Table Of ContentSpringer Tracts in Modern Physics 269
Youichi Murakami
Sumio Ishihara Editors
Resonant X-Ray
Scattering in
Correlated
Systems
Springer Tracts in Modern Physics
Volume 269
Series editors
Yan Chen, Department of Physics, Fudan University, Shanghai, China
Atsushi Fujimori, Department of Physics, University of Tokyo, Tokyo, Japan
William C. Stwalley, Storrs, CT, USA
Ulrike Woggon, Institut für Optik und Atomare Physik, Technische Universität
Berlin, Berlin, Germany
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Youichi Murakami Sumio Ishihara
(cid:129)
Editors
Resonant X-Ray Scattering
in Correlated Systems
123
Editors
YouichiMurakami Sumio Ishihara
Institute of Materials Structure Science, Department ofPhysics
CondensedMatter Research Center Tohoku University
HighEnergy Accelerator Research Sendai, Miyagi
Organization Japan
Tsukuba,Ibaraki
Japan
ISSN 0081-3869 ISSN 1615-0430 (electronic)
SpringerTracts inModern Physics
ISBN978-3-662-53225-6 ISBN978-3-662-53227-0 (eBook)
DOI 10.1007/978-3-662-53227-0
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Preface
Electronic and magnetic properties in condensed matters are dominated by the
electronicstructureaswellasthecrystalstructure.SynchrotronX-raydiffractionis
one of the most important methods to determine the crystal structure including the
electron density distribution, while spectroscopic experiments using the syn-
chrotronradiationhavebecomeindispensabletostudytheelectronicstructure.The
resonant X-ray scattering (RXS), which has the combined characters of diffraction
andspectroscopy,isapowerfultooltoinvestigatethephysicalpropertiesofsolids
andthinfilms.TheRXScanprovidevaluableinformationonthevalenceelectrons,
especially a variety of ordered states for the electron degrees of freedom. In the
d-electronsystems,wecalltheelectronicorderedstatesascharge,spin,andorbital
orders, while in the f-electron systems, they are referred to as multipole orders.
The RXS can give us the element- and site-specific information when the beam
energy is tuned to the corresponding absorption energy. We can also elucidate the
details of the ordered states using the polarization property of synchrotron X-rays.
When we change sample environments such as temperature, pressure, magnetic
field or electric field, we sometimes observe a phase transition accompanied by a
drastic change of electronic states, which are directly detected by the RXS. Some
examplesofthesein-situobservationsareshowninthisbook.Wealsohavelearned
overthelasttwodecadesthattheresonantinelasticX-rayscattering(RIXS)canbe
effective to detect electronic excitations such as charge, spin and orbital waves in
strongly correlated electron systems. In this way, the RXS and RIXS have played
increasingly significant roles in many scientific fields as well as condensed matter
physics.
This book is written with the intention of presenting systematic descriptions
of the RXS and RIXS techniques and the applications. In Chapter 1, the RXS and
RIXS are reviewed from theoretical point of view. The Chapters 2 and 3 contain
RXS studies of 3d and 4f electron systems, respectively. Magnetism study using
RXS is described in Chapter 4. The RXS using soft X-ray is introduced in
Chapter 5. Chapter 6 is dedicated to the description of the RIXS technique for the
study of electronic excitations. This book has been written by six authors who are
expertsatRXSandRIXSstudiesincondensedmatterphysics.Thereaderswillfind
v
vi Preface
the original points of view of these authors about physics in strongly correlated
electron systems. We hope this book will be a useful textbook for researchers and
students to study a variety of science using RXS and RIXS.
ItisapleasuretothankProf.AtsushiFujimoriforhisinvaluablehelpinediting
this book. The cooperation with Dr. Ute Heuser and Dr. Thorsten Schneider of
Springer has been extremely helpful.
Tsukuba, Japan Youichi Murakami
Sendai, Japan Sumio Ishihara
Contents
Resonant X-ray Scattering and Orbital Degree of Freedom
in Correlated Electron Systems .... .... .... .... .... .... ..... .... 1
Sumio Ishihara
Resonant X-ray Scattering in 3d Electron Systems. .... .... ..... .... 47
Hironori Nakao
Observation of Multipole Orderings in f-Electron Systems
by Resonant X-ray Diffraction..... .... .... .... .... .... ..... .... 85
T. Matsumura
Hard X-ray Resonant Scattering for Studying Magnetism .. ..... .... 119
Taka-hisa Arima
Resonant Soft X-Ray Scattering Studies
of Transition-Metal Oxides... ..... .... .... .... .... .... ..... .... 159
Hiroki Wadati
Resonant Inelastic X-Ray Scattering in Strongly Correlated
Copper Oxides. .... .... .... ..... .... .... .... .... .... ..... .... 197
Kenji Ishii
vii
Resonant X-ray Scattering and Orbital
Degree of Freedom in Correlated
Electron Systems
SumioIshihara
1 Introduction
The concept of the electronic orbital emerges in a wide variety of phenomena in
condensedmatterphysics.The2l+1-folddegeneracyoftheelectronicorbitalsin
anisolatedatomisliftedincrystallinesolids,inwhichthesphericalsymmetryina
potentialisreduced.Insomeclassesofsolidswithhighcrystallinesymmetries,the
orbital (quasi) degeneracy partially remains. In transition-metal compounds, elec-
tronsfillpartiallytheouter-mostdegeneratedorbitals.Thereisadegreeoffreedom
whatorbitalisoccupiedbyelectrons.Thisorbitaldegreeoffreedomcomesoutin
severalmagnetic,optical,andstructuralpropertiesincrystallinematerials.Thetwo
famous examples are known; the Cu 3dx2−y2 orbital characters of doped holes are
cruciallyimportantforthehightransition-temperaturesuperconductivityincuprates,
andthemultipleFe3dorbitalbandsgoverntheelectronicstructureatvicinityofthe
Fermilevelintheironbasedsuperconductors.
Insteadofthegreatprogressesoftheorbitalconceptincorrelatedelectronsys-
tem,thedirectexperimentalobservationshavebeenleftbehindforalongtime.A
reductionofthelatticesymmetryisusuallysupposedasaconsequenceofthespon-
taneousliftingofthedegeneratedelectronicorbitals.Thedirectobservationsofthe
anisotropic electronic wave functions and charge clouds have been recognized as
tough experimental works for a prolonged period of time. In 1998, the resonant
X-ray scattering (RXS) technique was applied to the layered manganites, and
observed directly the long-range orbital order [1, 2]. After this first observation,
thistechniquehasbeendevelopedwidelyanddeeply,andhassuccessfullyobserved
anumberoftheorbitalrelatedphenomena.
B
S.Ishihara( )
DepartmentofPhysics,TohokuUniversity,Sendai980-8578,Japan
e-mail:[email protected]
©Springer-VerlagBerlinHeidelberg2017 1
Y.MurakamiandS.Ishihara(eds.),ResonantX-RayScattering
inCorrelatedSystems,SpringerTractsinModernPhysics269,
DOI10.1007/978-3-662-53227-0_1
2 S.Ishihara
Inthischapter,wereviewRXSandresonantinelasticX-rayscatteiring(RIXS)in
thecorrelatedelectronsystemswiththeorbitaldegreesoffreedomfromthefunda-
mentalviewpoints.InSect.2,wereviewRXSandtheorbitalorders.Theinteracting
orbital models and several characteristics in the orbital orders are introduced in
Sect.2.1.AhistoricalreviewofobservationsoftheorbitalorderandRXSarepre-
sentedinSect.2.2.ThescatteringcrosssectionofRXSandRIXSareformulatedin
Sect.2.3.AsacasestudyofRXSappliedtothecorrelatedelectronsystemswiththe
orbital degree of freedom, theoretical and experimental studies in impurity effects
on the orbital order are introduced in Sect. 2.4. In Sect. 3, we review RIXS and
theorbitalexcitations.Thetheoreticalstudiesinthecollectiveorbitalandvibronic
excitationsareintroducedinSect.3.1.Thenon-resonantinelasticX-rayscattering
(NIXS)isanotherexperimentaltooltodetecttheorbitalexcitation.Webrieflyreview
NIXSfromtheorbitalexcitationsinSect.3.2.WeintroduceRIXSfromtheorbital
excitationsinSect.3.3,wherethepolarizationeffectsoftheX-raysarefocusedon.
Section4 is devoted to summary and future perspective of RXS and RIXS. Also
seeotherreviewsforRXSandRIXSincorrelatedelectronsystemswiththeorbital
degreeoffreedom[3–6].
2 RXSandOrbitalOrder
2.1 InteractingOrbitalModelandOrbitalOrder
TheRXSandRIXStechniquesarewidelyrecognizedasthepowerfulexperimental
toolstodetectthelong-rangedorbitalordersandtheorbitalexcitations,respectively,
whichoriginatefromtheinteractionsbetweentheelectronicorbitaldegreeoffree-
domincrystallinesolids.Inthissubsection,beforeexplaining theRXSandRIXS
for the orbital degree of freedom, we introduce the interacting orbital models and
severalcharacteristicsintheorbitalorders.
Theorbitaldegreeoffreedomisidentifiedastheelectronicmultipoledegreesof
freedominsolids.Inacrystalwiththeinversionsymmetry,theelectronicchargedis-
tributionsareclassifiedbythe2l-polesdegreeoffreedomwithapositiveeveninteger
l.ThisismathematicallyrepresentedbythesphericalharmonicfunctionYm(θ,φ)
l
where−l ≤m ≤l.Inparticular,thechargequadrupole(l =2)playsaleadingrole
in the d and f electron systems with strong electron correlation. In this chapter,
wemainlyfocusonthe3d orbitaldegreesoffreedominthetransition-metalcom-
pounds.The3d orbitalwavefunctions inatransition-metalionareapproximately
representedbythewavefunctionsinahydrogen-likeisolatedatomunderthecen-
trosymmetricpotentialduetotheeffectivepositivecharge.Thewavefunctionsare
givenasψ (r)= R (r)Ym(θ,φ)withn =3,l =2and−2≤m ≤2.Inacubic
nlm nl l
crystallinefield,thefive-folddegeneracyisliftedtothetwo-andthree-folddegen-
eratedorbitalstermedthedeg ={d3z2−y2,dx2−y2}anddt2g ={dyz,dzx,dxy}orbitals,
respectively.Theseareexplicitlygivenas
