Controlling Collective Electronic States

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Springer Theses
Recognizing Outstanding Ph.D. Research

Martin Bluschke

Controlling
Collective Electronic
States in Cuprates
and Nickelates
A Resonant X-ray Scattering Study
Springer Theses

Recognizing Outstanding Ph.D. Research

Aims and Scope

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Martin Bluschke

Controlling Collective
Electronic States in Cuprates
and Nickelates
A Resonant X-ray Scattering Study
Doctoral Thesis accepted by
the Technical University of Berlin, Germany

123
Author Supervisor
Dr. Martin Bluschke Prof. Bernhard Keimer
Department of Solid State Spectroscopy Department of Solid State Spectroscopy
Max-Planck-Institute for Solid Max-Planck-Institute for Solid
State Research State Research
Stuttgart, Baden-Württemberg, Germany Stuttgart, Baden-Württemberg, Germany

ISSN 2190-5053 ISSN 2190-5061 (electronic)

Springer Theses
ISBN 978-3-030-47901-5 ISBN 978-3-030-47902-2 (eBook)
https://doi.org/10.1007/978-3-030-47902-2
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Switzerland AG 2020
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of
illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
transmission or information storage and retrieval, electronic adaptation, computer software, or by similar
or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, expressed or implied, with respect to the material contained
herein or for any errors or omissions that may have been made. The publisher remains neutral with regard
to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
This work is dedicated to three inspirational
women:
Doris Passer, Christa Bluschke
and Gisela Menger.
Supervisor’s Foreword

Martin Bluschke’s dissertation describes a comprehensive set of resonant X-ray

scattering (RXS) experiments that were designed to elucidate charge order in
copper oxides and non-collinear magnetic order in nickel oxides. His results allow
novel insight into the origin of these phenomena.
Prior RXS experiments on high-temperature superconductors, including the
model compound YBa2 Cu3 O6 þ x (YBCO), had revealed charge order as the
dominant competitor of superconductivity, but left open basic questions about its
relationship to magnetic order and the “pseudogap” phenomenon which are also
ubiquitous in these materials. To address these questions, Martin performed a series
of RXS experiments on single crystals of the compound family (Cay La1y )
(Ba1:75y La0:25 þ y )Cu3 O6 þ x (CLBLCO), which has the advantage that the con-
centration of mobile holes in the CuO2 planes and the crystal structure can be
independently modified. In particular, the superexchange interaction J can be
modified by a judicious choice of the composition parameters x and y without
modifying the hole content. In this way, Martin identified opposing trends of J and
the onset of charge order, and concluded that magnetism is not the dominant driver
of charge ordering. By tracking both the onset of charge order and the onset of the
pseudogap as functions of composition, he further confirmed that charge order does
not cause the pseudogap.
Martin goes on to describe a second set of RXS experiments on charge ordering
in YBCO thin films epitaxially grown on SrTiO3 substrates. He discovered Bragg
reflection characteristics of a three-dimensionally long-range ordered CDW state
that is found in bulk YBCO only under high magnetic fields or high uniaxial strain.
Moreover, this state persists well above room temperature, much higher than
charge-ordered states in other high-temperature superconductors. By taking
advantage of the spectroscopic capabilities of RXS and by studying the lattice
structure of his films using non-resonant X-ray scattering, he obtained detailed
insight into the origin of the unusual stability of the charge ordered state. Epitaxial
growth thus opens up new routes towards targeted modification of the electronic
phase behavior of cuprate superconductors.

vii
viii Supervisor’s Foreword

In an independent RXS study, Martin investigated thin-film structures of nick-

elate perovskites, which had been the subject of intense prior work because of their
unusual magnetic properties. In particular, we had found earlier that LaNiO3 (which
is paramagnetic and metallic in bulk form) develops a commensurate spin density
wave (SDW) phase when three or fewer unit cells are confined between insulating
blocking layers. Martin studied superlattices in which LaNiO3 (with magnetic 3d
electrons on the Ni3 þ ions) alternated with DyScO3 layers containing magnetic 4f
electrons on the Dy sites, thus establishing a new model system for the interaction
between 3d and 4f magnetic moments. He discovered a reorientation of the Ni
spins upon cooling that does not occur if LaNiO3 is sandwiched between non-
magnetic layers. Based on a careful and comprehensive set of RXS and magneti-
zation measurements, he was able to attribute this effect to an imprint of the SDW
on the Dy moments induced by 3d-4f exchange interactions, which then elicits a
back-reaction on the Ni spins by virtue of the large magneto-crystalline anisotropy
of Dy. He developed a quantitative model of the resulting complex magnetic
structure and points out interesting perspectives for epitaxial integration of 3d and
4f electron systems.

Stuttgart, Germany Prof. Bernhard Keimer

March 2020
Abstract

In quantum materials, valence electrons experience strong mutual interactions,

which can lead to the spontaneous emergence of multifarious collective electronic
and magnetic phases. These include Mott insulating phases, superconductivity,
antiferromagnetism, as well as charge and orbital ordered phases. Often, various
nearly-degenerate electronic ordering tendencies exist within close proximity of one
another. In such cases, small variations in the material’s chemical and structural
landscape can effectively push the system toward one or the other ordered ground
state. In this sense, careful control of both chemical and structural degrees of
freedom may be harnessed to design collective states in strongly correlated systems.
Transition metal oxides represent a promising platform for the controlled manip-
ulation of collective states, due to the strongly correlated transition metal d states
and the wide variety of nearly isostructural compounds, which allow for elaborate
chemical substitutions and coherent epitaxial relationships between chemically
distinct phases. Progress in our understanding of these systems, and in particular the
set of tools available to control them, may allow these materials to form the basis of
future information and energy technologies ranging from spintronics and neuro-
morphic computation to superconducting quantum computers and superconducting
magnetic levitation.
In this thesis, a variety of solid state techniques are used to control the collective
behaviour of strongly correlated charge and spin degrees of freedom in Cu and
Ni based 3d transition metal oxides. We begin with the study of a copper-oxide
high-temperature superconductor with the chemical formula (Cax La1x )
(Ba1:75x La0:25 þ x )Cu3 Oy (CLBLCO), which hosts a 123-type structure closely
related to that of the well studied compound YBa2 Cu3 O6 þ x (YBCO). Isovalent
chemical substitution of Ba with Ca causes slight changes in the Cu-O bond angles and
distances, resulting in a dramatic variation of both electronic and magnetic correla-
tions. In the context of this thesis, we have used resonant X-ray scattering at the Cu L3
edge to produce the first report of charge order in the CLBLCO system, as well as to
characterize its response to the chemical substitution x and the oxygen content y. In
recent years, charge order correlations have been established as a ubiquitous

ix
x Abstract

component of the cuprate high-Tc phase diagram, often evidently competing with
superconductivity. In CLBLCO, the charge order onset temperature was found to
decrease by up to 90 K as a function of x, in contrast to superconductivity and
antiferromagnetism which are both strongly enhanced by the structural variations
associated with increasing x. Our results reveal a powerful mechanism by which
to control the complex interplay between charge density wave order and
superconductivity.
In the second part of this thesis, we study charge order correlations in the related
high-temperature superconductor YBCO. While charge order correlations in bulk
crystals of YBCO have been studied extensively since their discovery in 2011–
2012, this thesis presents the first systematic study of charge order in epitaxially
grown YBCO films. While charge order in the bulk system is characterized by
2-dimensional short range correlations, our resonant X-ray scattering study has
revealed the unexpected emergence of 3-dimensionally phase coherent charge order
in YBCO films grown on SrTiO3 substrates. Our results demonstrate how the
epitaxial relationship to a chemically and structurally distinct substrate is able to
couple to both structural and electronic degrees of freedom, thereby manipulating
the collective behaviour of charge order correlations in YBCO. This result is par-
alleled by the recent observation that 3-dimensional charge order can be induced in
the bulk system in the presence of strong magnetic fields or a uniaxial strain field.
In the final chapter of this thesis, we combine the control of structural degrees of
freedom facilitated by heteroepitaxy with the designed integration of two mag-
netically active materials with distinct anisotropies and exchange interactions. As a
model system we have chosen to incorporate ultrathin layers of metallic antifer-
romagnetic LaNiO3 with the orthorhombic and magnetically anisotropic DyScO3 in
superlattices grown on DyScO3 substrates. The resulting heterostructure adopts the
structural symmetry of the substrate material, while the coupled magnetic sublat-
tices inherit characteristics associated with both of the constituent materials. Our
resonant magnetic X-ray scattering study of this system reveals that the spiral
antiferromagnetic structure originating from the strong Ni-Ni exchange interactions
is induced on the Dy sites, whereas the strong Ising anisotropy of the Dy moments
is fed back across the interface to the otherwise nearly isotropic Ni spins.
Furthermore, the large Dy moments respond sensitively to applied magnetic fields,
thereby acting as “anchors” for the magnetic-field-induced manipulation of the Ni
spin-spiral orientation. The manipulation of spiral antiferromagnetic states via
external fields opens new perspectives for the control of spin-dependent transport
phenomena in antiferromagnetic spintronic devices.
In this work, we have exploited chemical and epitaxial degrees of freedom to
manipulate the lattice, electronic and magnetic structures in the 3d transition metal
oxides (Cax La1x )(Ba1:75x La0:25 þ x )Cu3 Oy , YBa2 Cu3 O6 þ x and LaNiO3 . In doing
so, we have contributed to an ongoing effort to understand the correlated phases in
these materials and have helped to characterize the set of tools available to control
Abstract xi

their collective behaviour. Finally, these case studies highlight the power of reso-
nant X-ray scattering to selectively probe lattice, charge, orbital and spin degrees of
freedom in an element-specific manner well suited to multinary transition metal
oxide compounds.
Publications Related to This Thesis

1. M Bluschke, M Yaari, E Schierle, G Bazalitsky, J Werner, E Weschke, and A

Keren. Adiabatic variation of the charge-density-wave phase diagram in the
123 cuprate (Cax La1x )(Ba1:75x La0:25 þ x ) Cu3 Oy . Physical Review B 100,
035129 (2019).

2. M Bluschke, A Frano, E Schierle, D Putzky, F Ghorbani, R Ortiz, H Suzuki, G

Christiani, G Logvenov, E Weschke, RJ Birgeneau, EH da Silva Neto, M
Minola, S Blanco-Canosa, and B Keimer. Stabilization of three-dimensional
charge order in YBa2 Cu3 O6 þ x via epitaxial growth. Nature Communications
9, 2978 (2018).

3. M Bluschke, A Frano, E Schierle, M Minola, M Hepting, G Christiani,

G Logvenov, E Weschke, E Benckiser, and B Keimer. Transfer of magnetic
order and anisotropy through epitaxial integration of 3d and 4f spin systems.
Physical Review Letters 118, 207203 (2017).

4. A Frano , M Bluschke*, Z Xu, B Frandsen, Y Lu, M Yi, R Marks, A Mehta, V

Borzenets, D Meyers, MPM Dean, F Baiutti, J Maier, G Kim, G Christiani, G
Logvenov, E Benckiser, B Keimer, and RJ Birgeneau. Control of dopant
crystallinity in electrochemically treated cuprate thin films. Physical Review
Materials 3, 063803 (2019).

5. G Kim, Yu Khaydukov, M Bluschke, YE Suyolcu, G Christiani, K Son, C

Dietl, T Keller, E Weschke, A Vorobiev, A Derishrili, PA van Aken, G
Logvenov, and B Keimer. Tunable perpendicular exchange bias in oxide
heterostructures. Physical Review Materials 3, 084420 (2019).

6. K Fürsich, Y Lu, D Betto, M Bluschke, J Porras, E Schierle, R Ortiz, H Suzuki,

G Christiani, G Logvenov, NB Brookes, MW Haverkort, G Khaliullin, M Le
Tacon, E Benckiser, M Minola, and B Keimer. Resonant inelastic x-ray scat-
tering study of bond order and spin excitations in nickelate thin-film structures.
Physical Review B 99, 165124 (2019).

7. KW Post, AS McLeod, M Hepting, M Bluschke, Y Wang, G Cristiani, G

Logvenov, A Charnukha, GX Ni, P Radhakrishnan, M Minola, A Pasupathy,
AV Boris, E Benckiser, KA Dahmen, EW Carleson, B Keimer, and DN Basov.
Coexisting first- and second-order electronic phase transitions in a correlated
oxide. Nature Physics 14, 1056–1061 (2018).

xiii
xiv Publications Related to This Thesis

8. M Hepting, RJ Green, Z Zhong, M Bluschke, YE Suyolcu, S Macke, A Frano,

S Catalano, M Gibert, R Sutarto, F He, G Christiani, G Logvenov, Y Wang, PA
van Aken, P Hansmann, M Le Tacon, J-M Triscone, GA Sawatzky, B Keimer,
and E Benckiser. Complex magnetic order in nickelate slabs. Nature Physics
14, 1097–1102 (2018).

9. EH Neto, M Minola, B Yu, W Tabis, M Bluschke, D Unruh, H Suzuki, Y Li,

G Yu, D Betto, K Kummer, F Yakhou, NB Brookes, M Le Tacon, M Greven, B
Keimer, and A Damascelli. Coupling between dynamic magnetic and
charge-order correlations in the cuprate superconductor Nd2x Cex CuO4 .
Physical Review B 98, 161114(R) (2018).

10. YY Peng, R Fumagalli, Y Ding, M Minola, S Caprara, D Betto, M Bluschke,

GM Luca, K Kummer, E Lefrançois, M Salluzzo, H Suzuki, M Le Tacon, XJ
Zhou, NB Brookes, B Keimer, L Braicovich, M Grilli, and G Ghiringhelli.
Re-entrant charge order in overdoped ðBi; PbÞ2:12 Sr1:88 CuO6 þ d outside the
pseudogap regime. Nature Materials 17, 697–702 (2018).

11. H Gretarsson, SM Souliou, S Jeong, J Porras, T Loew, M Bluschke, M Minola,

B Keimer, and M Le Tacon. Light-induced metastable state in charge-ordered
YBa2 Cu3 O6 þ x . Physical Review B 98, 075134 (2018).

12. F Wrobel, B Geisler, Y Wang, G Christiani, G Logvenov, M Bluschke, E

Schierle, PA van Aken, B Keimer, R Pentcheva, and E Benckiser. Digital
modulation of the nickel valence state in a cuprate-nickelate heterostructure.
Physical Review Materials 2, 035001 (2018).

13. Y He, S Wu, Y Song, W-S Lee, AH Said, A Alatas, A Bosak, A Girard, S-M
Souliou, A Ruiz, M Hepting, M Bluschke, E Schierle, E Weschke, J-S Lee, H
Jang, H Huang, M Hashimoto, D-H Lu, D Song, Y Yoshida, H Eisaki, Z-X
Shen, RJ Birgeneau, M Yi, and A Frano. Persistent low-energy phonon
broadening near the charge-order q vector in the bilayer cuprate
Bi2 Sr2 CaCu2 O8 þ d . Physical Review B 98, 035102 (2018).

14. W Tabis, B Yu, I Bialo, M Bluschke, T Kolodziej, A Kozlowski, E Blackburn,

K Sen, EM Forgan, M v Zimmermann, Y Tang, E Weschke, B Vignolle, M
Hepting, H Gretarsson, R Sutarto, F He, M Le Tacon, N Barišić, G Yu, M
Greven. Synchrotron x-ray scattering study of charge-density-wave order in
HgBa2 CuO4 þ d . Physical Review B 96, 134510 (2017).
Publications Related to This Thesis xv

15. EH da Silva Neto, B Yu, M Minola, R Sutarto, E Schierle, F Boschini, M

Zonno, M Bluschke, J Higgins, Y Li, G Yu, E Weschke, F He, M Le Tacon,
RL Greene, M Greven, GA Sawatzky, B Keimer, and A Damascelli.
Doping-dependent charge order correlations in electron-doped cuprates.
Science Advances 2, e1600782 (2016).

16. A Frano, S Blanco-Canosa, E Schierle, Y Lu, M Wu, M Bluschke, M Minola,

G Christiani, H-U Habermeier, G Logvenov, Y Wang, PA van Aken, E
Bencksier, E Weschke, M Le Tacon, and B Keimer. Long-range
charge-density-wave proximity effect at cuprate/manganate interfaces. Nature
Materials 15, 831–835 (2016).

17. Y Lu, A Frano, M Bluschke, M Hepting, S Macke, J Strempfer, P Wochner, G

Christiani, G Logvenov, H-U Habermeier, MW Haverkort, B Keimer, and E
Benckiser. Quantitative determination of bond order and lattice distortions in
nickel oxide heterostructures by resonant x-ray scattering. Physical Review B
93, 165121 (2016).

18. S Blanco-Canosa, A Frano, E Schierle, J Porras, T Loew, M Minola, M

Bluschke, E Weschke, B Keimer, and M Le Tacon. Resonant x-ray scattering
study of charge-density wave correlations in YBa2 Cu3 O6 þ x . Physical
Review B 90, 054513 (2014).

19. M Hepting, M Minola, A Frano, G Cristiani, G Logvenov, E Schierle, M Wu,

M Bluschke, E Weschke, H-U Habermeier, E Bencksier, M Le Tacon, and B
Keimer. Tunable charge and spin order in PrNiO3 thin films and superlattices.
Physical Review Letters 113, 227206 (2014).

20. S Macke, A Radi, JE Hamann-Borrero, A Verna, M Bluschke, S Brück, E

Goering, R Sutarto, F He, G Christiani, M Wu, E Benckiser, H-U Habermeier,
G Logvenov, N Gauquelin, GA Botton, AP Kajdos, S Stemmer, GA Sawatzky,
MW Haverkort, B Keimer, and V Hinkov. Element specific monolayer depth
profiling. Advanced Materials 26, 6554–6559 (2014).
Acknowledgements

I would like to begin by thanking my supervisor Bernhard Keimer for giving me the
opportunity to join a wonderful team of scientists and for providing me guidance
along the way. In particular, I applaud the progressive approach, which has fostered
a diverse group of young scientists, allowing many hard working and motivated
individuals a path to success irrespective of their significantly varying backgrounds.
Next, I would like to thank both Eva Benckiser and Matteo Minola for their
invaluable supervision and friendship. I greatly appreciate the freedom that I have
been afforded over the past years, as well as the immediate feedback and support,
which has been consistently available.
Thank you to Eugen Weschke, Enrico Schierle and Bella Lake, to whom I am
indebted for making it possible for me to live in Berlin and to take part in so many
thrilling beamtimes at UE46! In addition, I would thank Marie Haltod and Ines
Drochner for all of their administrative support throughout the years.
Thank you to Maurits Haverkort, Vladimir Hinkov, Ole Andersen, Sebastian
Macke, Meng Wu and Jorge Hamann-Borrero for getting me started many years ago.
Thank you to all of the beamline scientists who have helped me out along the
way: Enrico Schierle, Eugen Weschke, Peter Wochner, Andi Barbour, Stuart
Wilkins, Ron Marks, Apurva Mehta, Valery Borzenets, Ronny Sutarto, Feizhou He,
Sujoy Roy, Padraic Shafer, Elke Ahrenholz, Nick Brookes, Flora Yakhou-Harris,
Kurt Kummer, Markus Weigand, Michael Bechtel and Joerg Strempfer.
Thanks to everyone back in Stuttgart, who helped make the MPI my home away
from home. An incomplete list of the people who have made my many stays in
Stuttgart both fruitful and pleasant includes Parmida Shabestari, Mahdieh Schmidt,
Padma Radhakrishnan, Friederike Wrobel, Philipp Hansmann, George Jackelli,
Manfred Ohl, Michaela Souliou, Matthieu Le Tacon, Juan Porras, Eslam Khalaf,
Leslie Schoop, Grigory Zarubin, Avaise Mohammed, Gideok Kim, Toshinao Loew,
Luzia Germann, Jachym Sykora, Ciro Taranto, Hun-Ho Kim, Cissy Suen,
Mohamed Ouda, Huimei Liu, Matthias Hepting, Chris Dietl, Max Krautloher,
Daniel Weber, Ksenia Rabinovich, Joel Bertinshaw, Giulia Raimondi, Olle
Gunnarsson, Lichen Wang, Hlynur Gretarsson, Aliaksei Charnukha, Suguru
Nakata, Alaska Subedi, Marc Hoeppner, Tobias Holder, Maryam Nojabaee, Robert

xvii
xviii Acknowledgements

Dawson, Hakuto Suzuki, Hans Boschker, and Michael Schulz. Thank you to Sonja
Balkema, Frank Gottschalk, Michael Eppard, Anette Schleehauf, Simone Reich and
Dr. Zehender for doing such a great job! Finally, it is very important to me to
acknowledge all of the wonderful security personnel whose names I (regrettably)
never learned, but whose friendly faces I will never forget, and who always seemed
to know exactly who I am. Every time I took the last train from Berlin and arrived
in Büsnau at 1:00 AM, there was always someone there to wave me in and make me
feel welcome. Thank you!
Thank you to Georg Christiani and Gennady Logvenov for wonderful samples, it
wouldn’t have been possible without you. Thank you also to Ionela Vrejoiu.
Thank you to all of my fellow beamtimers out there, I would have quit by now if
it were not for you: Alex Frano, Enrico Schierle, Matteo Minola, Eduardo da Silva
Neto, Santiago Blanco-Canosa, Wojciech Tabis, Izabela Biało, Maayan Yaari, Yi
Lu, Katrin Fürsich, Davide Betto, Daniel Putzky, Fariba Ghorbani, Alejandro
Ruiz…. pull the aluminum foil off the coffee machine and grab the samples from
under the desk, its beam time!
I would like to acknowledge all of the students around me who have not received
due recognition for their efforts and accomplishments, either because of bad luck or
systematic disadvantage. I know that many of you have worked at least as hard as
myself, and the community has certainly benefited from your efforts.
A very special thank you to Raquel Queiroz for oh so many things, and thank
you to Maria-João, João, Ana, João, Jorge, Alvaro, Magdalena (and all the rest) for
all of your warmth and generosity.
Thank you and much love to all of my friends over the years, including but not
limited to: Achim, Keira, Alex Hallbom, Ramsay, Sebastian & Lu, Mike, Ozan,
Marta, Annika, Ori, Gamze, Olga, Marcel, Diana, Elif, Peter, Pia, Tomek, Nina
Joseph, Nina Hellmuth, Mikee Lifshitz, Gal, Nick, Felipe, Jeremy, Elise, Arman,
Ashkan, Freija, Conor, Carly, Adrian, Roopa, Lillian, Alex Woznica, Rupert,
Graeme, JP, Owen, Tristan, Sam, Jean, Beth, Dessa, Matthias, Fruzsi, Sophie,
Mafalda, Cartaxana, Nuno, Ladislau, Dieter (the mouse lover) and Tor.
Thank you to Amit Keren for challenging me, believing in me, and for being a
friend! An extra thank you goes to Wojtek for sharing everything with me, from
instant noodle soup, chocolatine and beer to your stories and your friends! An extra
thank you goes to Alex Frano for pulling me up and letting me hang on for the ride.
You are a good person and a great friend! A final extra thank you goes to Enrico
Schierle who is my role model. I have met no person more dedicated, wise, selfless,
caring, patient, intelligent, and interested than you. You’re actions have been a
continued source of inspiration for myself and many others around me.
Last and most importantly I would like to thank my family Inger, Armin, Sabine,
Ian, Doris, Christa, (Radim Max and Hubert), Maxine, Mo, Hart, Debbie, Renate, and
Arnold, as well as my extended family Gisela, Friedrich Wilhelm, Cordula, Christa
(and Klaus), Philipp, Nadja, David, Bruno, Nora, Susanne, Christoph, Leonie,
Vincent, Torsten, Katrin, Clemens, Claas, Jacob, Anja, Dirk, Florian, Niklas, Ralf,
Andreas, Tanja, Jenny, Jan, Hanna, Erika, Stephanie, Anke, Peter, Julius, Franka,
Mauricio Passer, Claudia, David, Lenka, Eva Límanová and Honza Zalabák. Thank
Acknowledgements xix

you to the family Schurr: Susanne, Gerhard, Friederike, Franziska, Felicia, and Elif
Philine for letting me be part of your lives. Eliphili you are the best! Franziska, you are
also the best! Thank you for supporting me while I wrote this thesis. I would still be
writing if not for you.
Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Resonant X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Linear Response Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Core-Level Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Light-Matter Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Introduction to Charge Order in the Cuprates . . . . . . . . . . . . . . . . . 27
3.1 Cuprate High-Temperature Superconductors . . . . . . . . . . . . . . . . . 27
3.1.1 Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 Antiferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.3 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.4 Pseudogap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Charge Order in the Cuprates . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Stripe Order in the 214 Cuprates . . . . . . . . . . . . . . . . . . . 35
3.2.2 Fermi Surface Reconstruction . . . . . . . . . . . . . . . . . . . . . . 37
3.2.3 Charge Order in YBa2 Cu3 O6 þ x . . . . . . . . . . . . . . . . . . . . 39
3.2.4 Charge Order in Bismuth-Based Cuprates . . . . . . . . . . . . . 45
3.2.5 Charge Order in HgBa2 CuO4 þ d . . . . . . . . . . . . . . . . . . . . 47
3.2.6 Charge Order in Electron-Doped Cuprates . . . . . . . . . . . . . 48
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Charge Order in (Cax La1x )(Ba1:75x La0:25 þ x )Cu3 Oy
Single Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 Introduction to (Cax La1x )(Ba1:75x La0:25 þ x )Cu3 Oy . . . . . . . . . . . . 57
4.1.1 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1.2 Hole Doping and Hole Doping Efficiency . . . . . . . . . . . . . 60

xxi
xxii Contents

4.1.3 Superconductivity, Antiferromagnetism

and the Pseudogap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Sample Growth and Preparation . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Crystal Growth and Characterization . . . . . . . . . . . . . . . . . 64
4.2.2 Crystal Alignment and Surface Preparation . . . . . . . . . . . . 64
4.3 Resonant X-ray Scattering from Charge Order Correlations . . . . . . 66
4.3.1 X-ray Energy and Polarization Dependence . . . . . . . . . . . . 67
4.3.2 Incommensurability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.3 Temperature-Doping Phase Diagram . . . . . . . . . . . . . . . . . 69
4.3.4 Charge Correlations Along c . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.1 Relation of Charge Order to the Pseudogap . . . . . . . . . . . . 74
4.4.2 Relation of Charge Order to Antiferromagnetism,
Superconductivity and Preformed Pairs . . . . . . . . . . ..... 75
4.4.3 Relation of Charge Order to Fermi-Surface
Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 77
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 77
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 78
5 Charge Order in YBa2 Cu3 O6 þ x Thin Films . . . . . . . . . . . . . . . . . . . 83
5.1 Growth and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.1 Pulsed Laser Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.2 Annealing and Oxygen Concentration . . . . . . . . . . . . . . . . 85
5.1.3 Structural X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . 86
5.1.4 Transport Characterization . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Resonant X-ray Scattering from 2D and 3D Charge Order
Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.1 Reciprocal Space Mapping . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.2 Scattering Geometry and Polarization Dependence . . . . . . . 94
5.2.3 Energy Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2.4 Temperature Dependence . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.5 Doping Dependence and Film Thickness . . . . . . . . . . . . . . 98
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6 Introduction to Antiferromagnetism in Ultrathin Nickelate
Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1 Antiferromagnetism in Quasi-2D LaNiO3 Layers . . . . . . . . . . . . . 105
6.1.1 Degrees of Freedom of the Ordered Phase . . . . . . . . . . . . 107
6.2 Epitaxial Strain Induced Magnetocrystalline Anisotropy . . . . . . . . 111
6.2.1 Orbital Polarization in Nickelate Heterostructures . . . . . . . 112
6.2.2 Control of the Spin-Spiral Orientation . . . . . . . . . . . . . . . . 112
6.3 Truncation of the Antiferromagnetic Spin Spiral . . . . . . . . . . . . . . 113
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Contents xxiii

7 Coupling Between 3d and 4f Spin Sublattices in LaNiO3 -Based

Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1 Rare-Earth Scandates as Magnetically Active Interlayer
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1.1 SQUID Magnetometry of Bulk DyScO3 and GdScO3 . . . . 120
7.1.2 Powder Diffraction Study of Bulk DyScO3 . . . . . . . . . . . . 123
7.2 Preparation and Characterization of LaNiO3 -Based
Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2.1 Pulsed Laser Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2.2 X-ray Diffraction and Transport Characterization . . . . . . . . 128
7.3 Resonant X-ray Scattering from LaNiO3 -DyScO3
Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.3.1 Dy Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.3.2 Ni Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3.3 Alternate Models of the Ni and Dy Magnetic
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.4 Magnetic Domains and Twinning . . . . . . . . . . . . . . . . . . . . . . . . 139
7.5 Resonant X-ray Scattering from LaNiO3 -GdScO3
Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.6 X-ray Magnetic Circular Dichroism Study of LaNiO3 -DyScO3
and LaNiO3 -GdScO3 Superlattices . . . . . . . . . . . . . . . . . . . . . . . . 144
7.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8 Closing Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Abbreviations

Bi2201 Bi2 Sr2 CuO6 þ d

Bi2212 Bi2 Sr2 CaCu2 O8 þ d
Bi2223 Bi2 Sr2 Ca2 Cu3 O10 þ d
BO Bond order
CDW Charge density wave
CLBLCO (Cax La1x )(Ba1:75x La0:25 þ x )Cu3 Oy
CO Charge order
DBCO DyBa2 Cu3 O6 þ x
DSO DyScO3
GSO GdScO3
Hg1201 HgBa2 CuO4 þ d
Hg1212 HgBa2 CaCu2 O6 þ d
Hg1223 HgBa2 Ca2 Cu3 O8 þ d
LAO LaAlO3
LCO La2 CuO4
LNO LaNiO3
LNSCO La1:6x Nd0:4 Srx CuO4
LSAO (LaSr)AlO4
LSAT (LaAlO3 )0:3 (Sr2 TaAlO6 )0:7
LSCO La2x Srx CuO4
LTT Low-temperature tetragonal
MIT Metal-insulator-transition
NCCO Nd2x Cex CuO4
NMR Nuclear magnetic resonance
PBCO PrBa2 Cu3 O6 þ x
PLD Pulsed laser deposition
r.l.u. Reciprocal lattice units
REXS Resonant elastic X-ray scattering
RIXS Resonant inelastic X-ray scattering
RXS Resonant X-ray scattering

xxv
xxvi Abbreviations

SDW Spin density wave

STM Scanning tunneling microscopy
STO SrTiO3
u.c. Unit cell
UHV Ultra high vacuum
UV Ultraviolet
XAS X-ray absorption spectroscopy
XMCD X-ray magnetic circular dichroism
YBCO YBa2 Cu3 O6 þ x
lSR Muon spin resonance
Chapter 1
Introduction

In transition metal oxides, strong correlations give rise to electronic states in which
charge, spin, orbital and lattice degrees of freedom are intertwined with one another
[1–4]. While these correlations can generate quantum electronic ground states with
macroscopic coherence, such as superconductivity, the strongly coupled spin, charge
and orbital degrees of freedom often result in a multitude of nearly degenerate
ordering tendencies. These can, in turn, compete with one another to produce
complex phases characterized by nanoscopic heterogeneity [5]. Well established
examples include colossal magnetoresistance observed in the rare-earth manganites
(A1−x Ax MnO3 , where A and A are rare- and alkaline-earth metals respectively), and
the pseudogap phase in cuprate high-temperature (high-Tc ) superconductors (a wide
class of compounds based on one or more CuO2 planes). In the former system, ferro-
magnetic metallic regions and charge-ordered antiferromagnetic insulating regions
coexist in a glassy mixture. In the latter class of materials, incommensurate spin and
charge density waves coexist with one another, as well as with electronic nematic
and superconducting correlations [3, 4]. In both of these systems the delicate balance
between competing ground states can be tipped via small perturbations. For example,
in rare earth manganites with doping-induced disorder (e.g. Pr0.65 Ca0.35 MnO3 ), weak
applied magnetic fields serve to align and grow nanoscale ferromagnetic domains
resulting in an insulator-to-metal transition [1, 5, 6]. In contrast, applying magnetic
fields to the underdoped cuprate YBa2 Cu3 O6+x results in a strengthening of charge
order correlations, rendering them 3-dimensionally (3D) phase coherent, and the
concomitant suppression of superconductivity [7–10]. In a more recent example, the
application of uniaxial strain to underdoped YBa2 Cu3 O6+x was shown to induce a
comparable transition to a 3D charge ordered state [11].
Alternative to perturbation via external fields, internal structural degrees of free-
dom can couple strongly to the collective electronic states in transition-metal oxides,
thereby providing an additional mechanism by which to select between nearly degen-
erate ground states. In La1−x Bax CuO4 , the first discovered high-Tc cuprate supercon-
ductor, a low-temperature layer-alternating uniaxial distortion of the lattice couples
to the low-energy charge and spin degrees of freedom producing a layer-alternating
© The Editor(s) (if applicable) and The Author(s), under exclusive 1
license to Springer Nature Switzerland AG 2020
M. Bluschke, Controlling Collective Electronic States in Cuprates
and Nickelates, Springer Theses,
https://doi.org/10.1007/978-3-030-47902-2_1
2 1 Introduction

uniaxial spin and charge stripe order [12]. Furthermore, isovalent substitution of La3+
with Eu3+ , as in La1.8−x Eu0.2 Srx CuO4 , increases the strength of this low-temperature
tetragonal (LTT) distortion, while simultaneously suppressing superconductivity.
Inspired by examples of this variety, we have used isovalent chemical substi-
tution and epitaxial integration as tools to control the structural, electronic and
magnetic properties of multinary oxides based on nickel [13] and copper [3]. By
epitaxial integration we designate the successive deposition of chemically distinct
but approximately isostructural compounds. The cuprates and nickelates represent
model systems for the study of strongly correlated electron physics, and in addition
to improving our understanding of the control mechanisms, we have also achieved
new insights regarding the correlated states which we control.
In order to investigate the response of our model systems to structural perturbations
we have performed resonant x-ray scattering experiments [14], using photon energies
in the soft x-ray regime corresponding to the electronic 2 p → 3d transitions (called
L 3 and L 2 resonances) on the transition-metal ions and 3d → 4f transitions (called
M5 and M4 resonances) on the rare-earth ions. When tuned to one of these resonant
energies, the incident photons are preferentially absorbed and scattered by the core
electrons associated with the initial states of these transitions, compared to all other
electrons of the ion. Upon scattering, the soft x-rays briefly induce Rabi-oscillations
between the core and valence states thereby endowing the scattering process with
valuable sensitivity to the system’s low-energy degrees of freedom, i.e. spin, charge
and orbital. Together with the additional sensitivity to the lattice structure, inherent
to both resonant and non-resonant scattering processes, resonant x-ray scattering is
an ideal tool for the study of transition-metal oxides.
While resonant x-ray scattering is a powerful tool, it comes also with a strong
set of limitations. In the case of resonant scattering at the transition metal L edges,
the relevant photon energies are so low (∼853 eV for Ni and ∼931 eV for Cu) that
the maximum possible momentum transfer to the system (i.e. in the backscattering
geometry) is not even sufficient to allow complete access to the first Brillouin zone.
Accordingly, a diffraction experiment with the incident photon energy tuned to one
of these resonances can only access electronic and magnetic modulations with a
sufficiently large spatial period (or at a sufficiently small momentum transfer). In
the cases of the (Cax La1−x )(Ba1.75−x La0.25+x )Cu3 O y (CLBLCO) and YBa2 Cu3 O6+x
(YBCO) compounds, which have been studied in this work, Cu L 3 edge resonant
scattering is able to access diffraction peaks associated with the charge density wave
modulation along the Cu-O bond directions, but is, for example, not able to access
the incommensurate spin excitations in the vicinity of the antiferromagnetic wave
vector (π , π ). Similarly in the rare-earth nickelates, resonant scattering at the Ni
L 3 edge is able to access the period-four antiferromagnetic modulation along the
pseudocubic body diagonal ( 41 41 14 )pc of the R ENiO3 perovskite structure, but is
not able to reach the period-two bond order which occurs along the same direction
( 21 21 21 )pc . Accordingly, in Chaps. 4 and 5 of this thesis we report on resonant scattering
studies of charge-density wave correlations in CLBLCO and YBCO, and in Chap. 7
we report a study of the unusual spiral antiferromagnetism present in LaNiO3 based
superlattices.
1 Introduction 3

Fig. 1.1 a The cubic perovskite unit cell corresponding to the chemical formula ABO3 . The
rotational symmetries of the octahedral point group associated with the crystal field at the transition-
metal B-site are indicated. b Real space basis functions for the d-shell electronic states of the
transition-metal ions. The subgroups labeled eg and t2g are split in energy from one another by the
octahedral crystal field, and correspond to the irreducible representations of the Oh point group.
Red and blue colouring indicates the alternating phase of the electronic wave function. From Ref.
[15]

Before discussing the tools we have used to control the collective ordering phe-
nomena in these three systems, we will begin with a brief introduction to the systems
which we have chosen to study. LaNiO3 hosts a perovskite type structure, which is
closely related to the slightly more complex layered perovskite structures of most
cuprate superconductors. The various types of layered cuprate structures are dis-
cussed in Sect. 3.1.1. In the basic ABO3 perovskite structure, the B-site transition
metal ion is octahedrally coordinated by 6 nearest neighbour oxygen ligands. This is
shown in Fig. 1.1a. The octahedral point-group symmetry Oh of the resulting crystal
field splits the transition-metal d states into 2 manifolds labeled t2g and eg . The 5 real-
space d-orbital basis functions are depicted in Fig. 1.1b. The x 2 − y 2 and 3z 2 − r 2
orbitals of the eg manifold are oriented directly towards the nearest-neighbour oxy-
gen ions and are therefore more energetic (for electrons) than the t2g orbitals which
have nodes in these directions.
As for all high-Tc cuprates, the superconducting CuO2 planes in YBCO and
CLBLCO host Cu2+ ions with a 3d 9 electronic configuration in the undoped (antifer-
romagnetic) limit. In contrast, the perovskite-type rare-earth nickelates, e.g. LaNiO3 ,
host a 3d 7 electronic configuration. These electronic configurations have key sim-
ilarities when considering the local crystal field symmetry. In particular, the large
crystal field splitting of the transition-metal d states into three lower-lying t2g states
and two upper-lying eg states implies that the low energy degrees of freedom in both
systems are dominated by the eg manifold. In the undoped cuprates, there are three
electrons in the eg manifold, and the degeneracy of the eg states is broken by the quasi
2-dimensionality of the CuO2 planes (i.e. the Cu point group symmetry is lower than
octahedral). In this case, the energy of planar x 2 − y 2 states is pulled above that of
the out-of-plane 3z 2 − r 2 states, implying a double occupation (integer filling) of the
latter and a single occupation (half filling) of the x 2 − y 2 states. In the case of the
nickelates, the eg manifold is singly occupied and the x 2 − y 2 and 3z 2 − r 2 states are
4 1 Introduction

degenerate with one another. This implies an orbital degree of freedom not present in
the cuprates. Nevertheless, the strong similarities between the two systems motivated
the prediction that the rare-earth nickelate compounds could be made to supercon-
duct if the energy of the x 2 − y 2 states in this system were to be pulled sufficiently
below that of the 3z 2 − r 2 states, thereby producing a single occupation of the planar
x 2 − y 2 states analogous to the cuprates [16–18]. Systematic efforts in this direction
have been made over the past decade, some of which are described in Sect. 6.2.1. Only
very recently, however, were the predictions of superconductivity confirmed by the
observation of a low-temperature zero-resistance state in the infinite-layer nickelate
Nd0.8 Sr0.2 NiO2 [19]. Detailed information about this superconducting state and pos-
sible proximate electronic phases in this newly-realized family of superconductors
has yet to be uncovered.
The phase diagram of the cuprate superconductors has been investigated exten-
sively. At zero doping, the electrons in the CuO2 planes find themselves in what is
referred to as a Mott insulating state. In contrast to a conventional band insulator, in
which the insulating behaviour arises from an integer band filling, Mott insulators
have half-filled bands (as in the singly occupied x 2 − y 2 states of the CuO2 planes)
and become insulating as a result of the strong onsite Coulomb interaction energy
U , which prevents electrons from hopping. Consider a single band Hubbard model
of the form  † 
H = −t ciσ c jσ + U n i↑ n i↓ (1.1)
i, j,σ i

†
where ciσ c jσ annihilates an electron with spin σ on site j and creates one with the
same spin on site i (i.e. hopping), and n i↑ n i↓ counts the total number electrons on
site i. In this model, the hopping integral t is a measure of the energy gain associated
with hopping and is proportional to the bandwidth W . Such a single band system
is in the Mott insulating regime when the onsite Coulomb interaction exceeds the
energy gain due to hopping, i.e. U > W , leading to a so-called Mott Hubbard gap
of size U − W . In this limit, the eigenstates of the Hamiltonian are localized wave
functions and the effect of hopping can be treated via perturbation theory. To second
order, this results in the Heisenberg model H = 21 i j Ji j Si Sj which describes the
hopping-mediated “exchange” interaction between neighbouring spins Si and S j .
The exchange constant J = 4ti2j /U measures the energy associated with parallel
(ferromagnetic) or antiparallel (antiferromagnetic) alignment of neighbouring spins.
The actual case in the cuprates is more complicated than the single-band Hub-
bard model due to the presence of the oxygen px and p y states near the Fermi level
(the chemical potential at T = 0 K). This corresponds roughly to the charge trans-
fer scenario depicted in Fig. 1.2. However, by considering only the lowest energy
states the multiband problem simplifies to a one band model with a renormalized
gap corresponding to the energy  required to transfer a hole from Cu to the neigh-
bouring oxygen ions minus the bandwidth [22]. When mediated by hopping via
the oxygen ions, the exchange interaction between neighbouring Cu ions is referred
to as the superexchange interaction. In order to allow holes from both Cu ions to
hop simultaneously to the same oxygen ion, Hund’s rule dictates that the holes on
1 Introduction 5

Fig. 1.2 Schematic depiction of the low energy band structure in a Mott–Hubbard insulator a charge
transfer insulator and a “self-doped” charge transfer insulator. When the onsite Coulomb energy
U exceeds the bandwidth W of the transition metal (TM) d band, a correlated gap of size U − W
opens at the Fermi level (E F ) splitting the valence band into the so called upper and lower Hubbard
bands (UHB and LHB respectively). A charge transfer insulator [20] is a Mott insulator in which
the oxygen 2 p band is more energetic than the lower Hubbard band, such that the lowest energy
charge excitations involve the transfer of holes from the transition metal 3d states to the oxygen 2 p
states. Adapted from Ref. [21]

neighbouring Cu ions should have opposite spins. Hence the superexchange inter-
action is generally antiferromagnetic in oxide systems. Accordingly, the undoped
cuprate is a strongly-correlated antiferromagnetic insulator.
Upon doping holes into the CuO2 planes long-range antiferromagnetic order is
quickly destabilized, but the strong electronic correlations persist and give rise to a
variety of phases. These include incommensurate spin order, incommensurate charge
order and superconductivity. The temperature/hole doping phase diagram of a generic
cuprate material is presented in Fig. 1.3. Overlying the underdoped regime of the
phase diagram is the enigmatic pseudogap phase. Here, underdoped refers to dop-
ings p < popt where popt is the optimal doping for superconductivity, i.e. where
Tc = Tcmax . The pseudogap phase has experimental signatures in both the spin and
charge channels, but the exact nature of its relationship to the proximate spin ordered,
charge ordered and superconducting phases is not agreed upon. The various corre-
lated phases present in the underdoped regime of the cuprates are reviewed in detail
in Chap. 3.
Whereas in the cuprates a Mott–Hubbard gap renders the partially filled eg states
insulating in the undoped limit, the rare-earth nickelates host a paramagnetic metal-
lic phase even without the addition of dopant ions, and despite the presence of a
6 1 Introduction

Fig. 1.3 Cuprate high-Tc phase diagram. Holes are added to the CuO2 planes by introducing
additional oxygen ions (as in YBa2 Cu3 O6+x ) or by chemical substitution (as in La2−x Srx CuO4 ).
Doping the antiferromagnetic Mott insulator (parent compound) results in the emergence of a
variety of ordering tendencies including incommensurate spin order, charge order and d-wave
superconductivity. Reprinted with permission from Ref. [3], Copyright (2015) Macmillan Publishers
Ltd

correlated gap. This discrepancy can be understood by considering the energy sep-
aration between the oxygen 2 p band and the upper Hubbard band (see Fig. 1.2).
In the case of the nickelates, the energy separating these bands is small, or even
negative, resulting in a “self-doped” ground state with holes on the ligand oxygens.
However, the nickelates exist on the boundary between metal and insulator and, with
the exception of LaNiO3 , they demonstrate a metal-insulator transition (MIT) as a
function of temperature (see Fig. 1.4). This MIT is accompanied by a simultaneous
transition to a bond-ordered phase, characterized by a sequence of expanded and con-
tracted NiO6 octahedra along the body diagonal of the pseudocubic perovskite unit
cell. Recent calculations of the nickelate charge- and spin-response functions based
on the random-phase approximation in a two-band Hubbard model have demon-
strated how interorbital charge fluctuations are responsible for driving the transition
to this bond-ordered insulating state at low temperature [23]. Inside the bond ordered
state, a competition between ferromagnetic double exchange and antiferromagnetic
superexchange interactions stabilizes an unusual period-four spiral antiferromag-
netic structure, propagating along the same direction as the bond order. This spiral
antiferromagnetism is described in detail in Chap. 6.
1 Introduction 7

Fig. 1.4 Rare-earth nickelate RNiO3 phase diagram. The transitions to the bond-ordered insulating
and antiferromagnetic phases are plotted for the series of rare-earth ions R and parameterized by the
corresponding Ni-O-Ni bond angle and the tolerance factor. The space groups of the various phases
are indicated, along with the ordering vectors associated with the bond order and antiferromagnetism
√
(expressed in pseudocubic notation). The tolerance factor is defined as t = d R-O / 2dNi-O , where
d R-O and dNi-O are the Ni-O and R-O ionic bond distances, such that t = 1 for the ideal (cubic)
perovskite structure. Data from Ref. [24], Figure reprinted from Ref. [15]

In addition to varying the temperature, one can also move across the MIT phase
boundary by applying structural distortions to the nickelate lattice. As the A-site
cation is varied from large (La) to small (Lu), a progressively increasing buckling
of the NiO6 octahedra occurs in an attempt to accommodate the smaller ionic radius
on the A-site. This buckling decreases the Ni-O-Ni bond angle (i.e. increases the
deviation from a straight 180◦ bond), thereby reducing both bandwidth and the self
doping effect. These coupled structural and electronic variations lead to dramatic
changes in the temperature scale associated with the simultaneous bond-order and
metal-insulator transitions, thereby highlighting the power of isovalent chemical sub-
stitution as a tool to manipulate electronic degrees of freedom by incurring slight
structural distortions. Figure 1.4 depicts the metallic, insulating, and antiferromag-
netic phase boundaries as a function of the Ni-O-Ni bond angle for the rare-earth
nickelate series RNiO3 .
In Chap. 4 of this thesis we have applied the technique of isovalent chemical
substitution to control and study charge order correlations in bulk single crystals of
the cuprate material (Cax La1−x )(Ba1.75−x La0.25+x )Cu3 O y , which hosts a ‘123’ type
structure similar to that of the well studied YBa2 Cu3 O6+x . The combined effort of
many research groups in the past decades has demonstrated that charge order correla-
tions are ubiquitous to the underdoped phase diagram of the cuprate superconductors
[7, 8, 12, 25–35]. Furthermore, competition between superconductivity and charge
order has been demonstrated, and it has been suggested that charge order correla-
tions may have a fundamental role in defining the features of the pseudogap phase. In
CLBLCO, the isovalent chemical substitution of Ba with Ca produces small changes
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dropped it into the fire, which her father had poked up to some
purpose—little dreaming for what an occasion it would serve.
Then Madeline went at last, and scrambled into her tea-gown with
haste, and was just down, luckily for herself, in the nick of time.
After dinner, she was quite feverishly gay. She meant to
thoroughly enjoy herself, without any arrières pensées. Her sword of
Damocles had been removed. She went to the piano, and sang song
after song with a feeling that she must do something to keep up her
somewhat limp self-esteem and her rapidly falling spirits.
 CHAPTER XXXI.
A FALSE ALARM.

Mr. West had enjoyed his dinner; his appetite was excellent—on a
par with his daughter’s spirits. He asked no more troublesome
questions, and departed to bed at an early hour. Mrs. Leach, too,
had retired (pleading fatigue), to enjoy a French novel and cocaine,
leaving Madeline to sing and make merry alone! After a while she
went over and sat on the fender-stool, and had a long conversation
with herself, and tried to persuade her conscience that she had done
right. She offered it a sop in assuring herself that the next morning
she would go down to the Holt farm and see Harry, and have a
comfortable talk with his nurse. Her father would not be out of bed till
twelve o’clock. Mrs. Leach, too, rarely appeared before lunch. The
coast would be clear. She carried out this resolution to the letter,
starting from Waterloo by an early train, arriving a little after ten at
the farm in the station fly, greatly to Mrs. Holt’s amazement.
She asked many questions, and was warmly assured that “though
little Harry was not to say a big, strong boy, like Tom the
ploughman’s child, of the same age, yet that nothing ailed him but
his teeth, and that his eye teeth were through, and that she (his
mother) need not give herself no uneasiness. Mr. Wynne was full of
fancies. He was down twice last week, and had been alarming her
for nothing.”
“Mr. Wynne—Mr. Wynne,” said Madeline, becoming agitated and
feeling a certain tightness in her throat; but knowing that the fact she
was about to disclose must come out sooner or later, and that the
first blow was half the battle; “Mr. Wynne and I have had a serious
disagreement. We have agreed to differ—and to part,” looking
steadily out of the window, whilst her face took a delicate shade of
red.
 “Laws! gracious mercy!” ejaculated her listener, nearly dropping
Master Wynne. “You don’t say so! Goodness gracious! you don’t
mean it, ma’am; you are joking.”
“No, indeed”—very decidedly—“I am not, Mrs. Holt; and you need
not call me ma’am any more, for though I am married, I am going
back to be Miss West—always. Please never call me Mrs. Wynne
again.”
“But you can’t do that,” exclaimed Mrs. Holt, in a loud tone of
expostulation; “you are married right and tight as I am, unless,”
lowering her voice, “it’s a divorce you are after getting?”
“Divorce? No. Nothing of the kind; but Mr. Wynne and I have
agreed to be—be strangers, and to forget that we have ever been
married; and as I am only known to most people as Miss West, it will
be quite easy.”
“It’s nothing of the sort, ma’am,” cried the other, energetically, “and
you are mad to think of it. Why, I might just as well go and call myself
Kate Fisher once more, and give out I was never wed to Holt! That
would be a fine how-do-you-do! And where there’s children it’s worse
and more wicked, and more ridiculous to think of still. What’s to be
said and done about this boy? Who is his mother? You can’t say
Miss West, now can you? Believe me,” seeing her visitor’s face of
crimson astonishment, “it won’t do. It’s just one of those common
squabbles among married folks that blow over. Why, Holt and I has
’ad many a tiff, and we are none the worse. You and Mr. Wynne just
make it up. You are both young, and maybe he is determined, and
likes to have his own way, as most men do; but—excuse me, ma’am,
as an humble friend and a much older woman than yourself, if I
make too bold—you are a bit trying. You see it’s not usual for a
young fellow to have his wife leave him, and go galavanting about as
a single lady; and then Mr. Wynne is greatly set upon the child. A
man, of course, expects that his wife will look after his children
herself. Excuse me again if I make too free, but I don’t like to see a
young girl going astray, whoever she be, without just giving her a
word,” wiping her face with a red-spotted handkerchief. (The family
was largely supplied with this favourite pattern.)
 Madeline sat in silence, feeling very uncomfortable and wretched;
but all the same, obstinately bent on her own way.
“Mrs. Holt, you forget there are two sides to a question,” she said
at last. “I know you mean very kindly; but I have to consider my
father. He has no one but me. He is an invalid, and I am his only
child, and must study his wishes.”
“Maybe if he wasn’t so rich, you wouldn’t think of him so much,”
put in Mrs. Holt, bluntly.
“Yes, I would,” retorted Madeline, stung by the sneer; “but I see
you are prejudiced, Mrs. Holt. You forget what the Bible says about
honouring your father and mother.”
“No, no, I don’t; but the Bible says a deal about husbands and
wives too. I don’t forget that. Stick to your husband; it’s the law o’ the
land and the law o’ the Bible,” said Mrs. Holt in her most unyielding
voice.
She said a great deal more, but she failed to persuade her visitor
or to bend her pride, and she soon perceived that it was of no avail.
Money and grandeur, she told herself, had turned her poor head.
Some day she would be sorry for what she was doing now; and,
anyway, it was an ill and thankless task for a third person to meddle
between a married couple. She had always known that he was the
better of the two; and maybe Holt would allow she was right now!
Here was a young lady, turning her back on husband and child,
taking her maiden name again, and going off to foreign countries.
Pretty doings! pretty doings!
At eleven o’clock the fly-man notified that time was up, and the
lady must go if she wanted to catch her train. She kissed little Harry
over and over again, and wept one or two tears as she said—
“How I wish I could take him with me, even if I could smuggle him
as my maid’s little boy!”
“Sakes and stars! Mrs. Wynne,” exclaimed Mrs. Holt, angrily.
“Whatever are you thinking of? I wish his father heard you pass him
off as a servant’s child. Well, upon my word! I never——” At this
crisis words ran short and utterance completely failed her.
 “Mind you write to me often, Mrs. Holt—even one line. I have left
you a packet of addressed and stamped envelopes. Please write at
least once a week,” and, with a hurried good-bye she stepped into
the fly, pulled down her veil, and was driven off, leaving Mrs. Holt
and her son upon the steps, the former exclaiming—
“Well, if she don’t beat all!” whilst Master Wynne dragged violently
at her apron, and, pointing to the rapidly disappearing carriage,
shouted gleefully—
“Gee-gee! Gee-gee!”

“It is all right, my dear,” whispered Mrs. Leach, receiving her with a
significant nod. “I told your father you had gone to lunch with the
Countess of Cabinteely, and he was perfectly satisfied.”
In another week Madeline was very pleasantly settled in a
charming villa at Nice looking out over the blue tideless sea and the
Promenade des Anglais. She had a landau and pair, a pony
carriage, and an “at home” day, for not a few of their London
acquaintances, early as it was, had come south.
Her father rapidly regained his usual health and amiability, and
lavished presents upon her. The horizon before her was literally and
metaphorically bright. She was surrounded by quite a brilliant
pageantry of flatterers and followers, and could not help feeling a
pardonable pride in the sensation she created and in her remarkable
social triumphs—in finding bouquets left daily at her door, in seeing
her name in enthusiastic little paragraphs in the local papers, in
hearing that the fact of her expected presence brought numbers to
an assembly or entertainment in order to see the lovely Miss West,
to know that she had not an ambition in the world unfulfilled.
Was not this all-sufficient to prove that her millennium of
happiness had commenced? She was the beauty of the season,
though she was in this particular the victim of an unsought
reputation; she had never aspired to the honour, and the character
had been forced upon her. All the same, she did not dislike the
position of social queen; and as to Mr. West, he gloried in the fact,
and basked in the light of her reflected splendour. He was even
content to be known as “Miss West’s father.” As some men pride
themselves on their family, their estates, race-horses, pictures,
collection of old china, or silver, he prided himself upon his daughter,
and was convinced that he got more enjoyment out of his hobby than
most people. She was always en evidence, and he could see the
curious, envious, and admiring eyes, as he drove with her about
Nice, walked with her on the British Quarterdeck at Monte Carlo, or
escorted her to concerts, receptions, balls, or garden parties.
Foreign dukes and princes were supremely affable to him—all on
account of the beaux yeux of his charming and celebrated Madeline.
Worth and Doucet had carte blanche, for Madeline’s costumes
must be worthy of her, and Madeline was not averse to the idea. A
new hat, which became the rage, was named after her. Such is
fame! A new yacht had been honoured by the same distinction.
Youth, beauty, wealth, celebrity—even Fortune seemed to go out of
her way to crowd favours upon this lucky young lady; but, alas! we
all know that fortune is a fickle jade, who smiles at one moment, and
who scowls the next. Thus, as a kind of social divinity in a gay,
earthly Paradise, winter glided on with Madeline. Spring had
appeared with a radiant face and a train of flowers; the turf under the
olives was covered with anemones, the valleys were starred with
primroses; jonquils, tea-roses, and narcissus filled the air with
fragrance. Sea and sky reflected one another—sunbeams glanced
from the waves, the water seemed to laugh, and the whole face of
Nature was one good-natured smile.
The Riviera was full, the carnival about to commence. Madeline
was in a state of feverish gaiety and exhilaration. She could not now
exist without excitement; she must always be doing something or
going somewhere, and required a rapid succession of amusements,
from a “promenade aux ânes” up the valleys, to riding a bicycle; from
a tea picnic to playing trente et quarante. All her regrets, and all her
little twinges of remorse (and she had experienced some) had
succumbed to the anodyne of a season on the Riviera—and such a
season! But on the very first day of the carnival her spirits received a
rude shock in the form of an ill-spelt scrawl from Mrs. Holt, which ran
as follows:—
“Honoured Madam,
“I think it rite to let you no, as little Harry has been verry poorly the
last two days; in case he is not better I think you ought to know, and
mite wish to come home. It’s his back teath. The Docter looked very
cerrius last evening, and spoke of konvulshions, but I don’t wish to
frighten you.
“I am your humble servant,
“Kate Holt.”
This was a heavy blow. The rush of maternal impulse swept
everything else out of her mind. Madeline thrust aside her diamonds,
ball dress, masks, bouquets, and hurried off on foot to the telegraph
office, and despatched a message—“If he is not better I start to-
night; reply paid.” And then she returned to the Villa Coralie,
quivering and trembling with impatience.
In case of the worst, she told Josephine to pack a few things, as
she might be going to England that night by the Rapide.
Josephine’s jaw dropped; she was enjoying herself enormously.
One of the waiters at the Cercle was her cousin. The carnival was
just commencing; this was terrible—must she he torn away too! Her
face expressed her feelings most accurately, and her mistress
hastened to reassure her.
“I shall not require you, Josephine; I only go to see a sick friend. If
I hear no good news, I start this evening; if the tidings are better, I
remain—but I am almost sure to go.”
“Et monsieur?” elevating hands and eyebrows.
Yes, how was she to announce her departure to her father? She
made the plunge at once. Her fears and her anxieties were not on
his account now. She was desperate, and ready to brave anything or
anybody.
 She ran down into his cool sanctum, with its wide-open windows
overlooking the bay, its gaudy, striped awnings, and verandah full of
flowers, and finding her parent smoking a cigarette and absorbed in
the Financial News, began at once.
“Papa, I’ve had bad news from England. A—one who is very dear
to me is ill, and if I don’t hear better news by telegram, I wish to start
to-night for London.”
“Madeline!” he cried, laying down the paper and gazing at her in
angry astonishment. “What are you thinking about? Your sick friend
has her own relatives; they would never expect you to go flying to
her bedside from the other end of France. Nonsense, nonsense!” he
concluded imperatively, once more taking up the news, and
arranging his pince-nez with grave deliberation.
The matter was decided. But Madeline was resolved to make an
equal show of determination, and said, in a stubborn tone—
“Papa, in this I must have my way. It is not often I take my own
course; I do everything and go everywhere to please you. You must
allow me to please myself for once.”
Mr. West pushed back his chair a full yard, and gazed at his
daughter.
“Do not throw any obstacle in my way, papa, nor seek to know
where I am going.”
“Ah, ah! Not a lover, I hope, madam?” he gasped. “The curate, the
—the drawing-master?”
“No; let that suffice, and let us understand one another, once for
all. I have been an obedient daughter to you; I have made sacrifices
that you have never dreamt of”—(Ah! the poor curate! thought Mr.
West)—“and you must give me more liberty. I am of age to go and
come as I please unquestioned. I will do nothing wrong; you may
trust me. I can take excellent care of myself, and I must have more
freedom.”
“Must, must, must! How many more ‘musts’? Well, at any rate, you
are a girl to be trusted, and there is something in what you say. I
dare say you have sacrificed some girlish fancy; you have nursed
me; you are a credit to me. Yes, and you shall come and go as you
please, on the trust-me-all-in-all principle, and the understanding that
you do not compromise yourself in any way; but you have your
advantages, Madeline—a fine home and position, and everything
money can buy. Remember, you will miss the best ball if you start to-
night, and the Princess Raggawuffinsky was to call for you. Have
you thought of that?”
“Oh!” with a frantic wave of her hand, “what is a ball?”
“Well, well, well! How much cash do you require, and when will
you be back?”
“I have plenty of money. If all goes well, I shall be back in a few
days—as soon as possible—for the regatta, perhaps.”
And so, with a few more remarks and assurances, and
expostulations on Mr. West’s part at her travelling alone, she
pocketed a cheque pressed upon her, and left the room victorious.
Her father was easier to deal with than she had anticipated.
Laurence was right—for once!
Then she ran upstairs to her own sanctum and locked the door,
pulled off her dress, put on her cool dressing-wrapper, and sat down
in a fever of mind and body to wait for the telegram. She remained
motionless, with her eyes fastened on the clock, a prey to the wildest
fears. Supposing the child was dead!—she shuddered involuntarily;
if it were, she would go out of her senses. Her anxiety increased with
every hour. She was in a frenzy of impatience, now pacing the room,
now sitting, now standing, now kneeling in prayer.
At last there was a knock at the door—Josephine’s knock.
Josephine’s voice, “Une dépêche pour vous, mademoiselle.”
Mademoiselle’s hand shook so much that she could hardly open
the door, hardly tear asunder the envelope, or read its contents—at a
gulp. Josephine had never seen her mistress in this frenzied,
distraught condition—her colour like death, her face haggard, her
eyes staring, her hair hanging in loose abandon. What did it mean?
The telegram brought good news. It said, “He is much better, and in
no danger. You need not come.”
The sender’s name was not notified. Whoever it was, it mattered
little; the relief was inexpressible. What a fright Mrs. Holt had given
her, and all for nothing!
Miss West went to the ball that night, and danced until the dawn
flickered along the horizon. She was one of the most brilliant figures
at the carnival, and received marked notice in distinguished quarters.
At the battle of flowers, she and her equipage were the cynosure of
all eyes. The open victoria was made to counterfeit a crown, and
covered with pink and white azaleas. Miss West was attired to
correspond. Four beautiful white horses were harnessed in pink, and
ridden by postilions in pink satin jackets; and the general effect was
such that the committee promptly awarded the first banner to “la
belle Anglaise,” despite the close rivalry of a celebrated demi-
mondaine, who furiously flung the second banner in the faces of the
judges, and, with her yellow flowers and four black ponies, had
whirled off in high dudgeon and a cloud of dust.
At last this enchanting period was brought to an end by the
Riviera’s own best patron—the sun. People melted away as if by
magic. Some went on to the Italian lakes, some to Switzerland, many
to England. Madeline and her father deferred their return until the
end of May, stopping in Paris en route; and when they reached home
the season was at its height, and the hall and library tables were
white from a heavy fall of visiting-cards and notes of invitation.
Lady Rachel and Lord Tony came in on the evening of their arrival
to pay a little neighbourly call, and to tell them that they must on no
account miss a great match—the final in a polo tournament at
Hurlingham—the next afternoon. Every one would be there.
This speech acted as a trumpet-call to Mr. West.
“Every one will see that we have returned,” he said to himself, and
it will save a lot of trouble. Then, aloud, “All right, then, Lady Rachel,
we shall certainly go. Madeline must trot out some one of her smart
Paris frocks. And, Madeline, you might send a wire over to Mrs.
Leach, and offer her a seat down.”
 CHAPTER XXXII.
MR. JESSOP’S SUGGESTION.

Laurence Wynne had taken but one person into his confidence,
and that was Mr. Jessop. As he sat smoking a post-midnight cigar
over the fire in his friend’s chambers, he told him that Mrs. Wynne no
longer existed. She preferred to stick to her name of West, and
wished to keep her marriage a secret always from—not alone her
father, but the whole world.
This much he had divulged. He felt that he must speak to some
one. His heart was so sore that he could not maintain total silence,
and who so fitting a confidant as his old friend Dick Jessop? He was
chivalrous to Madeline in spite of all that had come and gone, and
veiled her defects as skilfully as he could, not speaking out of the full
bitterness of his soul. But Mr. Jessop’s active imagination filled in all
the delicately traced outline—perhaps in rather too black a shading,
if the truth were known!
However, he kept his surmises discreetly to himself, and puffed
and pondered for a long time in silence. At last he spoke.
“I would let her alone, and not bother my head about her,
Laurence! She is bound to come back.”
“I don’t think so,” responded the other, curtly.
“Yes; she will return on account of the child.”
“And what would such a coming-back be worth to me? It will not
be for my sake,” said Wynne, holding his feelings under strong
restraint.
“I know of something that would bring her, like a shot out of a
seventy-four pounder,” observed Mr. Jessop after another pause,
surveying the coals meditatively as he spoke.
 “What?”
“Your paying attention to another woman. Get up a strong and
remarkable flirtation with some pretty, smart society matron. Lots of
them love your stories. Love me, love my stories. Love my stories,
love me, eh? Show yourself in the park, at theatres—better still, a
little dinner at the Savoy—and Mrs. Wynne will be on in the scene
before you can say Jack Robinson! Jealousy will fetch her!”
“I wouldn’t give a straw for the affection of a woman who was
influenced solely by what you have suggested. No, no; I married her
before she knew her own mind—before she had a chance of seeing
other people, and the world. Now she has seen other people, and
become acquainted with the world, she prefers both to me. On five
or six hundred a year, with no rich relations, Madeline and I would
have been happy enough. As it is, she is happy enough. I must get
on alone as well as I can. I made a mistake. I was too hasty.”
“Yes, marry in haste, and repent at leisure!” said Mr. Jessop,
grimly.
“I don’t mean that; I mean that I mulled that business at Mrs.
Harper’s. I should have wired to Mrs. Wolferton, or insisted on Mrs.
Harper taking Madeline back, and given her time to turn round and to
reflect; but I rushed the whole thing. However, I must now abide by
the position I am placed in with what fortitude I can.”
“You married her, and gave her a home, when she had no friend,”
put in Mr. Jessop, sharply. Mr. Jessop was devoted to Laurence, and
excessively angry with Laurence’s wife.
“It is not every one I would confide in, Dick,” said his companion;
“but you are my oldest chum. You are welcome to be introduced to
the skeleton in my cupboard—an old friend’s privilege. We need
never talk of this again. I suppose people get over these things in
time! There is nothing for it but work—plenty of work.”
Although he discoursed in this cool, self-restrained manner, Mr.
Jessop knew, by years of experience, that his friend—who never
made much, or, indeed, any, fuss about his feelings—had felt the
blow in every nerve of his body.
 “Do not think too hardly of her, Dicky,” he exclaimed, promptly
reading the other’s thoughts. “She is very young, and very pretty. I’m
only a poor, hard-working barrister; and she had an awful time once
—you know when! We must never forget how she came through that
ordeal. And, after all, I have no human rival. If she does not care for
me, she cares for no other man. She is blessed with a particularly
cool, unsusceptible temperament. My only rival is riches. It is the
money that has ousted me. The enormous strength of wealth has
pushed me out of her heart, and barred the door. Time, another
powerful engine, may thrust her out of mine!”
“Time! Bosh. Time will never thrust away the fact that she is the
mother of your child. He is a tie between you that neither time,
riches, nor any amount of balderdash you may talk—nor any number
of matrimonial squabbles—can ever break.”
“You are mistaken in your idea of the whole case, Jessop, and
under a totally wrong impression. Nothing can bridge the gulf
between Madeline and me, unless she chooses to come back of her
own accord, and unsay a good deal that she has said; and this she
will never do—never. She does not care a straw for me. I merely
remind her of days of squallor, sickness, and hideous poverty. She
was delighted to accept the freedom which I offered her——”
“And what a fool you were to do it!” exclaimed his listener,
contemptuously.
“Not at all; but I should be a fool were I to try to keep a wife, who is
not even one in name, and never casts a thought to me from month’s
end to month’s end. I shall be—nay, I am—free too.”
“But not in a legal sense, my dear boy; you cannot marry again.”
“No, thank you,” emphatically knocking the ashes off his cigar with
great deliberation as he spoke. “The burnt child dreads the fire. I
made a bad start this time, and even if I had the chance—which,
please God, I never shall have—I would not tempt Fate again, no
matter what the provocation. Women are a great mystery: their chief
faults and virtues are so unexpected. Look at Madeline: when we
were paupers she was a ministering angel. Now that she is rich, she
is merely, a smart society girl, and——”
“And milliners, jewellers, flatterers minister to her,” broke in
Jessop.
“I intend to make my profession my mistress, and to devote myself
to her heart and soul. The law is a steady old lady.”
“And a very cantankerous, hard, flinty-faced, capricious old hag
you’ll find the goddess of Justice, my dear fellow. I am going to give
up paying my addresses to her! My uncle has left me a tidy legacy. I
intend to settle down in comfort in his old manor-house—shoot, fish,
hunt, burn my wig, gown, and law books, and turn my back for ever
on the Inns of Court.”
“Jessop, you are not in earnest.”
“I am,” impressively; “and what’s one man’s loss is another man’s
gain. It will be all the better for you, Laurence, since you are so bent
upon the woolsack. I’ll give you a heave-up with pleasure. You will
now get all Bagge and Keepe’s business, for one thing—and, let me
tell you, that that is no trifle.”
 CHAPTER XXXIII.
“ONE OF YOUR GREATEST ADMIRERS.”

It was a perfect afternoon, and Hurlingham was crowded. Every

seat bordering the polo ground was occupied, and the brilliant hues
of hats, gowns, and parasols made a sort of ribbon border to the
brilliant green turf. Mr. West—a fussy or punctual man, according to
people’s point of view—had arrived early with his party, and, so to
speak, planted his fair charges under one of the umbrella awnings,
and in a most central and commanding situation, where Madeline, in
a white costume, which set off her vivid dark beauty, was seen and
greeted by many acquaintances. Lord Montycute, Captain Vansittart,
and a smart lady friend (Mrs. Veryphast) shared the shade of the
canvas umbrella, and spasmodically proffered morsels of the latest
and choicest news, for the polo was absorbing, the match very fast
and closely contested, the excitement intense. During an interval
Lady Rachel drifted near—clad in a rainbow costume, and talking
volubly and emphatically to a man. Her quick, roving eye caught
sight of Madeline’s comfortable little party, and she swept down upon
her at once.
“Oh, Maddie, my dear girl, how nice and cool you look, and I’m
half dead, standing baking in the sun, and not a chair to be had for
love or money! Ah, you have two to spare, I see! Here—here is
actually one for you.” She called to her escort, who had stopped to
speak to a passing friend. “Madeline,” she continued, “I think you
know Mr. Wynne, who writes. Mr. Wynne, Miss West is one of your
greatest admirers! She knows all your stories by heart.”
This was a fiction, invented on the spur of the moment. Her
ladyship coined many a little lie.
Madeline looked up bewildered. The gentleman who was taking off
his hat to her was—Laurence!—and yet not Laurence. What had he
done to himself? He had discarded his beard, and was fashionably
clean-shaven; moreover he was fashionably dressed in the orthodox
long frock-coat, and wore a flower in his buttonhole, and the most
absolutely correct gloves and tie.
So much depends upon the style, shape, and colour of a man’s tie
—and the very maker’s name! A rashly selected tie may stamp a
man’s taste quite as fatally as the wrong number and pattern of
buttons proclaim the date of his coat!
The removal of his beard had entirely changed Laurence Wynne’s
appearance. He looked much younger: he had a very square chin,
his mouth was expressive—more sarcastic than smiling—with thin,
firmly closed, but well-cut lips. Had she known of that mouth and
chin, had she guessed at them—well, she would have thought twice
before she married their proprietor. As she looked up she coloured to
her hair when she met his steady, cool glance. This meeting was no
surprise to him, for he had noted the entrée of the beauty, her
marvellous costume, and her train of admirers. He had not, however,
intended to come to such close quarters. He was taken unawares
when he found himself in her neighbourhood, and he was
determined to escape immediately, in spite of Lady Rachel. The
silence that followed Lady Rachel’s loud prattle was becoming
noticeable, and curious eyes were turned upon him when he said
very distinctly—
“I don’t know if I am so fortunate as to be remembered by—Miss
West?”
“Oh yes,” she answered, rather obviously avoiding looking at him,
with a bright patch of colour on either cheek.
“Miss West has such an enormous acquaintance of young men
that she must get a little confused sometimes—a little mixed, don’t
you, Maddie? Now, Mr. Wynne, I see what you are up to,” said Lady
Rachel; “but no, you shall not run away. Here, sit upon this chair. I
had great difficulty in capturing you, you are so run-after and spoilt,
and now I am not going to let you desert. You ought to be thankful
for a seat in the shade, and amongst such pleasant company!” As he
reluctantly seated himself at the very outskirts of the group, she
continued—“Now, you must not sit there looking like a snared
animal, watching for some chance of escape. Do tell me all about the
heroine of your last story. How is it that you are so familiar with all
our little ways, and weaknesses? You know too much. One would
almost suppose that you were a married man!”
“I think it must be time to go to tea,” said Madeline, glancing
appealingly at her father, who had just joined them.
“Tea! Don’t you wish you may get it! There is not a single vacant
table on the lawn. I’ve just been to look. Hullo! Ah—er—Wynne, how
do you do?”
Mr. Wynne had been pointed out to him as a rising junior at the bar
—a coming man in literature, who wielded an able pen, and was
quite one of the season’s minor celebrities. His sketches were a
feature of the day—a short one, naturally. Every one was talking of
him.
Mr. West loved a celebrity—if he was gentlemanly and in good
society, bien entendu—nearly as much as he loved a lord, but not
quite; and he added—
“I remember you were at our house last winter, and you are
interested in paintings and art. You must look us up, eh?—and come
and dine.”
“Thank you. You are very kind.”
“We’ve just come back from the Riviera. Delightful place! Were
you ever there?”
“No, I’ve never been nearer to it than Lyons.”
“But I’ve been there,” broke in Lady Rachel; “and I shall never go
again, on account of the earthquakes, although it was capital fun at
the time.”
“Fun!” repeated Mr. West, with a look of amazement.
“Yes, half the refugees were running about in blankets fastened
with hairpins, afraid to return for their clothes. Oh, they were too
absurd! A whole train full went to Paris in their dressing-gowns—
some in bare feet. Every one was different—‘out of themselves,’ as
they say in France. One old lady, in her mad excitement in speeding
some relations, actually tore off her wig and waved it after them.”
“Poor old dear! How she must have regretted it subsequently!”
said Lord Montycute. “My sister was there at the same time, and
paid twenty pounds a night for the luxury of sleeping in the hotel
omnibus. Nothing would induce her to go to bed indoors. The hotel
was cracked from top to bottom!”
“I don’t care for the Riviera,” remarked Lady Rachel. “It’s too hot,
and the scenery is ridiculously gaudy. It always reminded me of a
drop-scene. I declare to you, sitting on a promenade, facing the blue
sea and blue sky, and pale, buff promontories and palms, with a
band playing in the neighbourhood, I have felt as if I was in the stalls
of a theatre.”
“Oh, shame!” cried Mrs. Leach. “You have no feeling for the
beauties of Nature.”
“I thought Monte Carlo lovely—the garden too exquisite for words.”
“And the tables?” inquired Mr. West significantly.
“Yes, I had my own pet table; and at first I was successful. I always
went on the ‘doz-ens,’ or ‘passe.’ One day I made ninety pounds in
an hour; but, alas! I lost it all in about ten minutes.”
“The tables always do win in the long run,” said Mr. West,
sententiously.
“Yes,” agreed Lord Montycute, “they have no feeling, no emotions.
When they gain they are not excited; when they lose they are not
depressed; and this is their advantage.”
“Oh, but they cannot leave off if they are losing,” cried Lady
Rachel. “We score there.”
“You did not score, at any rate,” remarked Mrs. Leach, with a
smile.
“No; I wish I had left off. There is Mrs. Raymond Tufto. Did you see
her at Nice, Madeline?”
 “Oh yes; she went everywhere.”
“She is wearing that same flower toque. I am so sick of it,” cried
Mrs. Veryphast, impatiently.
“Nevertheless she is one of the prettiest women in London,”
observed Captain Vansittart. “She has such a saintly expression, and
she looks so good.”
“She is a horribly heartless wretch. She goes off for months on the
Continent, and leaves her children to nurses at home,” said Lady
Rachel, viciously. “She has one dear little tot of two, that actually
does not know her by sight.”
“It is quite the French fashion to board out babies,” remarked Mrs.
Leach, who was invariably in opposition to Lady Rachel.
“Turn them out to walk like young hounds,” drawled Captain
Vansittart.
“Mrs. Tufto, bad as she may be, is nothing to Lady Blazer,”
continued Mrs. Leach, impressively. “She has a nursery full of girls,
and yet, what do you think? When she was asked the other day to
subscribe to the Society for the Prevention of Cruelty to Animals, she
said, ‘Delighted! There is only one species of animal I loathe, and
that’s a child.’”
“Oh, I say—come! I don’t believe that,” cried Mr. West, “of any
woman—or even a man. I’m rather partial to nice small children
myself.”
“Mr. Wynne,” said Lady Rachel, turning on him suddenly, “why are
you so silent? You know it is your métier to talk.”
“Then why do you grudge me a well-earned holiday?” he asked
imperturbably.
“I believe you are studying us for your next sketch; taking us in
your literary kodak.”
“No, indeed! I am not a reporter for a society paper.”
“Oh, I don’t mean about our dresses and hats, or that; I mean
character sketches.”