Itinerant Spin Dynamics in Iron-Based Superconductors and Cerium-Based Heavy-Fermion Antiferromagnets

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Itinerant Spin Dynamics in Iron-Based Superconductors and Cerium-Based Heavy-Fermion Antiferromagnets Itinerant Spin Dynamics in Iron-based Superconductors and Cerium-based Heavy-Fermion Antiferromagnets Von der Fakultät Mathematik und Physik der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung vorgelegt von Gerd Friemel aus Meißen Hauptberichter: Prof. Dr. Bernhard Keimer Mitberichter: Prof. Dr. Martin Dressel Tag der mündlichen Prüfung: 26. Mai 2014 Max Planck Institut für Festkörperforschung Stuttgart 2014 Contents Abbreviations vii Zusammenfassung in deutscher Sprache ix Abstract xiii 1 Introduction1 1.1 Scope of the thesis.............................3 2 The phase diagram of correlated electron systems7 2.1 The family of iron arsenide superconductors...............7 2.1.1 Electronic structure and Fermi surface of FeSC......... 10 2.1.2 Reciprocal-space structure of the spin fluctuations in FeSC.. 12 2.1.3 Unconventional order parameter in the superconducting phase of FeSC............................... 13 2.2 The family of alkali-metal iron selenide superconductors........ 15 2.2.1 Electronic structure of the superconducting phase........ 16 2.2.2 AxFe2−ySe2: Phase separation into insulating A2Fe4Se5 and su- perconducting AxFe2Se2 ...................... 17 2.3 Unconventional superconductivity in heavy-fermion compounds.... 20 2.4 The magnetic phase diagram of CeB6 ................... 21 2.4.1 Crystal structure and ground state of CeB6 ............ 21 2.4.2 Magnetic structure in the antiferromagnetic and antiferroquadrupo- lar phase of CeB6 .......................... 23 2.4.3 Mean-field description of the phase diagram........... 26 2.4.4 Electronic properties of CeB6 ................... 29 2.4.5 Alternative approach to phase II................. 33 2.4.6 Appearance of phase IV in Ce1−xLaxB6 ............. 35 2.4.7 Non-Fermi-liquid regime of Ce1−xLaxB6 ............. 37 2.4.8 Status of the CeB6 problem at the outset of the thesis...... 38 3 Magnetism and spin dynamics in metals: theoretical considerations 41 3.1 The physics of heavy-fermion systems.................. 41 3.1.1 Kondo lattice systems....................... 43 3.1.2 Itinerant vs. localized behavior.................. 45 iii 3.2 Itinerant ferro- and antiferromagnetism.................. 47 3.2.1 Spin fluctuations in nearly ferro-and antiferromagnetic materials 50 3.2.2 Dynamical susceptibility in nearly antiferromagnetic heavy-fermion systems............................... 52 3.2.3 Spin waves in itinerant ferromagnets............... 53 3.3 The magnetic resonant mode........................ 54 4 Experimental Methods 57 4.1 Preparation of AxFe2−ySe2 (A = K, Rb) single crystals.......... 57 4.2 Preparation of Ce1−xLaxB6 single crystals................. 60 4.3 The experimental technique of neutron scattering............ 62 4.3.1 Triple-axis neutron spectroscopy................. 63 4.3.2 Resolution and background of a triple-axis spectrometer.... 65 4.3.3 Time-of-flight spectroscopy.................... 69 4.4 The theory of neutron scattering...................... 70 4.4.1 Magnetic neutron scattering.................... 71 5 Spin fluctuations in AxFe2−ySe2 79 5.1 The resonant mode in AxFe2−ySe2 ..................... 79 5.2 Spin excitations in Rb0:8Fe1:6Se2 ...................... 80 5.3 Spin excitations in KxFe2−ySe2 ....................... 85 5.4 The resonant-mode spectrum in AxFe2−ySe2 ............... 88 6 Neutron scattering studies on CeB6 93 6.1 Temp. and field dependence of the AFM and AFQ OP’s in Ce1−xLaxB6 93 6.1.1 Observation of a zero-field SDW order parameter in Ce1−xLaxB6 ............................. 93 6.1.2 Field dependence of the SDW and AFQ Bragg peaks in CeB6 . 96 6.1.3 The magnetic phase diagram of Ce0:82La0:18B6 ......... 97 6.1.4 The magnetic phase diagram of Ce0:77La0:23B6 ......... 99 6.1.5 The magnetic phase diagram of Ce0:72La0:28B6 ......... 100 6.1.6 Summary of the neutron diffraction studies of Ce1−xLaxB6 ... 106 6.2 Spin dynamics in Ce1−xLaxB6 ....................... 107 6.2.1 The observation of a resonant spin exciton in the AFM phase of CeB6 ............................... 107 6.2.2 The observation of ferromagnetic correlations in the AFM phase of CeB6 ............................... 110 6.2.3 Spin waves in the AFM state................... 112 6.2.4 Observation of a charge gap in the AFM state.......... 114 6.2.5 Itinerant description of the spin dynamics in CeB6 ....... 116 6.2.6 Magnetic-field dependence of the spin exciton in CeB6 ..... 119 6.2.7 Evolution of the spin exciton in Ce1−xLaxB6 ........... 120 6.2.8 Magnetic-field dependence of the ferromagnetic mode..... 127 6.3 Summary................................... 130 7 Summary and Discussion 133 7.1 Indications of strongly correlated physics in FeSe122.......... 133 7.2 The exciton in CeB6 as a fingerprint for itinerant spin dynamics.... 136 Appendices 139 Physical constants 143 Bibliography 145 Publication List 161 Acknowledgements 163 Abbreviations AFM ... Antiferromagnetic AFQ ... Antiferroquadrupolar ARPES ... Angle-resolved photoemission spectroscopy BCS ... Bardeen, Cooper and Schrieffer BZ ... Brillouin zone CEF ... Crystalline electric field cnts, cts ... Counts CW ... Curie-Weiss dHvA ... de Haas-van Alphen DOS ... Density of states EDX ... Energy-dispersive X-ray spectroscopy ESR ... Electron spin resonance ENS ... Elastic neutron scattering FeSC ... Iron-based superconductors FeSe122 ... Alkali-metal iron chalcogenides FWHM ... Full-width-half-maximum FL ... Fermi liquid FM ... Ferromagnetic FS ... Fermi surface f.u. ... Formula unit HWHM ... Half-width-half-maximum HF ... Heavy fermion INS ... Inelastic neutron scattering KL ... Kondo lattice LRO ... Long-range order MFA ... Mean-field approximation MPI-FKF ... Max Planck Institute for Solid State Research ND ... Neutron diffraction NFL ... Non-Fermi-liquid NMR ... Nuclear magnetic resonance OP ... Order parameter QCP ... Quantum critical point RKKY ... Rudermann-Kittel-Kasuya-Yosida RPA ... Random-phase approximation RXS ... Resonant X-ray scattering vii r.l.u. ... Reciprocal lattice units SC ... superconducting SCR ... Self-consistent renormalization SDW ... Spin-density wave s.d. ... Standard deviation SRO ... Short-range order STM, STS ... Scanning tunneling microscopy/spectroscopy TOF ... Time of flight µSR ... Muon-spin relaxation Zusammenfassung in deutscher Sprache Itinerante Spinanregungen in Eisen-basierten Supraleitern und Cer-basierten schweren Fermionen Im Rahmen dieser Dissertation wurden der Magnetismus und die Spindynamik von zwei unterschiedlichen metallischen Elektronensystemen mittels inelastischer Neutro- nenstreuung untersucht. Die Materialien umfassen die neue Familie der Alkali-Eisen- selenide (FeSe122) AxFe2−ySe2 (A=K, Rb) [1], welche strukturell den 2008 entdeck- ten unkonventionellen Eisen-basierten Hochtemperatursupraleitern, wie zum Beispiel LaOFeAs, ähneln [2] und eine beachtliche Sprungtemperatur von Tc = 32 K aufweisen. Jedoch besitzen diese Verbindungen eine qualitativ einzigartige elektronische Struk- tur unter den Eisen-basierten Supraleitern. Es wurde vorhergesagt [3], dass Spinfluk- tuationen die Cooper-Paarung, analog zu den Eisenpniktiden, vermitteln. Der Be- weis der Existenz und die Charakterisierung der Spinfluktuation konnten in der vor- liegenden Arbeit erbracht werden. Des Weiteren wurden die Spinanregungen in dem Schwerfermion-Antiferromagneten CeB6 gemessen. Dieses System ist vor allem durch die Realisierung einer antiferroorbitalen Quadrupolordnung (AFQ) der 4 f Elektronen 3+ von Ce , welche unterhalb von TQ = 3;2 K einsetzt, und einer antiferromagnetischen Ordnung unterhalb TN = 2;3 K vorausgeht, von Interesse. Beide Systeme verbindet eine verblüffende Veränderung der Spindynamik unterhalb ihrer jeweiligen Übergangstemperatur. In den FeSe122 Supraleitern konzentrieren sich 1 1 die Spinfluktuationen um den Wellenvektor Qsf = ( 2 4 ). Während das Einteilchen- ′′ Spinanregungsspektrum χ (Qsf;!), welches durch inelastische Neutronenstreuung di- rekt gemessen werden kann, im Normalzustand nahezu monoton und kontinuierlich ist, ändert sich es drastisch mit dem Öffnen der supraleitenden Energielücke 2∆ unter- 1 halb von Tc. Einteilchen-Anregungen unterhalb 2∆ sind normalerweise unterdrückt ′′ (χ0 (Qsf;!) = 0 für ! < 2∆). Jedoch wurde eine starke und energetisch schmale An- regung bei h̵!res = 14 meV < 2∆ beobachtet, die parallel mit der Energielücke un- terhalb von Tc erscheint. So eine Resonanzmode wurde schon in ähnlicher Form in den supraleitenden Kupraten und in den Eisenpniktiden beobachtet und gilt als Indika- tor für einen unkonventionellen Ordnungsparameter im supraleitenden Zustand. Das Wechselspiel zwischen Magnetismus und Supraleitung, welches die Beobachtung der Resonanzmode verkörpert, wird als Beweis der magnetisch vermittelten Supraleitung angeführt [5]. Die Ergebnisse dieser Dissertation unterstützen diese Hypothese und lie- fern weitere experimentelle Informationen, die das Verständnis des Mechanismus der 1 Im Fall der AxFe2−ySe2 Supraleiter beträgt die Energielücke ∆ = 10;3 meV [4]. ix Hochtemperatursupraleitung verbessern könnten. Im Gegensatz zu den Eisen-basierten Supraleitern wurde CeB6 mit dem Kondo- Gitter-Modell beschrieben, wo lokalisierte f -Spins in einem Meer von Leitungselek- tronen eingebettet sind. Der Grundzustand wird durch das Γ8 Multiplett gebildet, wel- ches zwei orbitale und zwei Spinfreiheitsgrade einschließt. Die AFQ und die AFM Ordnung heben jeweils die Orbital-und die Spinentartung auf. Die Quadrupole und die Spins verschiedener Ce-Atome sind dabei über die Rudermann-Kittel-Kasuya-Yosida
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