Resonant X-Ray Scattering in Correlated Systems PDF
Preview Resonant X-Ray Scattering in Correlated Systems
Springer 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 SpringerTractsinModernPhysicsprovidescomprehensiveandcritical reviewsof topics of current interest in physics. The following fields are emphasized: – Elementary Particle Physics – Condensed Matter Physics – Light Matter Interaction – Atomic and Molecular Physics – Complex Systems – Fundamental Astrophysics Suitable reviews of other fields can also be accepted. The Editors encourage prospectiveauthorstocorrespondwiththeminadvanceofsubmittingamanuscript. Forreviewsoftopicsbelongingtotheabovementionedfields,theyshouldaddress the responsible Editor as listed in “Contact the Editors”. More information about this series at http://www.springer.com/series/426 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 LibraryofCongressControlNumber:2016948268 ©Springer-VerlagBerlinHeidelberg2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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 authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringer-VerlagGmbHGermany Theregisteredcompanyaddressis:HeidelbergerPlatz3,14197Berlin,Germany 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
The list of books you might like
