magnetic field can be applied to align its spins with the beam (e.g. for ferro or paramagnetic materials) and maximize the momen-tum transfer from photons to electrons. Less commonly, a magnetic field can also be applied in order to generate a disproportionality between unoccupied states of spin up and down (e.g. in some weak diamagnetic systems). As a technique that comes from X-ray absorption spectroscopy (XAS), XMCD is also selective to the atomic orbital, and the magnetic signal intensity usually
extends from 10−1 to 10−4 fractions of the absorption jump for metallic
ele-ments. Higher dichroic signals are found in the soft X-ray region, where 3d
transition metals L2,3-edges (2p → 3d excitation) [3, 4] and rare earth and
ac-tinides elements M4,5-edges (3d → 4f and 5f , respectively) [5, 6, 7] directly
probe the large spin polarization of electronic states that carry the magnetization [8, 9]. However, these edges are in the energy range between 0.5 and 1.5 keV, which is incompatible with experiments under pressure in a diamond anvil cell (e.g. diamonds 100 µm thick reduce X-ray intensity in 12 orders of magnitude).
High-energy edges as transition metals K (1s to 4p excitation) [1] and L2,3 (2p
to 5d) of rare earths [10], between 5 and 13 keV, are ideal for XMCD exper-iments in a pressure cell because X-ray attenuation by diamond is low in this condition. The challenge for these resonances is that XMCD signals are weak (< 0.1%) due to the small spin induced polarization in the states 4p and 5d, and
also the absence of spin-orbit coupling in the initial state 1s of K-edges (l = 0, then the probabilities of exciting spins up or spin down are the same). Thus, XMCD experiments frequently requires high statistics and noise-filtering meth-ods to attain measurements with acceptable signal-to-noise ratio. One way to increase this ratio is guaranteeing maximum degree of circular polarization for the X-ray beam and high helicity switching rate with high photon flux, which can be achieved using a quarter wave plate. Therefore, in this dissertation I will present the development of an state-of-the-art instrumentation that com-bines a quarter wave plate with synchronous acquisition, and can be used in both conventional monochromatic and dispersive polychromatic X-ray optics. Furthermore, I will also present a method to probe the magnetization with ele-ment selectivity, as function of pressure and temperature, using a combination of XMCD measurements, X-ray diffraction and ab initio simulations, similarly to [11]. By simulating XAS and XMCD spectra using the DOS, the theoretical model for its computation can be validated.
This dissertation is divided in five chapters: this first one is a brief intro-duction so the reader gets the text overview; Chapter 2 contains a scientific background on synchrotron radiation, core level spectroscopy and dynamical theory of diffraction in order to set all the requirements for the instrumenta-tion; Chapter 3 shows the main goal of this work: the instrumentation devel-opment for efficient XMCD measurements, given the experimental difficulties
mentioned above; Chapter 4 presents the instrumentation commissioning with
a GdCo2 system under extreme conditions, together with an application of the
methodology to study magnetic materials in extreme conditions with element selectivity. Finally, Chapter 5 concludes the dissertation, with perspectives for the application of this instrumentation in the future.
Chapter 2
Scientific Background
This chapter address an overview on synchrotron radiation and core level spectroscopy to explain the developed instrumentation demands. Also, it will briefly show some aspects of dynamical theory of diffraction and birefringence in the X-ray range. These two later subjects were fundamental to understand the physics of quarter wave plates and enable their application as an experimental instrument. Then, Section 2.1 starts the scientific background with the main characteristics of synchrotron radiation and the beamlines where most of this project was carried out.
2.1
Synchrotron Radiation
Synchrotron radiation is electromagnetic radiation generated by charged par-ticles accelerated at relativistic velocities, when their trajectory is deflected by a magnetic field [12, 13]. It comprehends a large range of the electromagnetic
spectrum, from infrared to gamma rays, and is produced in specific particle ac-celerators, called synchrotron facilities. In these complex facilities, electrons are accelerated from rest to hundreds of MeV in a linear accelerator, to be in-jected in a circular booster that speeds them up to the kinetic energy of a few GeV, required to enter the storage ring. Once in this main ring, some elements are required to maintain the electrons trajectory: bending magnets (dipoles) de-viate electrons in a circular motion (typically) to produce radiation; and the ones placed at the synchrotron straight lines, responsible for correction issues re-garding the electron beam caused by the trajectory deflection, e.g. quadrupoles correct horizontal and vertical divergences, sextupoles correct chromatic aber-rations, RF-cavities input the energy lost when changing direction, and also sets of bending magnets of field alternating in opposite directions (insertion devices: wigglers and undulators) in order to produce brighter light. Brightness, Br, is an useful relation to classify radiation:
Br = F
A · Ω , (2.1)
where, F is the radiation flux, A is its source area, and Ω is the beam di-vergence. Synchrotron light from magnetic dipoles has higher flux, almost completely collimated in the orbit plane, and relative small divergence when compared to X-ray tube sources, then brighter. Besides brightness, high degree of polarization for a wide energy range is an important characteristic of
syn-chrotron radiation. This polarization degree exists because dipoles deflect elec-trons in the horizontal plane and the radiation, in the orbit plane, is emitted with electric field oscillating in the same plane, perpendicularly to the applied mag-netic field; i.e., the radiation has an in-plane linear polarization. From conser-vation of the electrons angular momentum, it is also possible to use
out-of-the-orbit-plane radiation to obtain some degree of circular polarization, PC (the
fur-ther from the orbit plane, the more circular polarization becomes) [14]. When it comes to insertion devices, wigglers produce horizontally polarized photons in and out of the orbit plane, due to mutual canceling of vertical component for polarization after deviating electrons for several times in a non-coherent way; while undulators can produce either linearly or circularly polarized in-orbit light (depending on the phase between sets of magnets), due to its coherent emission of radiation for every one of these sets.
This project was carried out at the Brazilian Synchrotron Light Laboratory (LNLS) of the Brazilian Center for Research in Energy and Materials (CN-PEM), in collaboration with the Institute of Physics ‘Gleb Wataghin’ (IFGW) at University of Campinas (UNICAMP). To develop the instrumentation, we considered the monochromatic undulator-based EMA beamline (Extreme
X-ray Methods of Analyses) of 3 GeV 4th generation source, Sirius. Meanwhile,
this instrumentation was developed to be versatile and to work with small adap-tations in different beamlines. Then, the experimental setup was initially tested
at dispersive-optics dipole-based D06A-DXAS beamline (Dispersive X-ray Ab-sorption Spectroscopy) [15] and the monochromatic wiggler-based W09A-XDS
beamline (X-ray Diffraction and Spectroscopy) [16] of the 1.34 GeV 2nd
gen-eration source, UVX.
Conventional monochromatic optics of the XDS beamline contains three main components: a pre-monochromator vertical collimating mirror (VCM), to adjust the beam vertical size before it reaches the monochromator; a dou-ble crystal monochromator (DCM) with two sets of Si reflections, to select the beam energy (from 5 to 30 keV); and a vertical focusing mirror (VFM) with bender for final focus adjustments. Figure 2.1 represents XDS beamline optics.
Figure 2.1: XDS beamline monochromatic optics. VCM possesses stripes of Pt, Rh and Si for rejection of Bragg reflection harmonics at DCM. VFM also contains Pt and Rh stripes, in plane and toroidal geometries for horizontal focusing. Figure adapted from https://www.lnls. cnpem.br/facilities/xds/.
In contrast to XDS, DXAS beamline is made of two principal optic devices: a Rh-coated mirror for vertical focusing and a curved Si monochromator. In dispersive optics, the source natural horizontal divergence must provide a beam with spot large enough when it reaches the monochromator. Then, the angle between beam and bent monochromator vary according to the position on the
crystal surface and, using Bragg’s Law (Eq. 2.2), each position reflects a beam with different energy.
mλ = 2d sin θB, (2.2)
where m ∈ N, d is the distance between a set of crystal reflection planes, θB
is the reflection Bragg angle, and λ = hc
E is the radiation wavelength (related to
energy, E, via the Planck constant, h, and the speed of light in vacuum, c). Using the monochromator reflection to focus, the focal position is a point (ideally) in space where the beam has a controlled energy range and where the sample is placed (Figure 2.2). Charge couple devices (CCDs), that are position sensitive devices (PST), are required to perform spectroscopic experiments in this beamline, as explained in Section 2.2.
After this rapid description of both beamlines, the next Section presents the main techniques I performed at XDS and DXAS with a theoretical and an ex-perimental point of view.
2.2
Core Level Spectroscopy
The goal of this Section is to present the two main X-ray techniques applied in this project: X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Cir-cular Dichroism (XMCD). These are both spectroscopy techniques in which the sample absorption cross section is measured as a function of the incident photon energy.
2.2.1 X-ray Absorption Spectroscopy
The interaction between radiation and matter happens in several ways, each occurring with probability depending on the incident radiation energy, which then relies on the majoritarian phenomenon that intermediates this interaction. For example, photons with ∼100 eV are more likely to excite photoelectrons from occupied states when absorbed, while MeV photons interact more strongly with the nuclei and enables pair production. In this work for the energy range we are interested in (the EMA beamline range: from 3 to 30 keV), radiation predominantly interacts with core electrons by photoabsorption (photons solely transfer energy) and with the atomic lattice via elastic scattering (there is only
momentum transfer). Inelastic scattering, in which photons transfer both energy and momentum to bind electrons, is a relevant interaction as well, but will not be discussed here.
Absorption spectroscopic techniques allows three possible manners to obtain information: considering the energy position where a certain event occurs, the energy width or bandwidth associated with this event, and the intensity of the event at a given energy. The position can be explained by energy conservation laws; width is related to lifetime processes through the Heisenberg uncertainty principle; and intensity is determined considering the absorption cross section of a given material, for which the Fermi golden rule (Eq. 2.3) is needed [17]. This is the equation that dictates the absorption process, stating that the absorp-tion cross secabsorp-tion (σ) is proporabsorp-tional to the transiabsorp-tion probability from an initial state (i) to a final state (f ) with a hamiltonian (H) governing the interaction between radiation and matter. Besides, σ is also proportional to the density of
unoccupied electronic states (ρ) at the final state energy (Ef):
σ = 2π
~ X
f
| hf |H|ii |2δ(Ef − Ei)ρ(Ef), (2.3)
where ~ is the Planck constant over 2π. When an incident photon has energy
(Ei) equal or greater than the electron binding energy, the photon is absorbed
by the material creating a photoelectron that is promoted to unoccupied levels
called absorption edge, and Figure 2.3(a) represents this process. After a few hundreds of attoseconds, other electrons decay from higher energy level in a cascade of probable decay processes to fill the core hole, ideally returning the atom to its ground state. In this process, energy must be released and there are two main ways of doing so: emitting fluorescent X-ray photons, with same energy as the difference between initial and final electronic states (relative to the excited atom); or emitting Auger electrons, which consists in emitting an electron with smaller binding energy than the total difference between initial and final electronic states. In both cases energy is conserved and these distinct processes are represented in Figure 2.3(b).
(a) (b)
Figure 2.3: (a) Schematic representation of the X-ray absorption process. (b) Electron decay from an upper level to fill a core hole created in the absorption process. Either an electron (Auger emission) or a photon (fluorescence channel) is emitted.
Considering this system hamiltonian given by the interaction between vector
momen-tum (~p), one can write H = e
mec
~
p · ~A, where e is the electron charge, me is the
electron mass. Using the plane wave approximation, | ~A| ∝ exp i(~k · ~r − ωt), it
is possible to solve Eq. 2.3 to obtain the famous selection rules for absorption
spectroscopy. Dipole selection rules appear after expanding ei~k·~r in Taylor
se-ries and selecting the zero order term, assuming that ~k · ~r 1 ⇒ λ r. If this
inequality is not satisfied, it is possible to use the expansion next term to obtain the quadrupole selection rules, and so on. Table 2.1 present these two particular cases of absorption selection rules.
Table 2.1: Dipole and quadrupole selection rules for absorption spectroscopy, where l is the electron orbital angular momentum, ml is its momentum component in ˆz direction, s is its spin
angular momentum, msits momentum projection in ˆz, and ∆ represents the difference between
initial and final states of these quantities. ∆mlvalues depend o light polarization: it is zero for
linearly polarized light and ±1, ±2 for circularly polarized. Dipole Quadrupole
∆l ±1 ±2
∆ml ±1, 0 ±2, ±1, 0
∆s 0 0
∆ms 0 0
In this project we are mostly interested in bulk materials, in which i is a core level with very well determined electron states (e.g. 1s, 2p). Therefore, XAS uses these electrons to probe empty bands, for the transitions allowed by the selection rules, and information obtained is related to electronic levels above Fermi energy. In summary, XAS provides several information about electronic properties of materials, from local symmetry and crystalline field to valence, charge transfer and oxidation states, in a way selective to the chemical element
and electronic orbital. In a absorption spectrum, these examples of informa-tion can be retrieved from two regions: X-ray Absorpinforma-tion Near Edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) (see Figure 2.4). XANES region is much influenced by neighboring electronic potentials, where the edge is defined as the energy in which the absorption jump derivative is maximum; and the white line is the region of maximum absorption by the material. EXAFS are oscillations that happens due to scattering of the excited photoelectron wave function in nearby atoms. In this project, experiments were performed focusing the XANES region, so EXAFS methods of analyses are not discussed in this dissertation. The reason is that the main objective is to develop an instrumentation to measure a dichroic signal, which is more intense in the XANES region.
Figure 2.4: XANES and EXAFS regions represented in a absorption spectrum at Fe K-edge of a Fe foil.
To use XAS to gather information about the electronic structure of a certain material, there are a few established experimental methods and I will describe the two approaches used in this project: transmission and fluorescence. It is noteworthy that these methods are not the only available for XAS; for exam-ple, one can measure an electric current due to Auger electron emission (which probability of occurring is higher for low energies, because in lighter elements as electrons are less bonded to the nuclei). Usually, the transmission method is used when the intensity of incident and transmitted photons can be properly distinguished for the energy range one is interested in (common for heavy el-ements). On the other hand, the fluorescence mode is generally applied when energy dependence of transmission cannot be determined, e.g. sample diluted
in solutions with concentration of ∼1% or lower, depending on the solvent. In transmission mode, Lambert-Beer’s Law dictates the experiment. It
re-lates the incident (I0) and transmitted intensities (I1) through a material of
thick-ness t:
I1 = I0 e−µt, (2.4)
where µ is the material total cross section (for the energy range employed
here, µ(E) ≈ σ(E)). Therefore, µ is related to the I1 and I0 by the relation
µ(E) ∝ lnI0(E)
I1(E)
. A setup to measure XAS in transmission is represented in Figure 2.5.
Figure 2.5: Schematics of a typical setup for measuring XAS using transmission geometry in a monochromatic beamline. Beam energy is scanned using a monochromator, I0 and I1 are
acquired with photodiodes or ion chambers before and after the sample, and XAS spectra are obtained by computing ln(I0/I1).
In fluorescence mode, the quantity measured is not the transmitted intensity, but the intensity of emitted photons (I) in fluorescence process. This intensity can be measured, for example, using a silicon drift detector (SDD) that cap-tures emitted photons and then µ(E) ∝ I(E). Figure 2.6 presents a setup for
measuring XAS in fluorescence mode.
Figure 2.6: Schematics of a typical setup for measuring XAS using fluorescence mode. Beam energy is scanned using a monochromator, I is acquired with a silicon drift detector (SDD) and XAS spectra are obtained directly from the SDD.
Figures 2.5 and 2.6 represented XAS experiments in conventional monochro-matic beamlines, but there are some differences when the optics is dispersive polychromatic. As presented in Section 2.1 and Figure 2.2, the sample is placed at the X-ray beam focus position, where typically a few hundreds of eV hits
the same point. I1 is obtained in a CCD, a detector that captures the intensity
of each point in space and relates them with different energies. To calculate
µ, I0 is acquired by simply removing the sample of the beam path and
captur-ing with the CCD. At the LNLS accelerator UVX, the advantages of dispersive optics when compared to monochromatic are: static and small focus, about a few hundreds of micrometers, required for small samples; possibility of time-resolved experiments, with resolution depending on the CCD frame rate; and static optics, which eliminates possible external noises, e.g. coming from floor vibration.
The next subsection presents the magnetic circular dichroism technique, which is derived from XAS, so dichroic experiments can be set up to be performed at either monochromatic or dispersive beamlines, using fluorescence or transmis-sion methods.
2.2.2 X-ray Magnetic Circular Dichroism
XMCD is a technique widely employed in synchrotrons to obtain informa-tion about the magnetism of a certain material [1, 2]. By definiinforma-tion, XMCD is the difference between a magnetic material absorption cross section by circu-larly polarized light to the left and to the right. In these absorption processes, with radiation of opposite helicities, photons transfer their non zero momen-tum to the electrons, promoting them to levels above Fermi energy with
spin-dependent probabilities. The XMCD signal, RXM CD, can be defined as the
normalized difference between absorption cross sections performed with right
circularly polarized (RCP) and left circularly polarized (LCP) radiation, σ+ and
σ−, respectively. Supposing ρ(E) is independent on the momentum projection
(ml) it is possible to write σ± as function of the electronic density of state with
spin up (ρ+) and down (ρ−):
RXM CD = PCPe
∆ρ
ρ , (2.5)
polarization. Pe is the Fano factor, which is related to the probability of the
photoelectron polarization created during the absorption process. At the atomic
limit, Pe assumes some typical values, e.g. 0.01 for 1s → p promotions and
0.25 for 2p3
2 → d excitation [14].
A magnetic material has a disproportionality between ρ+and ρ−, which is
di-rectly related to the material magnetic properties. Then, as a technique derived from XAS, measuring this disproportionality with XMCD gives magnetic in-formation with chemical and orbital selectivity. The two-step model for XMCD is an easy way to visualize this phenomenon: in the first step, circularly polar-ized X-rays transfer their angular momentum, generating photoelectrons from a core level. In the second step, following the absorption selection rules, the conduction band serves as a spin and orbital momentum detector for the photo-electron. Figure 2.7 represents the absorption processes for circularly polarized photons. This interaction between photon and electron is maximum when both photon angular momentum and electron spin are aligned (parallelly or antipar-allelly). Then, to maximize the dichroic signal, magnets that provide strong fields (e.g. large superconducting ∼5 T magnets) are desirable in order to study hard-to-magnetize samples with XMCD, even if their usage brings experimental difficulties like long time periods for field inversion.
(a) (b)
Figure 2.7: Representation of the spin-dependent X-ray absorption process in 3d metal L-edges. The magnetization direction was chosen such that the spin down electron band is totally filled and the spin up band is partially unfilled (only spin up transitions are allowed). Circularly po-larized X-rays are absorbed by core electrons with different probabilities according their spin. Equivalently, electrons have different probabilities of being excited by circularly polarized pho-tons with opposite helicities. For example, in a L3-edge, Phano effect accounts a chance of
62.5% for RCP radiation to excite spin up electrons, and 37.5% for LCP; while in L2-edges,
these percentages change to 25% for RCP radiation and 75% for LCP. The photon momentum (q, in units of ~) is transferred to the electrons and they are promoted to unoccupied states ac-cording to the absorption selection rules (Table 2.1). Differences on polarization-dependent ab-sorption spectra (and, consequently, XMCD) occurs due to the disproportionality on electronic allowed states above EF. This figure was adapted from reference [14], where (a) illustrates the
band model and (b) the atomic model.
Although this model properly explains XMCD for initial electronic states with l 6= 0, it is not valid for K-edge spectroscopy (where 1s electrons are
pro-moted). l = 0 implies in no spin-orbit coupling in the initial state, so electrons with spin up and down are selected with the same probability. The momentum transferred from the photon to the photoelectron pair allows spin-orbit coupling to occur in the final state, and a dichroic signal appears only if there is a
dif-ference between ρ+ and ρ− in the final state [1]. This effect makes K-edge
XMCD signal intensity from 10 to 100 times inferior when compared to L2,3
-edges (where 2p1
2 and 2p
3
2 are excited, and XMCD signals in transition metals
are large, usually with intensity of 10% of the absorption jump). It is also
note-worthy that the dichroic signal in L2,3-edges of rare earth elements and actinides
is more intense than K-edge XMCD, because there is spin-orbit coupling for
p-electrons; though, the signal is smaller than in the same L2,3-edges of 3d metals,
because XMCD experiments, via dipole selection rules, excite these p-electrons to empty 5d or 6d bands, providing an indirect measurement of unoccupied 4f or 5f states, responsible for the ion magnetic moment. Therefore this is why the instrumentation developed in this project is important, because it allows to per-form efficient XMCD experiments aiming on improving signal-to-noise ratio for these low intensity signals.
2.3
X-ray Diffraction and Birefringence
Diffraction is a phenomenon in which waves interfere constructively and destructively with itself around obstacles, creating patterns depending on the
obstacle geometry. When it comes to interaction of radiation and matter, this phenomenon is useful to reconstruct atomic structures from patterns formed af-ter X-rays elastically scataf-tering at a given sample. Using Bragg’s Law (Eq. 2.2), one can determine the d-spacing between sets of atomic planes aligned in
de-termined reflections, which diffracts with specific angles θB when the radiation
wavelength is known. Figure 2.8 represents Bragg diffraction condition.
Figure 2.8: Bragg diffraction, in which there is coherent interference if radiation with wavevec-tor ~KOis incident with an angle θB, and photons are diffracted with wavevector ~Kh.
There are two types of mathematical approaches to describe this theory: the kinematical and the dynamical theory of Diffraction [18, 19]. Kinemati-cal theory considers only one interaction between radiation and the crystalline planes, neglecting the interactions with other planes after photons were already reflected or transmitted by one plane. In contrast, the dynamical approach that takes into account the several interactions between incident, reflected and trans-mitted X-rays and the atomic planes in the crystal. Both theories neglect
mag-netic interactions and assume an electric isotropic medium. The dynamical the-ory of diffraction is a complex thethe-ory and, although it explains several effects that the kinematical approach is not capable of, its mathematical description is not the main objective of this work. However, two outcomes from the dynam-ical approach that are extremely important for this project development are: i) the Darwin width [13], that is a plateau in intensity of diffracted X-rays when varying the radiation incidence angle near Bragg condition. One would expect that, for perfect crystals, radiation has a Dirac delta-like reflection pattern, but Darwin showed there is an intrinsic width associated with the reflection. ii) birefringence [20], that is the main effect ruling the quarter wave plate physics used in this project. Birefringence is a property that states different velocities for wavefields propagating in different directions in a certain medium, which means different indexes of refraction according to directions in space. In the X-ray range, birefringence only occurs near absorption edges of anisotropic materials and close to Bragg condition. This happens because, different from the visible light regime, dielectric properties (related to the energy-independent
atomic form factor, f0) are not usually too sensitive to radiation at X-ray
wave-lengths; but when Bragg diffraction occurs, the predominant phenomenon is
also related to the dispersion corrections (f0 for scattering, and f00 for
absorp-tion) of the total atomic scattering factor, f = f0 + f0 + if00, which creates
calcu-lated using the coefficients for analytical approximation reported in the Actas of Crystallography [21], as I did in this work for some materials. Therefore, near a crystal Bragg condition, a photon with σ-polarization goes through the crystal with different velocity than a π-polarized, due to birefringence [22]. If they were in phase when entered the crystal, they will be dephased when both come out.
In this project, an X-ray phase retarder was applied in Bragg diffraction, in transmission mode. For certain geometric constrains according to the incoming beam, it converts incident linearly polarized radiation into circularly polarized (to the left or to the right). For this conversion to properly occur, radiation inten-sity must be equal in two directions: one is in the plane formed by diffracted and transmitted beams, called π-polarized; and the other is a plane perpendicular to π-direction and containing the transmitted beam, called σ-polarized. Figure 2.9 presents the Bragg transmission geometry and the σ and π planes in diffraction.
Figure 2.9: Radiation transmitted through a phase plate converted from linearly to circularly polarized, in a Bragg diffraction case. Figure taken from reference [23].
The equation that rules the dephasing, δ, between σ- and π-polarized photons inside the crystal (near Bragg condition) is related to the difference between the
complexes indexes of refraction in both directions, nσ and nπ:
δ = 2πk(nσ− nπ)t, (2.6)
where t is the effective crystal thickness. Then, nσ and nπ can be deduce
from the dynamical theory fundamental equations [24, 25], which relates the electrical susceptibility, χ, and local electric displacement, D, in the following fundamental equations:
2χODO − kCDh = 0
−kCDO + 2χhDh = 0,
where k = 2π
λ is the radiation wavenumber, C is a geometric factor relating
~
Dh, ~KO and ~Kh, and the sub-indexes O and h are associated with incoming
and diffracted radiation respectively. How to solve these equations are not in the scope of this project, so I will spare the reader from lots of mathematics and geometrical relations and go directly to the final equation that relates the dephasing, δ, between σ- and π-polarized photons:
δ = −π 2 re πV 2 λ3t <[FhFh¯] sin 2θB ∆θ , (2.7)
where re is the classical electron radius, V is the unit cell volume, Fh is the
crystal structure factor for Miller Indexes (hkl) at a given radiation wavelength
λ, and ∆θ = θ−θB is a small offset from Bragg angle, θB. With this equation, it
is possible to apply a phase retarder in a instrumentation to convert synchrotron radiation from linearly to circularly polarized, as it will be described in the next Chapter. Figure 2.10 exemplifies the difference on σ- and π-components in a Bragg diffraction case, with a great representation of the Darwin width considering the contribution of absorption for the peaks asymmetry (for more glazing angles, X-ray path is longer, making absorption more relevant than at
higher angles).
Figure 2.10: Difference between reflected σ- (magenta) and π-polarized photons (blue), as function of the crystal rotation angle around Si(333) Bragg peak at 10 keV. Figure adapted from reference [13].
Considering this theoretical overview, in the next Chapter dephasing and po-larization converting are then applied in an instrumentation to achieve radiation
Chapter 3
Instrumentation Development
This instrumentation is mainly based on two components: a quarter wave plate (QWP) for fast helicity switching of polarization, and synchronous acqui-sition for signal-to-noise ratio improvement. It was developed to be used at the monochromatic EMA beamline of Sirius, at LNLS, and was tested at monochro-matic W09A-XDS beamline of UVX, also at LNLS. In addition, it was also designed to be compatible with polychromatic dispersive geometry, then tested at D06A-DXAS beamline of UVX. This setup was based on the previous re-port of Suzuki et al. [26], with modifications to allow energy scanning, fast helicity switching, lock-in noise-filtering and capability to hold several QWPs. This setup is represented in Figure 3.1, together with the elements required to perform an XMCD experiment.
Figure 3.1: QWP experimental setup representation. A vacuum chamber is required because, at Sirius, the setup is directly connected to the EMA beamline vacuum. The inset details the motors assembly, which can be used for alignment corrections in many directions during an XMCD experiment, and the support for up to 10 diamond QWPs with different thicknesses to access many energy ranges. This schematic describes how a slit scans a dispersive beam for energy selection, to allow the use of transmission detectors for lock-in detection.
The instrumentation is composed of two supports to hold up to 5 QWP each, so there are different types of plates to cover a wide energy range (Figure 3.2). Below them, a pair of swivels is employed to adjust the angles for Bragg diffrac-tion condidiffrac-tion: as presented in Figure 2.9, the angle between the incoming beam polarization (horizontal) and the θ rotation axis must be 45 degrees in order to
achieve PC = 1. A piezoactuator (PZT) is responsible for rotating the QWP
by ∆θ, setting them at the positions around de Bragg peak for maximum right and left circular polarization degree. A pair of motors support all of these de-scribed elements, adding degrees of freedom in both vertical and horizontal
axes, in order to allow the selection of a proper QWP for a given energy, and also alignment corrections. This whole system is set inside a vacuum chamber and rotation to the plates Bragg angle in performed by an external θ-2θ
mo-tor. For a Bragg condition at θB, the diffracted beam can be measured at 2θB
by a photodiode also external to the chamber, coming out from a circular Be
window. This completes the setup, which is mounted roughly at 45◦ on top
of a translation table, that serves as another alignment motor (for conventional monochromatic beamlines) and scans the X-ray beam to select its energy (for dispersive polychromatic beamlines, as in subsection 3.1.1).
To perform an XMCD experiment using this instrumentation, we also need current amplifiers, that convert the small current (in most of the cases, from 100 pA to 10 nA) generated at the detectors (photodiodes or ion chambers) to
the voltage to be read on a computer or analogical calculator for lnI0
I1
. Then, for each point in energy, the monochromatic beam passes through the QWP
(positioned at θB ± ∆θ) to be converted to either PC to the right or to the left.
Two XAS experiments are performed with radiation of opposite helicities, so a dichroic signal is obtained by their subtraction. A next step to enhance the XMCD signal is using a lock-in amplifier to simultaneously obtain XANES
of different PC’s and automatically output the XMCD signal. This is called
synchronous acquisition and is described in Section 3.2.
this instrumentation application at XDS (monochromatic) and DXAS (poly-chromatic) beamlines.
3.1
Bragg Transmission Phase Retarder in Monochromatic
X-ray Optics
Since its theoretical description in the late 80’s [27], phase retarders have been used in synchrotrons monochromatic beamlines and opened up a field of study for its implementation and reliability in magnetic dichroism experiments [23, 28, 29, 30, 31]. In the 90’s, there were also advances regarding the insertion of QWPs in dispersive polychromatic beamlines, which is challenging mainly due to the high beam divergence and size, adding even more geometrical con-strains to experiments [24, 32, 33]. In this work, the instrumentation developed is unique due to its versatility: it is possible to be utilized in both dispersive and monochromatic beamlines, combining high degree of synchrotron polarization with synchronous acquisition (which is not possible in conventional dispersive optics and will be detailed further in Section 3.2).
A phase retarder is a single crystalline plate that enables changing the radi-ation polarizradi-ation. In this project, it is also called phase plate or quarter wave
plate (QWP), due to the required 90◦ dephasing between σ- and π-components
of the photons electric field, to achieve maximum PC. First, for the QWP to
both σ and π axes, the phase retarder must have its Bragg diffraction happening out of the horizontal (or vertical) plane. For total circularly polarized
transmit-ted photons, the rotation axis θ must be at a 45◦ angle with the horizontal plane,
so σ- and π-components of the radiation electric field have the same modulus. Otherwise, photons are said elliptically polarized. Then, according to Eq. 2.7,
maximum PC is obtained at a small offset from Bragg angle:
∆θ = ± re
πV
2
λ3t <[FhF¯h] sin 2θB. (3.1)
To calculate this value, I wrote a Mathematica code (Appendix A) in which
θB, ∆θ and the transmission through the phase plate were dependent on only
four variables: QWP material (e.g. Diamond, Germanium, Moissanite, Quartz, Sapphire and Silicon), crystalline reflection, plate thickness and photon energy. As mentioned before, this instrumentation was built to cover a large energy range, which requires several QWP to optimize both ∆θ and transmission. Us-ing the software I wrote, Figure 3.2 shows this correlation and allows choosUs-ing the suitable QWP.
2 0 µm G e r m a n i u m ( 2 , 2 , 0 ) 1 0 µm S i l i c o n ( 1 , 1 , 1 ) 5 0 µm S i l i c o n ( 4 , 0 , 0 ) 4 0 0 µm D i a m o n d ( 1 , 1 , 1 ) 1 0 0 0 µm D i a m o n d ( 2 , 2 , 0 ) 2 0 0 0 µm M o i s s a n i t e ( 3 , 3 , 0 ) 4 8 1 2 1 6 2 0 0 1 0 2 0 3 0 4 0 5 0 L a - L 3 G d - L 3 Y b - L 3 P t - L 3 P t - L2 U - L2 U - L3 Dq ( m ili d e g re e s ) E n e r g y ( k e V ) U - M 2 , 3 (a) 2 0 µm G e r m a n i u m ( 2 , 2 , 0 ) 1 0 µm S i l i c o n ( 1 , 1 , 1 ) 5 0 µm S i l i c o n ( 4 , 0 , 0 ) 4 0 0 µm D i a m o n d ( 1 , 1 , 1 ) 1 0 0 0 µm D i a m o n d ( 2 , 2 , 0 ) 2 0 0 0 µm M o i s s a n i t e ( 3 , 3 , 0 ) 4 8 1 2 1 6 2 0 0 2 0 4 0 6 0 8 0 1 0 0 T ra n s m is s io n ( % ) E n e r g y ( k e V ) U - L 3 U - L 2 P t - L 2 P t - L 3 Y b - L 3 G d - L 3 L a - L 3 U - M 2 , 3 (b)
Figure 3.2: (a) Offset from Bragg angle for maximum PC, for various materials and reflections.
(b) Transmission through QWPs at θB− ∆θ.
Due to ground vibrations at UVX, which seriously compromised the system precision and stability, there is an optimal range of desired ∆θ, usually being
above 0.005◦ = 5 mdeg (millidegrees). Besides, the angular positions cannot
be too close (about 1 or 2 mdeg) to the Bragg diffraction condition because this other phenomenon would be majoritarian and there would be no transmitted beam through the plate. There is a compromise with photon flux as well, so the thinner the QWP is, more it transmits and beam intensity is maximized. So,
using Gd L3-edge as an example, we have chosen the 400 µm-thick diamond
QWP in (1,1,1) reflection among the options presented in Figure 3.2, because
the transmission is about 30% and offset to obtain maximum PC is about 24
one goes to high energies, e.g. at U L3-edge, there is not much concern with
transmission so a thicker crystal can be employed, like a diamond 1 mm thick oriented at (2,2,0); but ∆θ is small (∼4 mdeg), requiring us to use a larger offset
and generating a smaller degree of circular polarization (0.5 < PC < 1).
After theoretical predictions, I performed polarization measurements for beam transmitted through a QWP and results are presented in Figure 3.3(b). This mea-surement was performed using photodiodes to determine the beam polarization components in horizontal and vertical projections, via Thompson scattering by air, which is polarization-selective: X-ray scattered to the vertical only has po-larization component on the horizontal plane and vice versa (Figure 3.3(a)). Degree of circular polarization is calculated according to Eq. 3.2:
PC = 2|Eσ||Eπ| |Eπ|2 + |Eσ|2 , (3.2) where, |Eσ| = √ IV and |Eπ| = √
IH are the electric field moduli of radiation
oscillating in σ and π planes, respectively. For a 400 µm thick C(111) plate, we successfully achieved ∼98% of circular polarization degree, as Figure 3.3(b) presents.
(a) 0 . 0 1 2 7 ° 0 . 0 1 3 7 ° - 0 . 0 2 0 . 0 0 0 . 0 2 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 C ir c u la r P o la ri z a ti o n D e g re e θ − θB ( d e g r e e s ) IV IH T ra n s m it te d I n te n s it y ( a .u .) B r a g g P e a k (b)
Figure 3.3: (a) Schematics of IV and IH measurements: intensities related to |Eσ| and |Eπ| are
measured with detectors positioned above and beside the X-ray beam, by elastic scattering by air. (b) 400 µm thick diamond plate (1,1,1) Bragg peak (black circles) and intensities IV (red
circles) and IH (blue circles) associated with the polarization components σ and π, respectively,
for an 9 keV incoming X-ray beam; and experimental curve for PC. Experiment performed at
XDS beamline.
In Figure 3.3, there is an asymmetry on offsets from Bragg angle. While we
have ∆θ =12.7 mdeg to reach maximum PC for one helicity (lets say
circu-larly polarized to the right), it is needed 13.7 mdeg to achieve the other helicity (left). This may be due to the crystal absorption, which is different when com-pared in both sides of the Bragg peak, as can be seen in Figure 3.3(b), black
be-tween the horizontal plane and the QWP θ-rotation axis. During an experiment
with polarization switching, we use a fixed ∆θ value, and this asymmetry in PC
can induce differences at XMCD intensities, called artifacts. To overcome the artifact appearance, in addition to helicity switching, we also perform XMCD experiments inverting the magnetic field direction between parallel and antipar-allel to the beam. This is another improvement provided by this versatile instru-mentation. Besides that, to minimize noise and measure small dichroic signals without artifacts, we can choose to perform XMCD experiments with a reduced degree of circular polarization (around 80%), offsetting the QWP further from
the peak of maximum PC. With this greater offset, the behavior of PC becomes
approximately linear with ∆θ. In Figure 3.3(b), we can interpolate straight lines in the regions 13 mdeg < |∆θ| < 40 mdeg and propagate errors to obtain the
following relation for the error in PC: ∆(PC) ≈ (30/mdeg) · ∆(∆θ). Therefore,
in these regions we have that an error of ∼ 0.001◦ in ∆θ causes an error of
∼ 3% in PC. This is a great precision in PC given ∆(∆θ) in the order of the
angular asymmetry to obtain maximum PC to the left and to the right.
Until now, every description of the QWP and experiments presented were related to monochromatic beamlines. Therefore, in the next subsection I present the challenges for XMCD experiments performed at the DXAS beamline with this instrumentation.
3.1.1 Dispersive Polychromatic X-ray Optics
Dispersive polychromatic beamlines are usually unable to perform
locked-in experiments due to its non-concomitant I0 and I1 acquisition. In order to
combine the dispersive geometry with the lock-in noise-filtering (as described in Section 3.2), a slit is required between the polychromator and the QWP position, to scan the incident polychromatic beam [34]. This defines and selects an energy bandwidth (δE) small enough for the beam to be considered monochromatic at each slit position, given the dispersive geometry contributions to the energy
resolution δEopt [15]. Then,
δE = q
(δEopt)2 + (δEs)2, (3.3)
where δEs is the slit aperture contribution to the total energy resolution. It
is possible to estimate the latter term using the relation δEs
∆E =
δLs
∆L, where ∆E
is the total energy bandwidth passing through a large region with length ∆L, at
the slit position, which has a small aperture δLs.
The monochromatic beam condition allows the use of ionization chambers
or photodiodes, instead of a CCD, to acquire the fast response of I0 and I1
si-multaneously, a requisition for lock-in noise-filtering. The QWP setup is placed between the slit and the first ionization chamber, as shown in Figure 3.1. More-over, there is a limitation in the available energy bandwidth associated with the distance from the QWP to the slit. This limitation is due to the coupled
translation of both slit and QWP, which causes a misalignment (∆X) between these two elements as the beam angle varies with the slit scan (as schematized on Figure 3.4). Therefore, a relative slit translation (correction) is required to maintain the QWP centered at the beam through an entire energy scan. Figure 3.4 also presents calculations for the bandwidth as function of both QWP width and distance from the QWP to the slit, according to:
BQW P =
Bbq
Fb(S − d)
wQW P sin θB, (3.4)
where BQW P is the energy bandwidth accepted by the QWP, Bb is the
beam-line bandwidth, q is the distance from the polychromator to the focus, Fb is the
beam footprint, (S − d) is QWP-to-slit distance, wQW P is the QWP horizontal
(a) 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 0 0 2 0 0 3 0 0 4 0 0 0 Q W P t o S l i t D i s t a n c e : 1 0 0 c m Q W P S i z e : 5 m m 0 E n e rg y B a n d w id th ( e V ) D i s t a n c e b e t w e e n Q W P a n d S l i t ( c m ) 0 B e a m l i n e @ 7 2 4 3 e V 2 0 4 0 6 0 8 0 1 0 0 Q W P s i z e ( m m ) (b)
Figure 3.4: (a) Developed QWP instrumentation (top view, without the vacuum chamber) in situations that dispersive optics could make the beam pass or not through the QWP. In the case of this instrumentation, S d. So as the slit scans across the dispersive beam, there is a condition when the beam does not hit the QWP. This alignment limitation causes the short spectral energy bandwidth, requiring a relative slit translation to maintain the QWP centered at the beam through an entire energy scan. (b) DXAS beamline energy bandwidth (black line) at a fixed energy of 7243 eV, p = 9.75 m and q = 1.5 m; and theoretical calculation for the bandwidth available for the XMCD experiment (red line), as a function of the distance from the QWP (∼5 x 5 mm2) to the slit. The blue line is the bandwidth calculation as a function of the
QWP size, for the same energy of 7243 eV, at a fixed distance of 100 cm between the QWP and the slit.
Considering the diameter of the QWP vacuum chamber and the distance from the polychromator to the focus, this setup would have a very small spectral energy bandwidth (about 20 eV). To maximize the energy bandwidth would be necessary to move the phase retarder closer to the slit or to move the QWP closer to the sample. However, usually it is not possible to move the QWP closer to the sample, because there is the need to use large superconducting magnets (usually with radius larger than 250 mm) to magnetize harder magnetic materials. In the other hand, it is not possible to move the slit closer to the QWP without
compromising energy resolution.
Then, to increase the energy bandwidth an algorithm was implemented: it concomitantly translates both slit and QWP according to the beam trajectories using triangles similarity. Looking at both Figures 3.4(a) and 3.5, the energy can be defined by the position of the slit aperture relative to the translation table, thus guaranteed the beam to always pass through the phase plate center. This implies that the energy of an X-ray beam at the position (X) with distance to the focus (M ) is given by
E(M, X) = ∆E
∆L S
MX, (3.5)
where ∆E and ∆L are taken at the slit position S. Therefore, the misalign-ment (∆X) for a specific energy would be due to the difference between the beam position as if the QWP was placed exactly at the slit position (S) instead of its real position (d), or simply:
∆X(E, S, d) = XS − Xd = ∆L ∆EE − ∆L ∆E S dE = ∆L ∆E E S(S − d), (3.6)
and the corrected energy would be
E(∆X, S, d) = ∆E
∆L S
Figure 3.5: Representation of the elements used to elaborate the correction for the QWP posi-tioning. An X-ray beam with energy E selected by the slit at a distance S from focus, positioned at a XSwith respect to the translation axis X. The QWP ideal position is than Xd, at a distance
d from the focal point. Then, equation 3.5 is obtained using the relation for energy resolution in space: ∆E
E =
∆L
L , and substituting L = S · X
M (because the energy bandwidth ∆L is selected at S), where X and M are variables in directions X and M . In particular, equation 3.4 can be obtained using this same schematics, and considering the widths of both QWP and slit aperture.
This relative slit translation allowed the energy range enlargement of XANES and XMCD spectra, from about 20 eV to the total beamline bandwidth as de-scribed above (∼400 eV at 7 keV for this case). Figure 3.6 compares XANES spectra before and after the correction was implemented. It also enabled to obtain a XAS and XMCD spectra in fluorescence mode at DXAS beamline. This is demonstrated in Figure 3.6 where we show a comparison between
trans-mission and fluorescence absorption spectroscopy at the Fe K-edge of a Fe2O3
- 2 0 - 1 0 0 1 0 2 0 3 0 0 . 0 0 . 5 1 . 0 1 . 5 N o rm a liz e d X A N E S ( a .u .) E - E 0 ( e V ) W i t h o u t c o r r e c t i o n W i t h c o r r e c t i o n G d L 3- e d g e X A N E S (a) - 3 0 0 3 0 6 0 9 0 0 . 0 0 . 5 1 . 0 1 . 5 N o rm a liz e d X A N E S ( a .u .) E - E 0 ( e V ) F l u o r e s c e n c e T r a n s m i s s i o n F e K - e d g e X A N E S (b)
Figure 3.6: (a) Comparison between spectra obtained with and without the implemented en-ergy/position correction. (b) Fluorescence mode XAS of Fe K-edge on a 10% diluted Fe2O3
obtained at the dispersive beamline compared to its transmission mode counter-part. The dis-tortions in fluorescence data are due to emitted photon being re-absorbed by the sample before reaching the SDD (self-absorption phenomenon).
To perform an XMCD spectrum, we have to scan the energy by moving the slit and concomitantly track the Bragg angle and the QWP relative position for each point of energy according to equation 3.6. This allows to use small dia-mond plates, which are easier to find and cheaper, even in the case of very large distances between the QWP and the focal plane. Moreover, this makes possible, for example, to use large superconducting magnet as mentioned before. XMCD results using this instrumentation are presented in the next Section, along with an explanation to synchronous detection.
3.2
Synchronous Acquisition
Experiments using synchronous acquisition require a lock-in: an instrument that measures signals with intensity comparable to noise, using both time and frequency domain to amplify signal/noise ratio. Basically, it consists in a elec-tronic circuit which receive as input the noisy measured oscillating signal and a pure-frequency reference signal (which has frequency equal to the signal one wants to extract from the noisy measurement), performs a Fourier Transform, and outputs the filtered signal amplitude and phase. This filtering capacity is re-lated to the lock-in time constant (tunable), a parameter for a low-pass filter that is employed after the Fourier Transform in order to amplify the DC component [35].
In this project, the desired measurement is the XMCD signal obtained by the difference of two absorption spectra with X-ray polarization of opposite helic-ities, as presented in Section 2.2 [36, 37]. The reference signal is the square
wave generated to set the QWP to both angular positions of maximum PC, as
explained in the previous Section, oscillating in 13 Hz. Therefore, each plateau of the square wave represents one XANES with LCP or RCP photons, and the amplitude parameter given by the lock-in is the difference between them, that is, the XMCD signal already filtered of all noises with frequencies different from 13 Hz. In particular, this oscillation frequency could be as high as the PZT settling time allows (about 100 Hz), and going to higher frequencies assists the
lock-in to filter low frequency noises. But, at UVX the frequency was main-tained in the order of Hz, because time for each square wave plateau is higher, increasing the photon flux for each XANES compared to higher oscillation fre-quencies. Figure 3.7 represents the oscilloscope screen monitored during an XMCD experiment.
Figure 3.7: Representation of oscilloscope channels during a locked-in XMCD experiment. Red line is the square wave generator input for the PZT, which oscillates the QWP. Blue line is the square wave reference signal input for lock-in, offseted from red signal by φ. Green and purple lines represent I0 and I1, respectively, with Bragg peaks appearing for every helicity
switch, and maximum circular polarization degree to right and to the left are obtained where the curves are constant in time. Yellow line is ln(I0/I1), which should be constant (in time, varying
with respect to energy), because variations in I0and I1due to the QWP are ideally canceled out
when calculating the intensities ratio.
Ideally, the lock-in reference signal is equal to the input for the PZT that oscillates the QWP. However, there is a dephasing between the PZT input and
the diamond Bragg position in time, due to the instrumentation mechanical and electronic time response. Simply shifting the lock-in reference square wave
solves this time response problem, as Figure 3.7 shows. I0, I1 and the logarithm
channels are useful to verify the detectors acquisition dynamics during the ex-periment: if the photon flux is too low, we have to “sacrifice” the low-noise acquisition mode at the current amplifiers, changing it to high bandwidth. By doing so, less noise is filtered by the electronics, but the acquisition response is faster, allowing a small photon count/current to be enough for the electronics. In particular, flux issues should not be a problem at EMA beamline due to better
beam conditions proportioned by a 4th generation storage ring. Even at Sirius,
from the oscilloscope screen it is possible to see how much information is re-quired and needs to be tracked to perform an XMCD experiment in the most ideal condition.
In order to compare the efficiency of application of lock-in noise-filtering, we performed XMCD measurements at XDS beamline with and without
syn-chronous acquisition, at Co K-edge of a GdCo2 sample. Figure 3.8 presents the
results obtained, in which the QWP oscillated between positions for maximum
- 2 0 - 1 0 0 1 0 2 0 3 0 - 0 . 1 0 - 0 . 0 5 0 . 0 0 0 . 0 5 0 . 1 0 G d C o 2 @ C o K - e d g e : W i t h l o c k - i n W i t h o u t l o c k - i n 1 0 2 X M C D ( a .u .) E - E 0 ( e V )
Figure 3.8: Comparison between XMCD spectra with and without synchronous acquisition per-formed at Co K-edge (7709 eV) of a GdCo2 sample. Both measurements were performed with
the same amount time (40 minutes each). This sample was grown by arc melting as described in the next Chapter, Section 4.1.
There is a clear signal improvement provided by the use of lock-in acqui-sition. However, this improvement will probably be more evident at EMA beamline, with better photon flux (because of the acquisition dynamics issues explained before) and much better floor stability. At XDS, the instrumenta-tion received external vibrainstrumenta-tions at low frequencies, coming from a poor floor isolation. To overcome this problem, a solution is to switch helicity at high fre-quencies, so the lock-in can discriminate and filter these low-frequency noises better. The setup was designed to oscillate up to 100 Hz, but the time period for XANES of opposite polarizations would be less than 5 ms, which would lead to an even smaller flux at UVX for lower energies. Although the beam conditions
limited this frequency to only a few Hz, the XMCD signal was indeed enhanced by synchronous acquisition.
Another important result obtained at XDS beamline is presented in Figure
3.2: an XMCD measurement of a UMn2Si2 sample performed at U L3-edge, at
XDS beamline. Despite of the U magnetic lattice ordering temperature being below 300 K, a dichroic signal was obtained because the Mn magnetic lattice ordering temperature is 377 K [38]. So this XMCD signal is due to an induced magnetism on U due to Mn. 1 7 . 1 5 1 7 . 1 6 1 7 . 1 7 1 7 . 1 8 1 7 . 1 9 0 . 0 0 0 . 0 3 0 . 0 6 0 . 0 9 0 . 1 2 6 d 1 0 2 X M C D ( a rb . u n it s ) E n e r g y ( k e V ) U M n 2S i2 @ U L 3 - e d g e 5 f 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 N o rm a liz e d X A N E S
Figure 3.9: XANES and XMCD spectra performed at U L3-edge of a UMn2Si2 sample. This
sample was also grown by arc melting.
Similar XMCD measurements on UMn2Si2 at U L3-edge were performed at
out-of-orbit elliptically polarized radiation, it was suggested that the two observed XMCD peaks were due to dipole (2p → 6d) and quadrupole (2p → 5f ) ab-sorption processes. The uncommonly seen quadrupole contribution is allowed
in this case because X-ray energy is high (E = 17 keV λ = 0.72929 ˚A), making
wavelength and orbital distances comparable. This explanation is in good agree-ment with ab initio simulations [11]. However, these peaks were not resolved in the XMCD presented in this work, even after several hours of measurement (and error bars smaller then the points presented in Figure 3.9). The reason may be due to the beamline energy resolution (and poor source conditions at the W09A port, as explained at Appendix B): ∆E ∼ 5 eV, which is the approximated distance between dipole and quadrupole channel peaks. Even with these dif-ficulties, the QWP commissioning at high energies was considered successful, because for plates with thickness that allow reasonable transmission, ∆θ is
usu-ally inferior to 5 mdeg, and it is hard to obtain PC because the angular position
for its maximum remains inside the Bragg peak. This affects the XMCD sig-nal diminishing both transmitted photon flux (Bragg diffraction is a competing
phenomenon) and PC for the experiment.
With this successful commissioning, the next step for this instrumentation
was to test it in a more challenging experimental condition: a GdCo2 sample
