Magnetism and Superconductivity in Iron-based Superconductors as Probed by Nuclear Magnetic Resonance

182 Pages·2012·5.548 MB·English

by  Franziska Hammerath (auth.)

Magnetism and Superconductivity in
Iron-based Superconductors as Probed
by Nuclear Magnetic Resonance
Franziska Hammerath
Magnetism and Super-
conductivity in Iron-
based Superconductors
as Probed by Nuclear
Magnetic Resonance
Foreword by Prof. Dr. Bernd Büchner
RESEARCH
Franziska Hammerath
Dresden, Germany
Vollständiger Abdruck der von der Fakultät für Mathematik und Naturwissenschaft en
der Technischen Universität Dresden zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaft en (Dr. rer. nat.) genehmigten Dissertation.
ISBN 978-3-8348-2422-6 ISBN 978-3-8348-2423-3 (eBook)
DOI 10.1007/978-3-8348-2423-3
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.
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Fu¨rMadeleine
Foreword
Sinceironanditscompoundsareoftenferromagnets-anotationthatoriginatesfromthe
latin word“ferrum” foriron-superconductivity is notthefirst property tocheck forin
aniron-basedcompound. Itwasthereforeevenmoresurprisingthatthesuperconducting
transitiontemperaturecouldberaisedupto55KshortlyafterKamiharaandco-workers
reported the discovery of superconductivity in the so-called iron pnictides in 2008. In
fact,thisisthehighesttransitiontemperatureever,secondedonlybythecuprates,which
werefoundin1986.
Similartothese, theobservationofanotherfamilyofhightemperaturesuperconductors
led to an enormous activity within the research community, resulting in thousands of
papers presenting surprising and also promising new results. For example, high critical
currentdensitiesandhighcriticalfieldsraisethehopethatthesematerialscouldbewell
usedforapplications. Ontheotherhand,themechanismofsuperconductivityisstillnot
clear. Whileasimplephonon-mediatedCooperpairingseemstobeexcludedbythehigh
transition temperatures, it is not yet established if antiferromagnetic spin fluctuations
can indeed mediate the pairing, or if they are just a remnant of a nearby spin density
phase. Also, the symmetry of the order parameter seems to change from compound to
compound. While most of the experimental results are in line with the theoretically
proposed s+−-symmetry, there is substantial evidence for d-wave symmetry from other
experiments. Even the possibility of p-wave superconductivity has been proposed, but
withcontradictoryresultsontheexperimentalside.
All these intriguing questions are addressed in the PhD thesis at hand. In this thesis,
FranziskaHammerathhasusedtheexperimentaltechniqueNuclearMagneticResonance
(NMR)inordertoinvestigateseveraldifferentcompoundsofsuperconductingironpnic-
tides. NMR has been invented already 60 years ago, and contributed to the field of
superconductivityfromthebeginningon. Tonamebutafewexamples,thepeculiartem-
perature dependence of the spin-lattice relaxation rate observed by Hebel and Slichter
inthesuperconducting stateofaluminum supportedthetheoryofsuperconductivity by
Bardeen, Cooper and Schrieffer, and the constant Knight shift in Sr RuO in the su-
2 4
perconducting state provided evidence for triplet superconductivity in this compound.
Furthermore,itslocalcharacterandthesensitivitytolowfrequencymagneticexcitations
renderitaperfecttooltoinvestigatealsothenormalstatepropertiesofanewsupercon-
ductingfamily,suchastheironpnictides.
viii Foreword
This thesis comprises a coherent summary of the basics of NMR as well as a brief de-
scription of the fundamental properties of the iron pnictides. With this at hand, the
interested reader can immerse into the enlightening results of Nuclear Magnetic Reso-
nanceoniron-basedsuperconductors,gainingadeeperinsightalsointothedetailsofthis
powerful experimental tool as well as a better understanding of the iron pnictides as a
newbearerofhopeintheresearchofhightemperaturesuperconductivity.
Prof. Dr. BerndBu¨chner
DirectoroftheInstituteofSolidStateResearch
IFWDresden
Contents
Foreword vii
List ofFigures xiii
List ofTables xv
1 Introduction 1
2 Basic Principles of NMR 3
2.1 IsolatedNuclearSpinsinaMagneticField . . . . . . . . . . . . . . . . . . 4
2.1.1 ASingleNuclearSpin . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 ManyNuclearSpins . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 MakingLifeInteresting: Interactions . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 InteractionsBetweenNuclearSpins-LineShapeI. . . . . . . . . . 7
2.2.2 MagneticHyperfineInteractions . . . . . . . . . . . . . . . . . . . . 8
2.2.3 ElectricQuadrupoleInteractions . . . . . . . . . . . . . . . . . . . 11
2.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 DynamicProcesses: Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 HowtoMeasureNuclearMagnetism? . . . . . . . . . . . . . . . . . 20
2.3.2 Spin-LatticeRelaxation . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2.1 SourcesofSpin-LatticeRelaxation . . . . . . . . . . . . . 22
2.3.2.2 InversionRecoveryMethodtoMeasureT−1 . . . . . . . . 24
1
2.3.2.3 Spin-LatticeRelaxationFunctions . . . . . . . . . . . . . 24
2.3.2.4 KorringaRelation . . . . . . . . . . . . . . . . . . . . . . 26
2.3.3 Spin-SpinRelaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 LineShapeII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 NMR in the Superconducting State 31
3.1 KnightShift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 SpinShift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.2 OrbitalShiftandSpin-OrbitScattering . . . . . . . . . . . . . . . . 32
3.1.3 DiamagneticShielding . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Spin-LatticeRelaxationRate . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 BCSCoherenceFactors. . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 BCSSpin-LatticeRelaxationRate . . . . . . . . . . . . . . . . . . 35
3.2.2.1 ComparisontoUltrasonicAttenuation . . . . . . . . . . . 37
3.2.3 AbsenceoftheHebel-SlichterPeak . . . . . . . . . . . . . . . . . . 38
3.2.4 WhattoExpectforPnictides?. . . . . . . . . . . . . . . . . . . . . 39
x Contents
4 Iron-based Superconductors 41
4.1 GeneralOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 CrystalStructureandElectronicStructure . . . . . . . . . . . . . . 41
4.1.2 GroundStatesandPhaseDiagrams . . . . . . . . . . . . . . . . . . 42
4.1.3 SymmetryoftheSuperconductingOrderParameter . . . . . . . . . 44
4.2 BasicpropertiesofLaO1−xFxFeAs. . . . . . . . . . . . . . . . . . . . . . . 47
4.3 BasicpropertiesofLiFeAs . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 Experimental Setup 53
5.1 MagnetsandCryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 ElectronicMeasurementEquipment . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.2 MainElementsoftheElectronics . . . . . . . . . . . . . . . . . . . 55
5.3 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.1 LaO1−xFxFeAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.2 LiFeAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.4 ProblemsandImprovements . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4.1 TemperatureControl . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4.2 SampleProbeforthe16TFieldSweepMagnet . . . . . . . . . . . 62
5.4.3 SampleHeating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 NMR on LaO1−xFxFeAs in the Normal State 67
6.1 KnightShift-StaticSusceptibility . . . . . . . . . . . . . . . . . . . . . . 67
6.1.1 Optimally-DopedLaO F FeAs . . . . . . . . . . . . . . . . . . . 67
0.9 0.1
6.1.2 LaO F FeAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
0.95 0.05
6.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.2 Spin-LatticeRelaxationRate-Dynamics . . . . . . . . . . . . . . . . . . . 76
6.2.1 Optimally-DopedLaO F FeAs . . . . . . . . . . . . . . . . . . . 77
0.9 0.1
6.2.2 UnderdopedLaO F FeAs . . . . . . . . . . . . . . . . . . . . . 81
0.95 0.05
6.2.3 OverallDopingDependence-RoleofSpinFluctuations . . . . . . . 82
6.2.3.1 QualitativeDiscussion . . . . . . . . . . . . . . . . . . . . 82
6.2.3.2 QuantitativeDiscussion . . . . . . . . . . . . . . . . . . . 85
6.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.3 KorringaRelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.3.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7 NMR and NQR on LaO1−xFxFeAs in the Superconducting State 97
7.1 Spin-LatticeRelaxationRateforx≥0.05 . . . . . . . . . . . . . . . . . . 97
7.2 TheEffectof’Smart’Deficiencies: LaO0.9F0.1FeAs1−δ . . . . . . . . . . . . 102
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Contents xi
8 NMR and NQR on LiFeAs 111
8.1 75As-NQR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.2 75As-NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.2.1 StaticNMRProperties-LinewidthandKnightShift . . . . . . . . 115
8.2.2 DynamicProperties-Spin-LatticeRelaxationRate . . . . . . . . . 120
8.3 Summaryof75AsNQRandNMRResults . . . . . . . . . . . . . . . . . . 124
8.4 7Li-NMR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.5 Summaryof7LiNMRResults . . . . . . . . . . . . . . . . . . . . . . . . . 130
9 Conclusions 131
A Appendix 135
A.1 NMRPowderSpectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.2 CalculationofSpin-LatticeRelaxationFunctions . . . . . . . . . . . . . . 139
A.3 StretchedExponentialRelaxationFunction . . . . . . . . . . . . . . . . . . 143
A.4 SpinDiffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Bibliography 151
Acknowledgement 171
List of Figures
2.1 Levelsplittingduetoquadrupoleeffectsinzerofield. . . . . . . . . . . . . 14
2.2 Level splitting due to first-order quadrupole effects in a strong magnetic
field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 SummaryofallpossibleinteractionsandtheresultingNMRspectra . . . . 17
2.4 Effectivefieldintherotatingframe(non-resonantcase) . . . . . . . . . . . 19
2.5 Effectivefieldintherotatingframeatresonance . . . . . . . . . . . . . . . 19
2.6 Relaxationandprecessionofthenuclearmagnetization . . . . . . . . . . . 20
2.7 Fouriertransformationofarectangularpulse . . . . . . . . . . . . . . . . . 21
2.8 Hahnspinechopulsesequence . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.9 Inversionrecoverymethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.10 Relaxationratesasfunctionofthecorrelationtimeτ . . . . . . . . . . . . 29
c
4.1 Crystalstructureofiron-basedsuperconductors . . . . . . . . . . . . . . . 42
4.2 ElectronicstructureofLaOFeAs . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 Phasediagramsofcupratesandpnictides . . . . . . . . . . . . . . . . . . . 45
4.4 EarlyNMRresultsinthesuperconductingstateofpnictides . . . . . . . . 46
4.5 Momentum-dependent superconductinggapinBa1−xKxFe2As2 . . . . . . . 46
4.6 PhasediagramofLaO1−xFxFeAs . . . . . . . . . . . . . . . . . . . . . . . 48
4.7 SusceptibilityofLaOFeAs . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.8 ARPESresultsonLaOFeAs . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.9 ARPESresultsonLiFeAs . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1 Resonantcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2 Experimentalsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3 FieldsweepspectraofalignedandmisalignedLaO F FeAspowder
0.9 0.1
samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4 75AsNQRresonancelineofLiFeAsatroomtemperature . . . . . . . . . . 59
5.5 7LiNMRspectraat200KinH =4.4994T. . . . . . . . . . . . . . . . . . 60
5.6 75(T T)−1 ofLaOFeAsuponcoolingwithnitrogenandhelium . . . . . . . 61
1
5.7 16Tsampleprobebeforeandafterimprovements . . . . . . . . . . . . . . 63
5.8 Effectofsampleheatingonthe75AsNQRfrequencyofLiFeAs . . . . . . . 65
6.1 75As-NMRresonancelineofab-alignedLaO F FeAs . . . . . . . . . . . 68
0.9 0.1
6.2 KnightshiftvsmacroscopicsusceptibilityinLaO F FeAs . . . . . . . . 69
0.9 0.1
6.3 Pseudogapfiton75K forLaO F FeAs . . . . . . . . . . . . . . . . . . 70
ab 0.9 0.1
6.4 HyperfinecouplingconstantsforLaO F FeAs . . . . . . . . . . . . . . . 71
0.9 0.1
6.5 75AsKnightshiftofLaO F FeAs . . . . . . . . . . . . . . . . . . . . . 74
0.95 0.05
6.6 Scalingof75K andχ(T)forLaO F FeAs. . . . . . . . . . . . . . . . 75
ab 0.95 0.05
6.7 75As(T T)−1 ofLaO F FeAs . . . . . . . . . . . . . . . . . . . . . . . . 78
1 0.9 0.1