Instituto de F´ısica “Gleb Wataghin”
Ulisses Ferreira Kaneko
Phase Transitions and Electronic Fluctuations in
Iron-Based Pnictides
Transic
¸ ˜
oes de Fase e Flutuac
¸ ˜
oes Eletrˆ
onicas em
Pnict´ıdeos `
a Base de Ferro
Campinas 2017
Phase Transitions and Electronic Fluctuations in
Iron-Based Pnictides
Transic
¸ ˜
oes de Fase e Flutuac
¸ ˜
oes Eletrˆ
onicas em
Pnict´ıdeos `
a Base de Ferro
Thesis presented to the ”Gleb Wataghin” Insti-tute of Physics at University of Campinas in par-tial fulfillment of the requirements for the degree of Ph.D. in Sciences.
Tese apresentada ao Instituto de F´ısica ”Gleb Wataghin” da Universidade Estadual de Camp-inas como parte dos requisitos exigidos para a obten¸c˜ao do t´ıtulo de Doutor em Ciˆencias.
Advisor/Orientador: Prof. Dr. Eduardo Granado Monteiro da Silva
ESTE EXEMPLAR CORRESPONDE ´A VERS ˜AO FINAL DA TESE DE DOUTORADO DEFENDIDA PELO ALUNO ULISSES FERREIRA KANEKO E ORIENTADO PELO PROF. DR. EDUARDO GRANADO MONTEIRO DA SILVA.
Campinas 2017
Ficha catalográfica
Universidade Estadual de Campinas Biblioteca do Instituto de Física Gleb Wataghin Lucimeire de Oliveira Silva da Rocha - CRB 8/9174
Kaneko, Ulisses Ferreira,
K131p KanPhase transitions and electronic fluctuations in iron-based pnictides /
Ulisses Ferreira Kaneko. – Campinas, SP : [s.n.], 2017.
KanOrientador: Eduardo Granado Monteiro da Silva.
KanTese (doutorado) – Universidade Estadual de Campinas, Instituto de Física
Gleb Wataghin.
Kan1. Flutuações nemáticas. 2. Supercondutores à base de ferro. 3.
Espectroscopia Raman. I. Silva, Eduardo Granado Monteiro da,1974-. II. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. III. Título.
Informações para Biblioteca Digital
Título em outro idioma: Transições de fase e flutuações eletrônicas em pnictídeos à base de ferro
Palavras-chave em inglês: Nematic fluctuations
Iron-based superconductors Raman spectroscopy
Área de concentração: Física Titulação: Doutor em Ciências Banca examinadora:
Eduardo Granado Monteiro da Silva [Orientador] Eduardo Miranda
Iakov Veniaminovitch Kopelevich Eduardo Matzenbacher Bittar Carlos William de Araujo Paschoal Data de defesa: 23-02-2017
Programa de Pós-Graduação: Física
MEMBROS DA COMISSÃO JULGADORA DA TESE DE DOUTORADO DE
ULISSES FERREIRA KANEKO – RA: 036325 APRESENTADA E APROVADA
AO INSTITUTO DE FÍSICA “GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 23/02/2017.
COMISSÃO JULGADORA:
-
Prof. Dr
.Eduardo Granado Monteiro da Silva
-
Prof. Dr. Eduardo Miranda
-
Prof. Dr. Iakov Veniaminovitch Kopelevitch
-
Prof. Dr. Eduardo Matzenbacher Bittar
-
Prof. Dr. Carlos William de Araujo Paschoal
A Ata de Defesa, assinada pelos membros da Comissão Examinadora, consta no processo de vida acadêmica do aluno.
CAMPINAS 2017
First of all, I want to thank my advisor Professor Eduardo Granado. It has been an honor to work with such a brilliant scientist like him. His patience and ability to teach physics always helped me during my doctorate. He was always ready to give me a hand in the laboratory and was kindly opened to discuss whatsoever results we had. He gave me total freedom and time to explore the challenges of this work, and to me, his advice was always enlightening. Thank you Professor.
I am also grateful to Professors Pascoal Pagliuso, Ricardo Urbano, Carlos Rettori and Gaston Barberis for raising the level of the discussions at our meetings and for valuable ideas that contributed to my thesis. Thanks also to the fellows of our group who have synthesized iron-based single crystals, Dr. Thales Garitezi, Dr. Dina Tobia, Dr. Camilo Bruno R. Jesus, Dr. Guilherme Gorgen Lesseux, Dr. M´ario Moda Paiva and MSc. Matheus Radaelli.
I would also like to thank Professor David Vaknin from Ames Laboratory, USA, for his collaboration on the main theme of this thesis. Professor Vaknin has been in our department as a Visiting Professor at the beginning of my Ph.D., in that opportunity he provided me with the high-quality LaFeAsO single crystals. Even though by email, he was always ready to discuss our findings with Raman spectroscopy in LaFeAsO.
I would like to express my gratitude to Professor Raimundo Lora Serrano who pro-vided samples for neutron scattering studies and also to Professor Fernando Garcia who enthusiastically work with us in this samples resulting in a fair Physical Review B publi-cation.
I am indebted to the secretaries of our department Val´eria Scatolin and Rose Meire Ferreira for their bureaucratic work who helped me a lot, and to the technicians of our department Celso Alves, Zairo Crispin and Sanclair Dini who always helped me with problems in the laser cooling system, electrical energy and other repairs in the Lab.
Ardito, Dr. Hirohito Terashita, Dr. Kousik Samanta, Msc. Damaris Maimone, Msc. Danilo Rigitano and Msc. Carlos Galdino. Somehow, these friends shared the journey with me and it was a pleasure to work with them.
I must thank my parents, Edgard and Marcia, and my brother Homero, for all the love and support they gave me during my Ph.D. In special, thank you, grandma Dirce for your unconditional love, support and mainly for the worth values you taught me.
I would like to thank three people who left us last year, my uncle Ton, my father in law Jos´e and my lovely and young brother Alan Kaneko. “If I die tomorrow, I’d be all right, because I believe that after we’re gone, the spirit carries on”.
I also thank the financial support of the Fapesp and CNPq that made possible the development of my Ph.D.
And now I end by thanking my beloved wife Debora who is the reason of my life. Dear, thank you for being my love and support during all these years together.
Nesta tese, empregamos espectroscopia Raman para realizar um estudo detalhado dos fˆonons e das respostas eletrˆonicas em monocristais de LaFeAsO. N´os observamos as sime-trias e frequˆencias dos fˆonons nas fases tetragonal e ortorrˆombica e tamb´em a dependˆencia com a temperatura de um pico quase-el´astico (do inglˆes: QEP) na simetria B1g com
in-tensidade m´axima em torno da transi¸c˜ao magn´etica TN. A ´area e a altura do QEP B1g
foram atribu´ıdas `as flutua¸c˜oes nem´aticas de spin, enquanto que a largura do QEP B1g
foi relacionada com taxa de relaxa¸c˜ao dessas flutua¸c˜oes. Atrav´es da an´alise da largura do QEP B1g propomos que a transi¸c˜ao estrutural est´a relacionada a um congelamento
gradual das flutua¸c˜oes nem´aticas de spin, o que deve ser um fenˆomeno geral presente nos demais supercondutores `a base de Fe. Esse estudo foi complementado por medidas de espectroscopia Raman em BaFe2As2 e de difra¸c˜ao de raios-X com luz s´ıncrotron em
LaFeAsO, BaFe2As2 e SrFe2As2 dopado com Co. Paralelamente, n´os estudamos as
estru-turas cristalinas e magn´eticas em compostos da s´erie Ba1−xLaxTi1/2Mn1/2O3 atrav´es da
t´ecnica de difra¸c˜ao de nˆeutrons.
In this thesis, we employed Raman spectroscopy to perform a detailed study of the phonons and electronic responses in single crystals of the LaFeAsO. We observed the sym-metries and frequencies of the phonons in the tetragonal and orthorhombic phases and also the temperature dependence of the quasi-elastic peak (QEP) in the B1g symmetry with
maximum intensity around the magnetic transition TN. The B1g QEP area and height
were ascribed to spin nematic fluctuations, while the B1g QEP width was related to the
re-laxation rate of these fluctuations. From the B1g QEP width analysis we propose that the
structural transition is related to a gradual freezing of the spin nematic fluctuations, which may be a general phenomenon present in other Fe-based superconductors. This study was complemented by measurements of Raman spectroscopy in BaFe2As2 and synchrotron
X-ray diffraction in LaFeAsO, BaFe2As2 and Co-doped SrFe2As2. In parallel, we studied
the crystal and magnetic structures in compounds of the series Ba1−xLaxTi1/2Mn1/2O3
through the neutron diffraction technique.
From this thesis the following works have been prepared to publication.
1. U. F. Kaneko, P. F. Gomes, A. F. Garc´ıa-Flores, G. E. Barberis, J.-Q. Yan, T. A. Lograsso, D. Vaknin, and E. Granado. “Nematic Fluctuations and Phase Transitions in LaFeAsO: a Raman scattering study”. Submitted (under review), see the manuscript in AppendixE and in arXiv:1702.03774 [cond-mat.str-el]
2. U. F. Kaneko, E. Granado et al., “Magnetic Field-Dependence of the Crystal Struc-tures of BaFe2As2 and Sr(Fe0.8Co0.2)2As2”− (In preparation)
3. G. G. Lesseux, M. M. Piva, M. Saleta, U. Kaneko, E. Granado, P. L. Kuhns, A. P. Reyes, Z. Fisk, X. Wang, R. M. Fernandes, P. G. Pagliuso and R. R. Urbano. “Unravelling the structural/nematic-magnetic transitions in BaFe2As2” (In final stage of preparation)
4. F. A. Garcia, U. F. Kaneko, E. Granado, J. Sichelschmidt, M. Hlzel, J. G. S. Duque, C. A. J. Nunes, R. P. Amaral, P. Marques-Ferreira, R. Lora-Serrano.“ Magnetic dimers and trimers in the disordered S = 3/2 spin system BaTi1/2Mn1/2O3” − (Published in
1.1 Phase diagram of (a) LaFeAsO1−xFx from [26] and of (b) BaFe2−xCoxAs2
from [27]. . . 31
1.2 Crystal structures of (a) LaFeAsO in tetragonal phase (P 4/nmm) and of
(b) BaFe2As2 in tetragonal phase (I4/mmm). In diagrams, layers of
Fe-As are separated by (a) La-O or (b) Ba layers. In the ab plane the iron ions form a planar square lattice showed as blue dashed squares in both
structures. The software VESTA was used to produce the drawings [32]. . 32
1.3 ab plane projections of the LaFeAsO crystal structure in the (a) tetragonal phase (blue dashed square) and in the (b) orthorhombic phase (red dashed square). Spheres indicate the atoms, La (green), Fe (red), As (violet) and O (blue). The black arrows show the lattice parameters in both phases. Lattice parameters values were extracted from [12] and the software VESTA
was used to produce the drawings [32]. . . 33
1.4 Two-dimensional iron atoms lattice (red spheres) with arsenic atoms placed above (violet) and below (green) the ab plane. Two twin domains A and
B are mirrored by a twin boundary, adapted from [34]. . . 33
1.5 Two interpenetrating blue and red N´eel lattices configuring an magnetic stripe order in iron pnictides. The blue and red spheres represent the iron atoms while the arrows over them are the spins. Along the orthorhombic
axes aO and bO the spins are aligned antiferromagnetically and
dyz + dxy and the Y with orbitals dxz + dxy point and the hole pockets
around the Γ point with the orbitals dxz+ dyz and (b) on top the 2Fe unit
cell and its correspondent folded BZ at the bottom with new symmetry ˜Y ,
˜
X and ˜M points. . . 35
1.7 Illustration of ellipsoidal nematic molecules in (a) isotropic phase and in
(b) nematic phase. . . 36
1.8 Temperature dependence of ab-plane resistivity ρa (green) and ρb (red)
of BaFe2As2. Solid line indicates the transition temperatures TS = TN.
Figure extracted from [34]. . . 36
1.9 Electronic distributions of the (a) 3dxz and (b) 3dyz orbitals showing its
fours lobes at the top. At the bottom the projection of the orbitals on the ab-plane showing two lobes pointing along the (a) b direction and (b) a
orthorhombic directions. . . 37
1.10 (a) Projection of the 3dxz and 3dyz orbitals in the ab-plane showing two
lobes each oriented along bO and aO directions, respectively, at tetragonal
phase (T > Tnem). (b) Two possible configurations for the Ising orbital
nematic order in which (top) the 3dyz orbitals extend along aO and the
3dxz shrink along bO or (bottom) the 3dyz orbitals shrink along aO and the
3dxz extend along bO. . . 39
1.11 (a) Spins randomly oriented at the tetragonal/paramagnetic phase for a
temperature T > Tnem. (b) Two configurations of the Ising spin nematic
order in which (top) there is a short-range ferromagnetic spin correlation
along bO with a short-range antiferromagnetic spin correlation along aO
or (bottom) there is a short-range ferromagnetic spin correlation along
aO with a short-range antiferromagnetic spin correlation along bO. For a
temperature TN ≤ T ≤ Tnemthe system choose one of these configurations
and is still paramagnetic. (c) Magnetic stripe order coming from the chosen
octahedra, the metal ions B and the interstitial charge reservoir ions A (violet). (c) The oxygen octahedron showing the displacement of the center
ion B and the direction of the electric polarization. . . 42
1.13 Planar projected view of an ordered double perovskite showing the oxygens O (blue) the metal ions B and B’ (violet and green) and the charge reservoir
ions A (orange). . . 43
2.1 Diagram showing the energy levels of an atom showing the (a) absorption
(b) spontaneous emission and (c) stimulated emission. The wavy arrows
are the photons and the black circles are the electrons. . . 45
2.2 Diagram showing the energy levels of an atom for (a) three-level and (b)
four-level laser systems.. . . 46
2.3 Diagram showing a resonator with two mirrors of curvature radii R1 and
R2 separated by distance L. A gain medium was placed in the center of
the resonator. . . 47
2.4 Transverse electromagnetic modes TEMmn. . . 47
2.5 Gaussian profile. . . 48
2.6 (a) Longitudinal modes of a resonator with characteristic distance L and the envelope representing the broadening of gain medium and (b) result of a
convolution between the longitudinal modes and the broadening mechanisms. 49
2.7 Schematic reactor core showing the uranium fuel (dark green), the control bars (black) the moderator tank (light blue), the hot source (dark blue), the cold source (red), the shielding tank (greenish), the concrete wall (grey),
the neutron beam tubes and the exchanger heat water circuit. . . 52
2.8 Illustration of a neutron reactor facility showing the building around the reactor core and the neutron guide Hall. The geometric figures representing the different instruments in each building and the grey narrow rectangles
beam, the blue circle is the target and the green lines are the neutrons which
are guided to the instruments. . . 54
2.10 Sealed-glass X-ray tube and a diagram with its principal parts extracted
from [48]. . . 55
2.11 X-ray spectrum of molybdenum as a function of wavelength and applied
voltage, adapted from [49]. . . 56
2.12 Diagram of the main parts of a synchrotron light source with a linac coupled to a booster (blue), bending magnet dipoles (red), vacuum chamber in the
straight sections (grey), RF-cavity (pink), wriggler and undulator (green). . 57
2.13 (a) The Raman experiment setup showing a laser beam (cyan), mirrors (black lines), lens (blue), the sample (orange), one diffraction grating (grey) and a CCD (magenta). (b) Illustrative Raman spectrum presenting the
Rayleigh, Stokes and AntiStokes lines. . . 58
2.14 Energy levels involved in the Raman scattering process. The wavy arrows
are the incident and scattered photons. . . 59
2.15 Diagrams of (a) Stokes energy conservation and (b) anti-Stokes energy con-servation (b) Stokes momentum concon-servation (d) anti-Stokes momentum
conservation in the Raman process. . . 60
2.16 Lattice with atoms (blue circles) and hkl planes (black lines). The distance between two adjacent planes is d. Two incident lines 1 and 2 and its respectively reflected lines 1’ and 2’. The angle between the incident and
reflected lines with the planes is θ.. . . 65
2.17 Illustrations of diffractograms showing a (a) perfect Bragg peak and a (b)
realistic Bragg peak. . . 67
2.18 The Debye-Scherrer camera on top with an incident x-ray a film (grey) around the sample (red), two Debye-Scherrer cones and its intersection with the film (thick line). At the bottom the intersection of the cones and
the film are shown as curved lines around 0 and 180 ◦ which represent the
diffraction angles. . . 68
sample.. . . 76
3.3 Iron lattice represented by red spheres showing the ab-plane of 1111-type
and 122-type iron pnictides. 2Fe tetragonal, 4Fe orthorhombic, and 1Fe pseudo unit cells are represented by dashed blue squares, green square, and black square, respectively. Black double arrows indicate cross and parallel polarizations adopted. Black arrows over the Fe spheres are spins
in the stripe configuration. . . 79
3.4 LaFeAsO unit cells in the tetragonal phase. Spheres represent La (green),
Fe (red), As (purple) and O (blue) atoms, while arrows with the same colors
represent normal modes A1g for La, As and B1g for Fe, O atoms, adapted
from [54] . . . 80
3.5 Polarized Raman spectra of LaFeAsO#Pol. dataset at four polarizations (YY, Y’Y’, X’Y’ and XY) at (a) 290 K and (b) 20 K. The allowed
symme-tries and phonon central frequencies are indicated in each spectrum. . . 84
3.6 T -dependence of the 20-point smoothed Raman responses of LaFeAsO#i dataset at (a) YY and (b) XY polarizations. The dashed line marks the
frequency of the Ag (As) phonon as 164 cm−1 at T = 290 K. . . 85
3.7 T -dependence of the 20-point smoothed Raman responses of LaFeAsO#1
dataset at XY polarization (a) above TN = 140 K and (b) below TN = 140
K. . . 86
3.8 T -dependence of the 20-point smoothed Raman responses of LaFeAsO#2
dataset at XY polarization (a) above TN = 140 K and (b) below TN = 140
K. . . 87
3.9 T -dependence of the 20-point smoothed Raman responses of LaFeAsO#ii
dataset. . . 88
3.10 Polarized Raman spectra of LaFeAsO#TwoMag1. dataset at 300 K (black)
and at 40 K (red) in Y Y polarization measured up to 6000 cm−1. . . . 88
3.11 Polarized Raman spectra of LaFeAsO#TwoMag2 dataset at 40 K in four
polarizations measured up to 6000 cm−1 showing a broad peak structure
3.13 T -dependence of the relative intensity IXY/IYY of the Ag peak around 164
cm−1 in XY and YY polarizations. . . . 91
3.14 T -dependence of the 20-point smoothed χ00(ω, T )/ω for LaFeAsO#1 dataset
at XY polarization in B1g symmetry (1Fe unit cell) for (a) T ≥ TN (b)
T < TN. The red lines are the Lorentzian fittings. . . 95
3.15 T -dependence of the 20-point smoothed χ00(ω, T )/ω for LaFeAsO#2 dataset
at XY polarization in the B1g symmetry (1Fe unit cell) for (a) T ≥ TN (b)
T < TN. The red lines are the Lorentzian fittings. . . 96
3.16 8-point smoothed B1g Raman response χ00(ω, T ) at selected temperatures
of the LaFeAsO#1 dataset. The red lines are the fittings with Eq. 3.10, while the solid magenta and dashed blue lines are the linear and damped
Lorentzian terms of the fittings. . . 97
3.17 8-point smoothed B1g Raman response χ00(ω, T ) at selected temperatures
of the LaFeAsO#2 dataset. The red lines are the fittings with Eq. 3.10, while the solid magenta and dashed blue lines are the linear and damped
Lorentzian terms of the fittings. . . 98
3.18 T -dependence of the (a) As phonon and B1g QEP (b) width (c) area (d)
initial slope at XY polarization for LaFeAsO#1 dataset. . . 100
3.19 T -dependence of the (a) As phonon and B1g QEP (b) width (c) area (d)
initial slope at XY polarization for LaFeAsO#2 dataset. . . 101
3.20 T -dependence of the B1g QEP intial slope of LaFeAsO#1. The red line is
the Curie-Weiss fitting. . . 102
3.21 T -dependence of the B1g QEP intial slope of LaFeAsO#2. The red line is
the Curie-Weiss fitting. . . 102
3.22 Detailed T -dependence of the B1g QEP width of LaFeAsO#1. . . 103
3.23 Detailed T -dependence of the B1g QEP width of LaFeAsO#2. . . 103
3.24 T -dependence of the shear modulus C44/CRT of LaFeAsO from [68] (yellow
squares) and fittings using the B1g QEP area (pink diamonds) and the
ini-tial slope (violet circles) of LaFeAsO#1 dataset in the functions indicated
the initial slope (violet circles) of LaFeAsO#2 dataset in the functions
indicated inside the figure. . . 105
3.26 T -dependence of the 20-point smoothed χ00(ω, T )/ω of LaFeAsO#ii dataset
in YY polarization for (a) T > TS (b) TN < T < TS and (c) T < TN. The
red solid lines are the Lorentzian fittings centered at the zero frequency. . . 106
3.27 T -dependence of the QEP (a) width (b) area and (c) initial slope at YY
polarization for LaFeAsO#ii dataset. . . 107
3.28 Iron spins (black) arranged in the magnetic stripe order. The lattice is composed by two interpenetrating N´eel sublattices (dashed squares). The arsenic atoms are represented by blue and violet spheres above and below
the iron lattice. At the bottom of the lattice are shown the J1-J2 and
J1a-J1b-J2 models for the exchange integrals. . . 110
3.29 Cartoon of the two-magnon scattering. The red and blue arrows are spins in stripe magnetic order, yellow rays are incoming and scattered photons, and the black dotted lines are the z broken exchange bonds. Adapted
from [77]. . . 111
3.30 Raman spectra with Gaussian fittings at 40 K for (a) X0Y0 and (b) XY
polarizations . . . 112
3.31 Polarized Raman spectra of BaFe2As2at four polarizations (YY, Y’Y’, X’Y’
and XY) at (a) 292 K and (b) 18 K. The incident laser power was 10 mW
and the spectrum acquisition time was 7200 s. . . 112
3.32 (a) Selected polarized Raman spectra of BaFe2As2 at X’Y’ polarization as
a function of temperature and (b) details of spectra series around the B1g
peak. The incident laser power was 10 mW and the spectrum acquisition
time was 1800 s.. . . 113
3.33 T -dependence of the central frequency of the B1g Fe phonon of BaFe2As2
in neutron diffraction of BaFe2As2. The neutron diffraction data were
obtained from Ref. [83] and both data were normalized. . . 116
3.35 Illustration of the experimental sample mounting. Selected sample (green) is pasted on the sample holder (orange). Incident and scattered X-rays
(light blue arrows) are shown in perspective making the angles θi and θs,
respectively, with the sample surface. The projection of the X-rays on the sample surface are orthogonal to magnetic field direction (blue arrow) that
is aligned with one orthorhombic direction. . . 118
3.36 XDS beamline hutch of the Brazilian Synchrotron Light Source, showing the X-ray diffractometer with 6+2 degrees of freedom, the blue lines in-dicate the X-ray path and the red, black and yellow lines inin-dicate the
cryostat, magnet and detector, respectively. . . 119
3.37 X-ray diffraction θ-2θ-scans of BaFe2As2 for (a) (0 0 6) reflection and
(b) (2 2 12) reflection at 150 K. The red lines are Gaussian fittings. . . 121
3.38 False color intensity maps from (h h 12)-scans around the (2 2 12) reflection
as a function of temperature of BaFe2As2 single crystal with (a) B = 0 T
and (b) B = 5.9 T. . . 122
3.39 False color intensity maps from (0 0 l)-scans around the (0 0 6) reflection
as a function of temperature of BaFe2As2 single crystal with (a) B = 0 T
and (b) B = 5.9 T. . . 123
3.40 (h h 12) scans around the (2 2 12) reflection at T = 135 K as a function
of magnetic field for (a) BaFe2As2#1 and (b) BaFe2As2#2 measurements.. 124
3.41 (a) Left peak area (AL) plus right peak area (AR) divided by the central
peak area (AC) as a function of the magnetic field at 135 K obtained from
three Gaussian fitting of diffractograms from Fig. 3.40. . . 125
3.42 X-ray diffraction θ-2θ-scans of BaFe2As2 for (a) (0 0 24) reflection and (b)
(2 2 24) reflection at 155 K. Black lines are Gaussian fittings. . . 125
3.43 False color intensity map from (h h 24)-scans around the (4 4 24) reflection
extracted 2θc are shown inside figure. . . 127
3.45 False color intensity map from (h h 14)-scans around the (2 2 14) reflection
as a function of temperature of LaFeAsO single crystal. . . 128
3.46 X-ray diffraction θ-2θ-scans of Co-doped SrFe2As2 at 165 K for (a) (0 0
20) reflection with one Gaussian fitting and (b) (2 2 20) reflection with two
Gaussian function fitting. The extracted 2θc are shown inside figure. . . 129
3.47 False color (h h 20)-intensity maps around the (2 2 20) reflection of the
Co-doped SrFe2As2 single crystal as a function of temperature with (a) B
= 0 T and (b) B = 3.49 T. . . 130
3.48 Comparison between the (h h 20)-scans around (2 2 20) reflection of the
Co-doped SrFe2As2 single crystal with B = 0 T and with B = 3.49 T for
selected temperatures. . . 131
3.49 X-ray diffraction of Ba1−xLaxMn1/2Ti1/2O3 family for La dopings x = 0.0
- 0.6 performed by R. Serrano. . . 134
3.50 Raman spectroscopy of the Ba1−xLaxMn1/2Ti1/2O3 series for La dopings of
x = 0.0 - 0.5 accomplished in my Master’s thesis [85]. . . 135
3.51 Magnetic susceptibility measurements as a function of temperature of the
Ba1−xLaxMn1/2Ti1/2O3 family for La concentrations x = 0.0 - 0.6,
per-formed by R. Serrano. . . 136
3.52 Comparison between the preliminary X-ray diffractograms of the system
Ba1−xLaxMn1/2Ti1/2O3(blue) and diffractograms from references (red) [86–
89] for x = 0.0 (a), x = 0.5 (b), x = 0.9 (c) e x = 1.0 (d), respectively. . . 137
3.53 Schematic experimental setup of the SPODI used in the neutron powder
diffraction of Ba1−xLaxTi1/2Mn1/2O3. . . 139
3.54 (a) Diffractograms obtained from neutron powder diffraction at the SPODI
instrument for BaMn1/2Ti1/2O3at 3.6 K, 100 K and room temperature (RT)
(b) Detailed diffractograms at low angles. . . 140
3.55 (a) Diffractograms obtained from neutron powder diffraction at the SPODI
instrument for Ba0.5La0.5Mn1/2Ti1/2O3 at 3.6 K, 100 K and room
ature (RT) (b) Detailed diffractograms at low angles. . . 141
3.57 (a) Diffractograms obtained from neutron powder diffraction at the SPODI
instrument for LaMn1/2Ti1/2O3at 3.6 K, 100 K and room temperature (RT)
(b) Detailed diffractograms at low angles. . . 141
3.58 Rietveld refinement of BaTi1/2Mn1/2O3. Cross symbols (black) and solid
lines (red) represent the observed and calculated patterns, respectively. Below the patterns the expected Bragg peak positions (vertical bars) and the difference between observed and calculated patterns (blue line) are
presented. . . 143
3.59 Diagram of the structural model of BaTi1/2Mn1/2O3 composed by trimers
of face-sharing oxygen octahedra connected by corner-sharing oxygent oc-tahedra along the c-axis. There are two Ba (orange spheres) and two O (red spheres) sites, and three transition metal sites, M(1) (violet sphere)
occupied by Mn4+ and M(3) (blue sphere) by Ti4+ ions, while in M(2)
(violet/blue sphere) there is Mn4+/Ti4+ mixed occupation [93]. . . . 144
3.60 Temperature dependence of lattice parameters of BaTi1/2Mn1/2O3 . . . 145
3.61 Temperature dependence of magnetic susceptibility in Zero-Field-Cooling
(ZFC) and Field-Cooling (FC) regimes of Ba0.5La0.5Mn1/2Ti1/2O3performed
by R. Serrano. . . 146
3.62 Temperture dependece of integrated area of the magnetic peak 2θ ≈ 18◦
observed in the neutron diffraction pattern for x = 0.5. Gaussian fittings
were accomplished to get the areas. . . 146
3.64 Diagram of the structural model of Ba0.5La0.5Mn1/2Ti1/2O3. There is one
Ba/La mixed site (orange/green spheres), one O site (red spheres) and one
Ti/Mn mixed transition metal site (violet/blue spheres). . . 148
3.63 Rietveld refinement of Ba0.5La0.5Ti1/2Mn1/2O3. Cross symbols (black) and
solid lines (red) represent the observed and calculated patterns, respec-tively. Below the patterns the expected Bragg peak positions as vertical bars in main phase (magenta) and in the secondary phase (cyan), and the
Cross symbols (black) and solid lines (red) represent the observed and cal-culated patterns, respectively. Below the patterns the expected Bragg peak positions (vertical bars) and the difference between observed and calculated
patterns (blue line) are presented. . . 150
3.67 Diagram of the structural model of Ba1−xLaxMn1/2Ti1/2O3 for (a) x = 0.9
and (b) x = 1.0. There is one La site (green spheres), one O site (red spheres) and one Ti/Mn mixed transition metal site (violet/blue) for x = 1.0, while for x = 0.9 a small concentration of the Ba (orange sphere)
occupies the La site. . . 151
3.68 Temperature dependence of lattice parameters of (a) Ba0.1La0.9Ti1/2Mn1/2O3
and (b) LaTi1/2Mn1/2O3 . . . 151
C.1 T -dependence of the χ00(ω, T )/ω for LaFeAsO#3 data at XY polarization
in the B1g symmetry for (a) T ≥ TN (b) T < TN. The red lines are the
Lorentzian fittings. . . 179
C.2 T -dependence of the (a) As phonon and B1g QEP (b) width (c) area (d)
initial slope at XY polarization for LaFeAsO#3. . . 180
C.3 Detailed T -dependence of the B1g QEP width of LaFeAsO#3. . . 181
C.4 T -dependence of the B1g QEP intial slope of LaFeAsO#3. The red line is
the Curie-Weiss fitting. . . 181
C.5 T -dependence of the shear modulus C44/CRT of LaFeAsO from [68] (yellow
squares) and fittings using the B1g QEP area (pink diamonds) and the
initial slope (violet circles) of LaFeAsO#3 in the functions indicated inside
the figure. . . 182
C.6 T -ependence of the χ00(Ω, T ) for LaFeAsO#4 data at XY polarization in
the B1g symmetry for (a) T ≥ TN (b) T < TN. The red lines are the
Lorentzian fittings. . . 183
C.7 T -dependence of the (a) As-phonon and B1g QEP (b) width (c) area (d)
initial slope at XY polarization for LaFeAsO#4 measurement. . . 184
C.10 T -dependence of the shear modulus C44/CRT of LaFeAsO from [68] (yellow
squares) and fittings using the B1g QEP area (pink diamonds) and the
initial slope (violet circles) of LaFeAsO#4 in the functions indicated inside
the figure. . . 186
D.1 Rietveld refinement of BaTi1/2Mn1/2O3 at (a) 3.6 K and (b) 100 K. Cross
symbols (black) and solid lines (red) represent the observed and calcu-lated patterns, respectively. Below the patterns are presented the expected Bragg peak positions (vertical bars) and the difference between observed
and calculated patterns (blue line). . . 187
D.2 Rietveld refinement of Ba0.5La0.5Ti1/2Mn1/2O3 at (a) 3.6 K and (b) 100
K. Cross symbols (black) and solid lines (red) represent the observed and calculated patterns, respectively. Below the patterns are presented the expected Bragg peak positions as vertical bars in main phase (magenta) and in the secondary phase (cyan), and the difference between observed
and calculated patterns (blue line). . . 189
D.3 Rietveld refinement of Ba0.1La0.9Ti1/2Mn1/2O3 at (a) 3.6 K and (b) 100 K
and of LaTi1/2Mn1/2O3 at (c) 3.6 K and (d) 100 K. Cross symbols (black)
and solid lines (red) represent the observed and calculated patterns, respec-tively. Below the patterns are presented the expected Bragg peak positions (vertical bars) and the difference between observed and calculated patterns
1.1 Goldschmidt tolerance factor of perovskites classification. . . 42
2.1 Usual classification of neutron wavelength band. . . 52
2.2 Coherent scattering lengths total and absorption cross sections, X-rays form
factor (f ) for selected elements. Table extracted from [50]. . . 71
3.1 Symmetry analysis for LaFeAsO in tetragonal phase (Space Group: P 4/nmm
– Point Group D4h (4mmm)). . . 77
3.2 Symmetry analysis for LaFeAsO in orthorhombic phase (Space Group Cmma
– Point Group D2h (mmm)). . . 77
3.3 Symmetry analysis for BaFe2As2in tetragonal phase (Space Group: I4/mmm
– Point Group D4h (4mmm)). . . 78
3.4 Symmetry analysis for BaFe2As2 in orthorhombic phase (Space Group
F mmm – Point Group D2h (mmm)). . . 78
3.5 Raman Tensors of the point groups (a) D4h (4mmm) and (b)D2h (mmm). 80
3.6 Summarized symmetries according to polarizations in the tetragonal and
orthorhombic phases of LaFeAsO and BaFe2As2 for the 2Fe unit cell. . . . 81
3.7 Summarized symmetries according to polarizations in the tetragonal and
orthorhombic phases of LaFeAsO and BaFe2As2 in 1Fe picture used in the
analysis of the electronic Raman. . . 81
3.8 Summarized symmetries according to polarizations for tetragonal and
or-thorhombic phases of LaFeAsO and BaFe2As2 in 1Fe picture used in the
analysis of the electronic Raman. . . 83
3.9 Masses of Ba1−xLaxTi1/2Mn1/2O3 used in neutron diffraction. . . 138
3.10 Refined structural parameters and relevant bond lengths for BaTi1/2Mn1/2O3
at room temperature. . . 149
3.13 Refined structural parameters and relevant bond lengths for Ba0.1La0.9Ti1/2Mn1/2O3
at room temperature. . . 152
3.14 Refined structural parameters and relevant bond lengths for LaTi1/2Mn1/2O3
at room temperature. . . 152
B.1 Voigt Notation . . . 175
D.1 Refined structural parameters and relevant bond lengths for BaTi1/2Mn1/2O3
at 100 K. . . 188
D.2 Refined structural parameters and relevant bond lengths for BaTi1/2Mn1/2O3
at 3 K. . . 188
D.3 Refined structural parameters and relevant bond lengths for Ba0.5La0.5Ti1/2Mn1/2O3
at 100 K. . . 189
D.4 Refined structural parameters and relevant bond lengths for Ba0.5La0.5Ti1/2Mn1/2O3
at 3 K. . . 190
D.5 Refined structural parameters and relevant bond lengths for Ba0.1La0.9Ti1/2Mn1/2O3
at 100K. . . 190
D.6 Refined structural parameters and relevant bond lengths for Ba0.1La0.9Ti1/2Mn1/2O3
at 3K. . . 191
D.7 Refined structural parameters and relevant bond lengths for LaTi1/2Mn1/2O3
at 100K. . . 192
D.8 Refined structural parameters and relevant bond lengths for LaTi1/2Mn1/2O3
List of Figures 10
List of Tables 22
Introduction 27
1 Fundamentals of Iron Pnictides and Perovskites 30
1.1 Fe-Based Pnictides . . . 30
1.2 Perovskites . . . 40
2 Experimental Probes 44
2.1 Laser, Neutron and X-Ray Production . . . 44
2.1.1 Basics of Laser . . . 44
2.1.2 Basics of Neutrons . . . 50
2.1.3 Basics of X-Rays . . . 54
2.2 Light Scattering . . . 57
2.2.1 Raman Spectroscopy . . . 58
2.2.2 Mathematical Description of the Raman Process . . . 61
2.2.3 The intensity of the Raman spectrum . . . 63
2.3 X-Ray Diffraction . . . 64
2.3.1 Bragg’s Law . . . 64
2.3.2 X-ray Diffraction Methods . . . 67
2.3.3 The Origin of X-ray Scattering . . . 67
2.3.4 The Intensity of the X-ray Diffraction . . . 69
2.4 Neutron Scattering . . . 70
3 Results and Discussions 73
3.1 Raman Spectroscopy in Iron Pnictides . . . 73
3.1.1 Experimental Details . . . 73
3.1.2 Iron Pnictides Symmetry Analysis . . . 76
3.1.3 Results in LaFeAsO. . . 81
3.1.4 Analysis and Discussion . . . 89
3.1.5 Results in BaFe2As2 . . . 112
3.1.6 Discussion . . . 114
3.1.7 Partial Conclusions . . . 116
3.2 Synchrotron X-ray Diffraction in FeSCs . . . 117
3.2.1 Experimental Details . . . 117
3.2.2 Results . . . 120
3.2.3 Discussion . . . 131
3.2.4 Partial Conclusions . . . 132
3.3 Neutron Powder Diffraction in Perovskites . . . 133
3.3.1 Experimental Details . . . 133
3.3.2 Neutron Powder Diffractometer - SPODI . . . 138
3.3.3 Results in Ba1−xLaxTi1/2Mn1/2O3 . . . 139 3.3.4 BaTi1/2Mn1/2O3 . . . 141 3.3.5 Ba0.5La0.5Ti1/2Mn1/2O3 . . . 145 3.3.6 Ba1−xLaxTi1/2Mn1/2O3 (x = 0.9 and 1.0) . . . 150 3.3.7 Partial Conclusions . . . 152 4 General Conclusions 154 5 References 156 Appendices 165 A Raman Tensors 166 B Shear Modulus 174
D Supplementary materials of neutron measurements in Ba1−xLaxTi1/2Mn1/2O3
187
Introduction
Superconductivity is a phenomenon that has called attention for more than a century since 1911 when Kamerlingh Onnes (1853-1926) found null resistance in mercury at 4.3 K [1]. Four decades after the discovery of superconductivity, the BCS1 theory provided
a microscopic explanation of the phenomenon in terms of an electron pairing mechanism driven by phonons [2]. Materials that follow BCS theory should present an upper limit in the critical temperature around TC = 28 K [3]. However, it was observed higher critical
temperatures in magnesium diboride (MgB2), with TC = 39 K [4] and also in the recently
reported sulfur hydride gas (H2S) under 90 GPa pressure with TC = 203 K [5]. In these
materials the superconducting electron pairing seems to be mediated by phonons. Other two classes of materials that present superconductivity are the cuprates [6] and iron-based superconductors (FeSCs) [7]. In the former, the highest reported critical temperature is 153 K at 150 kbar [8], while in latter it was reported TC = 109 K in FeSe films at room
pressure [9]. In FeSCs, it was suggested that magnetic fluctuations are important in the electron pairing mechanism, possibly due to the proximity between the superconduct-ing state (SC) and a stripe spin-density wave (s-SDW) instability [10]. Together with the s-SDW transition that occurs at a temperature TN, the FeSCs present a
tetragonal-to-orthorhombic (T-O) transition at a temperature TS. In the case of BaFe2As2, the
transition temperatures are nearly the same TN ∼ TS. While in LaFeAsO, TS is a few
Kelvin above TN. Thus, the separation between TN and TS reveals that the structural
distortion cannot be exclusively due to the long-range magnetic order [11]. At the struc-tural transition temperature TS, the orthorhombic distortion measured by the difference
between the in plane lattice parameters of the order of 0.5 % does not seem to be large enough to justify the large reported in-plane resistivity anisotropy, which is of the order of 10 %. [12,13]. This anisotropy is also observed above TS in electronic properties like
optical conductivity and magnetic susceptibility. In this scenario, one may argue that electronic nematic order and fluctuations are responsible for the structural transition. At the nematic transition temperature Tnem ∼ TS, the nematic phase spontaneously breaks
the in plane rotational C4 symmetry although preserving translational symmetry [11,14].
What electronic degree of freedom (spin/orbital/charge) drives the structural transition in FeSCs is an unsettled question and the nematic fluctuations involved in the struc-tural/nematic transition can play an important role in the electron pairing mechanism in FeSCs. [14].
Recently, it became clear that Raman spectroscopy is an important technique to probe electronic nematic fluctuations in FeSCs through the renormalization of the low-energy part of the Raman spectrum in the B1g symmetry. Such renormalization resembles a
quasi-elastic peak (QEP) and it has been observed in A(Fe1−xCox)2As2 (A = Ca, Sr,
Ba,Eu) [15–21], Ba1−pKpFe2As2 [21], FeSe [22,23] and NaFe1−xCoxAs [24]. The nature of
the B1gQEP is interpreted in terms of charge/orbital [17] or spin [19] nematic fluctuations.
Despite such extensive investigation in several systems, no Raman study of the electronic nematic fluctuations in LaFeAsO has been carried out yet, to the best of our knowledge. Therefore, filling this gap and sheding light on the nature of the electronic nematic fluc-tuations in LaFeAsO was the main purpose of this thesis. To this end, we accomplished a detailed study of both phononic and electronic Raman scattering in LaFeAsO single crys-tals. In the phononic sector, we measured and assigned the symmetries of the phonons at the tetragonal and orthorhombic phases. Also, we observed an enhancement of the As phonon below TN in the crossed polarization that seems to be due to the coupling between
the phonon and an anisotropic electronic state. In the electronic sector, we probed the B1g
QEP signal in the Raman response divided by the frequency χ00(ω, T )/ω, which presented
criticality around TN and was assigned to spin nematic fluctuations. Then, we analyzed
the the B1g QEP height and width, identified as the static spin nematic susceptibility
and relaxation rate of the electronic fluctuations, respectively. These quantities provided insight into the role of the nematic fluctuations in the structural transition at TS and
into the origin of the large TN-TS splitting in LaFeAsO. Complementary, we employed
Raman spectroscopy to study the phonons of BaFe2As2 at the tetragonal and
orthorhom-bic phases. In this study we also measured the Fe phonon as a function of temperature and we observed a deviation of the frequency from the anharmonic decay of the phonons.
As an auxiliary technique in the study of the FeSCs we performed synchrotron X-ray diffraction in LaFeAsO, BaFe2As2 and Co-doped SrFe2As2. In this study, we followed
the structural evolution of the samples as a function of the temperature and magnetic field. In parallel to the investigations of the FeSCs, we also investigated the crystal and magnetic structures of the perovskite-derived system Ba1−xLaxTi1/2Mn1/2O3 employing
neutron powder diffraction.
In Chapter 1 we describe, from a point of view of the available literature, the funda-mental properties of the FeSCs and double perovskite systems. Chapter 2 is separated in two parts, in the first part we describe the production of the laser light, neutrons and X-rays that were the probes that we used in the scattering experiments performed in this thesis. Then, in the second part we make a brief description of Raman spectroscopy, X-ray diffraction and neutron powder diffraction. The Chapter 3 is the most important part of this thesis that is divided in three parts. In the first part we present the results and discussion about Raman spectroscopy in LaFeAsO and BaFe2As2. In the second part we
present the results and discussion of two experiments using synchrotron X-ray diffraction in BaFe2As2, LaFeAsO and also in Co-doped SrFe2As2. Then, in the third part we show
the results and discussion of neutron powder diffraction in Ba1−xLaxTi1/2Mn1/2O3 for x
Chapter 1
Fundamentals of Iron Pnictides and
Perovskites
In the first section of this chapter we present the main properties from the literature of the Fe-based superconductors (FeSCs). We start with the phase diagram of two different classes of FeSCs by describing their structural, magnetic and electronic structures. In the following, we present the properties of the nematic phase from the charge/orbital and spin nematic fluctuations point of views. At last, we describe the structure of the perovskite system and how such structures can be designed to show multiferroicity.
1.1
Fe-Based Pnictides
The discovery of superconductivity in fluorine-doped LaFeAsO in 2008 [7] was a break-through in the field of the superconducting materials. Soon, other materials with the binaries Fe-As and Fe-Se in their structures were also shown to present the supercon-ducting state and we can organize these materials in four main types with the par-ent structures of the LaFeAsO (1111-type), SrFe2As2 (122-type), LiFeAs (111-type) and
Fe1+x(Te-Se) (11-type) [12]. In these FeSCs, the superconducting electron pairing
mech-anism does not seem to be mediated by the phonons as in the BCS superconductors. De-spite the moderate critical temperature of the inaugurating compound F-doped LaFeAsO (TC = 26 K), critical temperatures as high as TC = 100 K were observed for FeSe films
at room pressure [9]. Although the electron pairing mechanism was initially attributed to magnetic fluctuations [25], recent reports reveal that nematic fluctuations may be related
with the mechanism that drives the superconductivity in FeSCs [14,18].
(a)
(b)
LaFeAsO
1-xF
xBa(Fe
1-xCo
x)
2As
2 Tetragonal SDW Ortorhombic Orthorhombictype-1111
type-122
Figure 1.1: Phase diagram of (a) LaFeAsO1−xFx from [26] and of (b) BaFe2−xCoxAs2
from [27].
From the phase diagrams of LaFeAsO1−xFx and Ba(Fe1−xCox)2As2 presented in Figs.
1.1(a) and (b), respectively, which condense several measurements of structural, mag-netic and transport properties, we can identify the main signatures of the FeSCs. First of all, superconductivity appears when the parent compounds are doped, however, these compounds also become superconductors under pressure [28–31]. Both systems present an antiferromagnetic spin density-wave (SDW) order, which is totally suppressed in LaFeAsO1−xFx for x > 0.04, while for approximately 0.025 < x < 0.06 in BaFe2−xCoxAs2
it is possible to observe the SDW phase and superconductivity, however, at different crit-ical temperatures. In both phase diagrams there is a tetragonal phase and for certain values of x there is a tetragonal-to-orthorhombic (T -O) phase transition followed by a magnetic ordering transition to the SDW phase on cooling. Interesting, in the parent compounds (x = 0.0) the structural and magnetic transitions are split in LaFeAsO, being TS ∼ 155 K and TN ∼ 140 K, respectively, while in BaFe2As2 both transitions are nearly
(a) LaFeAsO (b) BaFe2As2
1111-type 122-type
Figure 1.2: Crystal structures of (a) LaFeAsO in tetragonal phase (P 4/nmm) and of (b) BaFe2As2 in tetragonal phase (I4/mmm). In diagrams, layers of Fe-As are separated by
(a) La-O or (b) Ba layers. In the ab plane the iron ions form a planar square lattice showed as blue dashed squares in both structures. The software VESTA was used to produce the drawings [32].
Figure 1.2 (a) and (b) show layers of La-O and Ba that are separeted by layers of Fe-As in the LaFeAsO and BaFeAs crystal structures, respectively. At room temperature the parent compounds LaFeAsO and BaFe2As2 are in the tetragonal phases (P 4/nmm
and I4/mmm) and undergo structural transitions to orthorhombic phases (Cmma and F mmm) at TS ∼ 155 K and TS ∼ 140 K, respectively. These structural transitions are due
to slight atom displacements from their original positions. In this way, the orthorhombic axes aO and bO are rotated by 45◦ in the ab plane with respect to the tetragonal axes aT
and bT, leading to a doubling of the unit cell area as illustrated in Figs. 1.3(a) and (b).
In general, the orthorhombic axes aO of the FeSCs become slightly greater than the bO
and are observed the formation of structural twin domains below TS [13,33,34] in these
materials and Fig. 1.4 shows an example of a twinned structure where two twin domains A and B are mirrored across the twin boundary.
Long-range antiferromagnetic transition occurs at TN ∼ 140 K for LaFeAsO, a
tem-perature below the structural transition TS = 155 K [35]. However, for BaFe2As2 the
structural and magnetic phases occur at nearly the same temperature TS = TN ∼ 140 K.
Itinerant, localized or even a mixed itinerant/localized points of view have been applied to explain the antiferromagnetic order in FeSCs [25,36,37]. From the itinerant point of view the antiferromagnetic order is due to the spin density-wave (SDW) instability with
(a) Tetragonal (b) Orthorhombic 0301 . 4 T T b a T a T T a b 7099 . 5 O a 6820 . 5 O b O a O b 7368 . 8 T c 8.7265 O c La Fe As O
Figure 1.3: ab plane projections of the LaFeAsO crystal structure in the (a) tetrago-nal phase (blue dashed square) and in the (b) orthorhombic phase (red dashed square). Spheres indicate the atoms, La (green), Fe (red), As (violet) and O (blue). The black ar-rows show the lattice parameters in both phases. Lattice parameters values were extracted from [12] and the software VESTA was used to produce the drawings [32].
Twin Boundary domain A domain B
ao
bo ao
bo
Figure 1.4: Two-dimensional iron atoms lattice (red spheres) with arsenic atoms placed above (violet) and below (green) the ab plane. Two twin domains A and B are mirrored by a twin boundary, adapted from [34].
wave vectors connecting the localized Fermi surfaces known as electron and hole pockets that we will discuss later (see Fig. 1.6). From a localized point of view, two interpen-etrating N´eel sub-lattices produce the magnetic stripe order in iron pnictides. In this order the spins are aligned antiferromagnetically along the orthorhombic axis aO and are
alligned ferromagnetically along the orthorhombic axis bO, as shown Fig 1.5. Concerning
the Fe magnetic moment in LaFeAsO, first-principles calculations indicate magnetic mo-ments between 2.6 µB and 0.48 µB [36,37], while neutron diffraction measurement gives
0.8 µB [35]. Such discrepancies should be due to the weak metallicity of the FeSCs that
allows for a mixed itinerant and localized magnetic state.
Magnetic Stripe Order
bO aO
FM AFM
Figure 1.5: Two interpenetrating blue and red N´eel lattices configuring an magnetic stripe order in iron pnictides. The blue and red spheres represent the iron atoms while the arrows over them are the spins. Along the orthorhombic axes aO and bO the spins are aligned
antiferromagnetically and ferromagnetically, respectively.
First-principles calculations show that the density of states around the Fermi energy is caused only by 3d Fe2+ ions [25,38]. In this condition, the calculated band structure
leads to the localized Fermi surfaces around symmetry points in the Brillouin Zone (BZ) known as hole and electron pockets. Figure 1.6(a) shows the unfolded BZ for 1Fe unit cell with the electron pockets around Y and X points and the hole pockets around the Γ point. The orbitals of Y and X electron pockets are dxz+ dxy and dyz+ dxy, respectively,
while for the hole pockets around Γ point are dxz+ dyz. The folded BZ is the reciprocal
of the 2Fe unit cell in the real space and as shown in Fig. 1.6(b), which is half of the area of the unfolded BZ with the reciprocal axes rotated by 45◦ along k
z from the unfolded
G Orbital Y: dxz+ dxy X: dyz+ dxy G: dxz+ dyz G 1Fe Electron pocket hole pocket Qnesting (p,p) Qnesting (0,p) 2Fe (a) (b) Y X M Y X M ~ ~ ~
Figure 1.6: (a) On top the 1Fe unit cell and at bottom the correspondent unfolded BZ showing the elliptical electron pockets around the X with orbital content dyz+ dxy and
the Y with orbitals dxz + dxy point and the hole pockets around the Γ point with the
orbitals dxz+ dyz and (b) on top the 2Fe unit cell and its correspondent folded BZ at the
bottom with new symmetry ˜Y , ˜X and ˜M points.
pockets are around Γ point. Almost perfect nesting vectors (0, π) and (π, π) connect points between hole and electron pockets for unfolded and folded BZ, respectively [25].
Another important property of the FeSCs is the nematic phase, which is a quantum analogy to the classical liquid crystal (LC) nematic phase. In Figure1.7(a) the molecules of the LCs with ellipsoidal format are randomly oriented in the LC isotropic phase. How-ever, the molecules can align their axes with the direction of an external electric field or this alignment can be due to the external pressure, configuring a LC nematic phase as shown in Fig. 1.7(b). The order parameter of this LC nematic phase defines a director along the alignment, which breaks the rotational symmetry but preserves the transla-tional symmetry of the compound. Similarly, in the FeSCs the nematic phase breaks the rotational symmetry of the tetragonal ab plane by making the directions a and b different but preserving the time-reversal and translational symmetries. As the nematic phase in FeSCs is developed in a solid, the symmetry breaking is related to the host symmetry, which requires that the director align itself with one of the orthorhombic axes.
As can be noticed from Fig. 1.3, the orthorhombic distortion a/b is around 0.5 % while the resistivity anisotropy characterized by ρb/ρa at TS = TN is approximately 10 % as can
be calculated from Fig. 1.8, and we also observed that such anisotropy appears well above the transition temperature. Several measurements of the electronic properties obtained
LC-Isotropic Phase
director
LC-Nematic Phase
(a)
(b)
Figure 1.7: Illustration of ellipsoidal nematic molecules in (a) isotropic phase and in (b) nematic phase.
BaFe2As2
Figure 1.8: Temperature dependence of ab-plane resistivity ρa (green) and ρb (red) of
BaFe2As2. Solid line indicates the transition temperatures TS = TN. Figure extracted
bo
ao
3d
yz
- orbital
3d
xz
- orbital
(a)
(b)
Figure 1.9: Electronic distributions of the (a) 3dxz and (b) 3dyz orbitals showing its fours
lobes at the top. At the bottom the projection of the orbitals on the ab-plane showing two lobes pointing along the (a) b direction and (b) a orthorhombic directions.
from resistivity, optical conductivity, ARPES, magnetic susceptibility measurements have been performed in 1111-type and 122-type iron pnictides [13,39–44]. All of them have reported anisotropy in the electronic properties between the orthorhombic axes and these anisotropies were observed quite above the structural transition temperature. Thus, from these high anisotropies observed in the electronic properties compared to the magnitude of the orthorhombic distortion, it is attributed an electronic origin to the nematic phase in FeSCs, which can be associated either to the orbital/charge or spin electronic degrees of freedom, or both. Which electronic degree of freedom drives the nematic phase is an open question because once the ‘primary’ phase establishes a long-range ordering it triggers the secondary electronic phase and also the structural ordering in a feedback process [14]. In this way, we can conceive the orbital/charge and the spin fluctuations points of view to explain the electronic nematic phase.
From an electronic orbital/charge degree of freedom point of view, at the tetragonal phase the degenerate 3dxz and 3dyz orbitals form the four lobe distributions along the
bisectors of the xz-plane and yz-plane, as illustrated on the top of Fig. 1.9(a) and (b), respectively. While the projected 3dxz orbitals have two lobes and are oriented along
the orthorhombic direction bO, the projected 3dyz orbitals also have two lobes but are
oriented along the orthorhombic direction aO, as presented at the bottom of Fig. 1.9(a)
and (b), respectively. Above Tnem, in the tetragonal phase, the degenerate orbitals form
chains of 3dxz two lobes and 3dyz two lobes along the bO and aO direction, as presented
in Fig. 1.10(a). At Tnem, the orbital/charge fluctuations induce one of the two possible
states, which are the projected 3dyz extended along ao and the projected 3dxz shrunk
along bO or the contrary, the projected 3dxz extended along bO and the projected 3dyz
shrunk along aO. When the system chooses one of these states, the rotational symmetry is
broken, which configures the Ising-orbital/charge nematic phase. From this point of view the idea of anisotropic resistivity between the aO and bO directions becomes clear due
to the formation of “electronic rivers” in the direction of the extended projected orbitals with overlapping electronic cloud. The orbital/charge nematic fluctuations above Tnem
between those two Ising orbital/charge nematic states has been argued to be measurable by electronic Raman spectroscopy [17,18]. In this scenario, the charge/orbital nematic fluctuations enhances the attractive inter-pocket interaction potential and favors a s++
T > TS T ≤ Tnem~TS 3dxz 3dyz bo ao Tetragonal Phase
Ising Orbital Nematic Order
(a)
(b)
Figure 1.10: (a) Projection of the 3dxz and 3dyz orbitals in the ab-plane showing two lobes
each oriented along bO and aO directions, respectively, at tetragonal phase (T > Tnem).
(b) Two possible configurations for the Ising orbital nematic order in which (top) the 3dyz
orbitals extend along aO and the 3dxz shrink along bOor (bottom) the 3dyz orbitals shrink
along aO and the 3dxz extend along bO.
pockets [14].
From the electronic spin degree of freedom point of view, for T > Tnem the spins are
randomly oriented at the tetragonal/paramagnetic phase and for T < TN the spins are
arranged in one of two possible magnetic stripe configurations, as shown in Fig. 1.11(a) and (c), respectively. For an intermediate temperature Tnem ≤ T ≤ TN, the system
chooses one of two possible states, which configures the Ising-spin nematic phase, as illustrated in Fig. 1.11(b). In the first possible state, there is an short antiferromagnetic spin correlation along aO and a short ferromagnetic spin correlation along bO, while in
the second possible state there is a short ferromagnetic spin correlation along aO and an
short antiferromagnetic spin correlation along bO. When the system chooses one of these
two states, the rotational symmetry is broken but the time-inversion and translational symmetries are preserved implying that the system is still paramagnetic, however with short spin correlations directed towards to a stripe magnetic order. In this spirit, we should expect spin fluctuations down to TN. These fluctuations also should be observable
in the electronic channel of the Raman response [19,45]. In this scenario, the spin nematic fluctuations enhance the repulsive inter-pocket interaction potential and favors a s+−
superconductor state, in which the gap functions change the signals between the pockets or a dx2−y2
superconducting state [14].
Ising Spin Nematic Order Tetragonal/Paramagnetic
scFM
scAFM
T
<
T
nem~
T
ST
N<
T
<
T
nem~
T
ST
<
T
NStripe Magnetic Order
scAFM
scFM
bo
ao
(a)
(b)
(c)
Figure 1.11: (a) Spins randomly oriented at the tetragonal/paramagnetic phase for a temperature T > Tnem. (b) Two configurations of the Ising spin nematic order in which
(top) there is a short-range ferromagnetic spin correlation along bO with a short-range
an-tiferromagnetic spin correlation along aOor (bottom) there is a short-range ferromagnetic
spin correlation along aO with a short-range antiferromagnetic spin correlation along bO.
For a temperature TN ≤ T ≤ Tnem the system choose one of these configurations and is
still paramagnetic. (c) Magnetic stripe order coming from the chosen Ising spin nematic order for a temperature T < TN, adapted from [11].
1.2
Perovskites
Ferromagnetism and ferroelectricity occur due to the spontaneous ordering of the mag-netic moment M1 and electric dipole P2, respectively. Also, external magnetic field H can
change the sign of M as well as external electric field E can alter the sign of P. Multifer-roic materials exhibit two or more ferMultifer-roic phases like ferromagnetism and ferroelectricity, that may be independent of each other as in the type-I multiferroics. Nonetheless, for the
1M: Magnetization
so-called type-II multiferroic materials, a coupling between ferromagnetic and ferroelec-tric phases may occur, in which the magnetic field can change the elecferroelec-tric polarization sign or electric field can modulate the magnetization.
There is a keen interest in discovering new type-II materials due to the possible appli-cations in the data storage industry, and structures like perovskites containing transition metals surrounded by oxygen octahedra can be a starting point. Transition metals with d0 orbital such as Ti4+at the center of the oxygen octahedra induce ferroelectricity.
Non-occupied d0 states can form covalent bonds with the electrons of the surrounding oxygens
and these bonds can displace the transition metal from the octahedra center, which in-duces charge polarization of the oxygen cage. Furthermore, for a partial filled dntransition
metal, such as Mn4+, at the center of the oxygen octahedron, an unpaired electron creates
magnetism. In this context, a possible attempt to find multiferroicity is to synthesize ma-terials with d0and dntransition metals at the center of the oxygen octahedra in perovskite
structures [46]. The disordered double perovskite system Ba1−xLaxTi1/2Mn1/2O3 was
pro-posed by Professor Raimundo Lora Serrano3 as a prototype to find multiferroicity. Our
collaboration task was to identify all the crystal and magnetic structures employing neu-tron powder diffraction. Thus, in the rest of this section we describe the crystal structure of the perovskite systems.
Figure 1.12(a) shows one oxygen octahedron (O6) with the transition metal (B) at
its center. In simple cubic perovskites with ABO3 formula, the oxygen octahedra are
connected by the corner oxygens leaving interstitial sites that are occupied by the alkaline earth or rare earth metals (A), as shown in Fig. 1.12(b). Simple cubic double perovskite with A2BB’O6 formula has each oxygen octahedra with transition metal (B) connected by
six oxygen octahedra with transition metal (B’) and in this configurationg the transition metals sites (B) and (B’) are interchanged throughout the structure, as shown in Fig.
1.13. Additionally, in the disordered double perovskite with AB1/2B’1/2O3, it occurs a
mixed occupation (B/B’) of transition metal sites. In this direction, double perovskites allow for the d0 and dn transition metals to share the same structure and these structures
might present multiferroicity.
Distortion from the ideal cubic perovskite structure due to its incompatibility with the ion sizes (A, B and B’) lowers the unit cell symmetry. Eq. 1.1shows the Goldschmidt
O
B
A
p
( a )
( b )
( c )
Figure 1.12: (a) Oxygen (blue) octahedron with a metal ion B (green) in the center. (b) Planar projected view of a simple perovskite structure with the oxygen octahedra, the metal ions B and the interstitial charge reservoir ions A (violet). (c) The oxygen octahedron showing the displacement of the center ion B and the direction of the electric polarization.
tolerance factor t of the compatibility between the ions and structure using the A, B and B’ ionic radii rA, rB and rB0. Table 3.11 presents the expected symmetries/structures according to t values.
t = √ 2 (rA+ rO) 2 (rB+ rB0 + 2rO)
(1.1)
Table 1.1: Goldschmidt tolerance factor of perovskites classification.
t Structure
>1 Hexagonal
0.9−1.0 Cubic
0.71−0.9 Orthohombic/Rhombohedral
O
B
B’
A
Figure 1.13: Planar projected view of an ordered double perovskite showing the oxygens O (blue) the metal ions B and B’ (violet and green) and the charge reservoir ions A (orange).
Chapter 2
Experimental Probes
In this chapter we first describe the production of laser light, synchroton X-rays and neutrons, which were the experimental probes used in this work. Next, we give a brief review of Raman spectroscopy, X-ray diffraction and neutron scattering techniques, which were the employed experimental techniques in this thesis.
2.1
Laser, Neutron and X-Ray Production
2.1.1
Basics of Laser
Laser is the acronym for “Light Amplification by Stimulated Emission of Radiation”. Generally, a laser device converts electric energy in a monochromatic, narrow and coherent beam of light. The term monochromatic means that the waves in a laser beam should have only one color. However, due to uncertainty principle the laser beam contains a very small but non-null bandwidth. The waves in the laser travel nearly in the same direction resulting in a small divergence angle, which allows one to focus the beam in very small diameters with great intensity. If the beam waves keep their monochromatic and directionality properties with no phase difference, it has spatial and temporal coherence. An important component of the lasers is the gain medium, which can be solid-state as in Nd:YAG laser and in semiconductor diode laser, organic state as in Dye laser and gas state as in Ar, Kr, He, and CO2 gas lasers. In general, commercial lasers can be found
from the ultraviolet to the far infrared (100 nm - 1 mm) wavelengths with powers from miliwatts to hundreds of watts. Lasers can emit light in continuous-wave (CW) mode or in short pulses containing a bunch of photons.
In industry, laser beams are used for cutting, melting, drilling, heat-treating metals and other materials. In telecommunications, lasers are used to transmit information through the optical fibers more efficiently than the copper wires. In medicine, laser is used in ophthalmic surgery and in skin cancer treatments. Other laser applications are write and read CD’s, DVD’s, Blu-Rays and bar codes, laser printers, distance detection and aiming and guiding weapons. Lasers are fundamental tools in scientific research being used for several tasks, from the production of non-invasive biological images to the study of high energy particles in ultra-high laser-generated electromagnetic fields. In this thesis, a laser in continuous-wave (CW) mode was used to investigate the vibrational, electronic and magnetic properties of solids in Raman scattering experiments, and it is worth to give a brief description of the fundamental properties of a laser.
Fundamental properties
In a laser device, photon stimulated emission of a gain medium, with population inver-sion, must be amplified in a resonator to produce a monocromatic, narrow and coherent beam. The light can interact with the matter via absorption, spontaneous emission or stimulated emission as depicted in Fig. 2.1.
E E E E Energy (a) (b) photon photon
e-absorption spontaneous emission
E E E E Energy (c) photon photon e-stimulated emission photon
Figure 2.1: Diagram showing the energy levels of an atom showing the (a) absorption (b) spontaneous emission and (c) stimulated emission. The wavy arrows are the photons and the black circles are the electrons.
An electron in the ground state can absorb a photon, being promoted to an excited energy level. When the electron returns to the ground state a photon is emitted with the same energy of the incoming photon with random direction and phase, in a spontaneous emission process. In the stimulated emission, the electron in a higher energy level than
the ground state is stimulated by the incoming photon and it decays to a lower energy level, emitting an additional photon which leaves the atom with the same energy, direction and phase of the incoming photon. According to the Boltzmann distribution, in thermal equilibrium a higher-energy electronic level in an atom is always less occupied than a lower-energy electronic state. In this way, to obtain the amplification achieved by stimulated emission, it is necessary to create a population inversion in the energy levels of the gain medium. Usually, the population inversion is reached by a pumping process as shown in Fig. 2.2 using an external energy source (electrical, chemical or optical).
pump level
(a)
(b)
Three Levels
ground state
upper level upper level
pump level lower level Four Levels ground state photon photon E0 E2 E0 E1 E2 E3 E1
Figure 2.2: Diagram showing the energy levels of an atom for (a) three-level and (b) four-level laser systems.
In a three-level system, the pumping source promotes the electrons to the energy level E2 which rapidly decay to E1 releasing heat. In this energy level the electrons can
be stimulated emitted returning to the ground state E0. In the four-level system the
electrons are pumped to an energy level E3, also they decay releasing heat to an energy
level E2 where they can be stimulated emitted. After emission, the electrons decay to an
energy level E1 above the ground state and decay to the ground state E0 releasing heat.
In a medium with population inversion a single spontaneous emission can produce stimulated emission. These emitted photons can stimulate further emissions but eventu-ally they will escape the medium and it would not be a self-sustained process. Fortunately, using a resonator, the emitted photon returns to the medium in order to increase the stim-ulated emission, turning the material into a gain medium.
mirrors is highly reflective while the other allows partially photon transmission, necessary to produce an output beam. The optical axis of the mirrors are aligned each other and are separated by a distance of L and the R1,R2 are the curvature radii which can be ∞,
negative and positive for plane, convex and concave mirrors, respectively.
R R
L gain medium
Figure 2.3: Diagram showing a resonator with two mirrors of curvature radii R1 and R2
separated by distance L. A gain medium was placed in the center of the resonator.
Photons reflect back and forth in the mirrors passing several times inside the gain medium, which increases the stimulated emission. Nonetheless, for each round trip, losses occur because of mirror transmittance and imperfections. When the balance between the gain and loss reach the steady-state, an almost constant power circulates inside the resonator and the output power is a small fraction of the circulating power. The transverse and longitudinal laser modes can be naturally accommodated by the resonator. The transverse electromagnetic modes TEMmnshown in Fig. 2.4are solutions of the Maxwell’s
equations, described by Hermite-Gauss funtions, with the resonator boundary conditions. 00
10
01 11
22 50 55
