The NMR Probe of High-Tc Materials

272 Pages·2008·7.766 MB·English

by  Russel E. Walstedt (auth.)

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R.E. Walstedt
The NMR Probe
of High-T Materials
c
123
RussellE.Walstedt
UniversityofMichigan
DepartmentofPhysics
AnnArbor,MI48104,USA
[email protected]
R.E. Walstedt, The NMR Probe of High-T Materials, STMP 228 (Springer, Berlin
c
Heidelberg2008),DOI10.1007/978-3-540-75565-4
LibraryofCongressControlNumber:2007936864
PhysicsandAstronomyClassificationScheme(PACS):
NMRSTUDIESINGENERAL 76.60.-K
CUPRATESUPERCONDUCTORS 74.72.-H
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To Erwin, Vince, and Hiroshi
Preface
To the old saying that if you want to learn something about a subject, teach
a course on it, I would add the much more arduous option of writing a book
about it. The upside, of course,is that youmay gaina perspective ona long-
time favorite subject which can be achieved in no other way. The fact is that
the opportunity to write such a book as this is, indeed, a rare opportunity.
This is especially so for someonewho,by the calendar,is wellinto retirement
years.
While high T itself is the opportunity of a lifetime for those of us who
c
experienced it, and revisiting the old milestones in writing this monograph
was a genuine nostalgia trip, it is also important to reflect on the purpose
of such a book as this. Now that the great majority of experimental high-T
c
studies are finished, who could be interested in such a book? To give some
kindofanswertothis,letmepinpointthe 2006M2SConferenceinDresden.1
Notonlywasitatthisconferencethattheideaforthisbookwashatched,but
the conference itself evinced an astonishingly high level of interest in high-T
c
issues, especially the theoretical aspects. Since it is now a number of years
since a review of high-T studies with NMR has appeared, there may be a
c
need on the part of theorists and other interested parties for an organized
summary of results and of the ideas which have been advanced to bind them
together.
The foregoingoffersa partialanswerto the “Why now?”question,butlet
me note that excellent answers to that question also emerge from the sub-
ject itself. Although many issues were settled as of 10 years ago, new ideas
and even new phenomena have appeared since that time. Let me offer two
examples.TheconfirmationbyN.Curroandco-workersofadynamicalexpo-
nent crossover in the high-temperature phase diagram opens up a new arena
of potential experimental activity. D. Pines and co-workers had predicted
suchaneffect andothertheorists,including C.Varma,hadpredictedaphase
1 This was the 8th International Conference on Materials and Mechanisms of Su-
perconductivityandHighTemperatureSuperconductors,Dresden,July9–14,2006.
VIII Preface
boundary in that region. Another interpretive breakthrough is to be cred-
ited to A. Uldry and P.F. Meier, who in 2005 created a new, general method
for analyzing relaxation (T ) data in terms of temperature-dependent spin–
1
spincorrelationcoefficientsforclose-neighborcoppersites.Discussedatsome
length in this volume, this method rests on a very firm theoretical founda-
tion.Ithasthegreatvirtuethatitseparatesspin-spinthesecorrelationeffects
fromthe temperature dependence of the quasiparticledynamics, itself, which
theoretical modelers have been trying to get at. If this extraordinarilysimple
method had been “available” 15 years ago, I suggest that our understanding
of these issues would be greatly advanced from where it is.
As for regrets, they come mainly under the heading of omissions. There
are many excellent pieces of work which are not included, simply for want
of time and space. The book was conceived of as a monograph and is in no
sense an encyclopedia, not even within the narrow purview of high-T NMR.
c
As an example, I greatly regret omitting the large and fascinating subject of
impurity doping in cuprates, from which we have nonetheless learned a lot.
Let me conclude by mentioning just a few of the people who have con-
tributed, directly and indirectly, to the initiation and creation of this book.
First let me thank Prof. Hiroshi Yasuoka, for bringing me to Tokai-mura
in Japan for a 5-plus year extension of my career in solid-state NMR, and
through which I also became involvedin the European physics scene. Let me
thank Prof. Dr. Frank Steglich for his support during my extensive visits to
Dresden in 2006 and 2007. Invaluable support came from the Department of
Physicsatthe UniversityofMichiganinprovidingworkspaceandthelibrary
facilities required for a project such as this. I want especially to thank Prof.
Chandra Varma at the University of California at Riverside, for shepherding
this book into existence throughhis roleas editor for SpringerVerlag andfor
his reading of much of the manuscript, giving penetrating, enlightening, and
invaluable comments on the presentation. I also thank Jinan Yang for help
with computer issues and with the preparation of the figures.
Ann Arbor, MI, Russell E. Walstedt
June 2007
Contents
1 Introduction............................................... 1
1.1 The Basic Phenomenology of High-T Materials ............. 1
c
1.2 Carrier Doping and the Master Phase Diagram.............. 2
1.3 The NMR Probe ........................................ 4
1.4 Outline of the Remaining Chapters ........................ 6
1.4.1 Summary of Chapter 2 – NMR Review............... 6
1.4.2 Summary of Chapter 3 – Preliminary Cuprate NMR... 7
1.4.3 Summary of Chapter 4 – The Pseudogap ............. 7
1.4.4 Summary of Chapter 5 – T Models ................. 8
1
1.4.5 Summary of Chapter 6 – The Dynamical Susceptibility. 9
References .................................................. 10
2 Introduction to NMR Studies of Metals, Metallic
Compounds, and Superconductors ......................... 13
2.1 Basic NMR Phenomenology .............................. 13
2.1.1 The Basic Hamiltonian for NMR Spectra............. 14
2.1.2 Observation of NMR/NQR Signals .................. 17
2.1.3 Definition and Interpretation of NMR parameters: T .. 19
2
2.1.4 Definition and Interpretation of NMR parameters:
The shift tensor K ............................... 21
αβ
2.1.5 Definition and Interpretation of NMR parameters: T .. 23
1
2.2 NMR Probe of sp-Band Metals and Type I Superconductors .. 32
2.2.1 NMRShiftsandRelaxationinSimplePauliParamagnets 33
2.2.2 The Moriya Theory of Exchange Enhancement
in Simple Metals .................................. 36
2.2.3 NMR in the Superconducting State of Simple Metals .. 38
2.3 Static and Dynamic Magnetism in d-band Metals............ 44
2.3.1 The d-Electron HF Interactions ..................... 45
2.3.2 Orbital Shift and Susceptibility ..................... 46
2.3.3 Spin-Lattice Relaxation Effects for d-Band Electrons... 50
2.3.4 NMR Studies of 3d Metals as Type-II Superconductors. 53
X Contents
2.3.5 T Phenomenology for Type-II Superconductors....... 58
1
References .................................................. 63
3 The Superconducting Cuprates: Preliminary Steps
in their Investigation via NMR ............................ 67
3.1 Cuprate Structures and Doping Effects: LSCO and YBCO.... 68
3.1.1 LSCO: A superconductor with T (max)(cid:2)40K ....... 68
c
3.1.2 The 92K Superconductor YBa2Cu3O7−x (YBCO)..... 70
3.1.3 Physical Models of Itinerant Quasiparticles in Cuprates 71
3.2 Early NMR/NQR Studies: The Early Predominance of YBCO 72
3.2.1 NMR Shift and Relaxation of the 89Y in YBCO7...... 73
3.2.2 Establishing the Site Assignment for the Cu(1) and
Cu(2) NQR Spectra ............................... 75
3.2.3 Variation of the 89Y shift K (x) with x for YBCO6+x. 76
89
3.2.4 Physical Models for the Relaxation of 63Cu(2) in
YBCO7 .......................................... 79
3.2.5 Introduction of the Spin Hamiltonian Model for the
Cu2+ ............................................ 79
3.2.6 Experimental Breakthrough:Oriented Powder Samples. 80
3.3 The Mila-Rice-ShastryModel: A UniversalHF Tensor for the
Cuprates ............................................... 81
3.3.1 General Definition of the HF Tensors ................ 82
3.3.2 Extracting the Cu(1,2) HF tensors for YBCO7
from Shift and Susceptibility Data Using the Spin
Hamiltonian Model ................................ 84
3.3.3 Quantum Chemistry of YBCO7 and the Hyperfine
Tensor ........................................... 87
3.3.4 T Ratios and Electron Spin Correlation Effects....... 90
1
3.4 Incorporating 17O and 89Y data into the Mila-Rice-Shastry
Picture................................................. 92
3.4.1 Measurements of T for 17O in YBCO7 .............. 97
1
3.4.2 The One-Band, Two-Band Debate: 89Y and 17O(2,3)
NMR in YBCO ................................... 98
3.5 Formulation of T in Terms of χ(cid:2)(cid:2)(q,ω) and q-Dependent HF
1
Couplings .............................................. 99
3.5.1 Derivation of Dynamical Susceptibility T Equation ... 99
1
3.5.2 The Fluctuation-Dissipation Theorem................101
3.6 A d-Wave Model for the NMR Shift and T at T <T ........104
1 c
3.6.1 The NMR Shift Behavior for T <T .................105
c
3.6.2 The Monien-Pines Calculations of NMR Shifts below T 107
c
3.6.3 Calculating the Relaxation Decay Curve..............108
References ..................................................112
Contents XI
4 Pseudogap Effects in Cuprate NMR Studies ...............115
4.1 The Pseudogapin Oxygen–Deficient YBCO7-x..............117
4.1.1 HF Parameters for YBCO6.63 from Scaling of Shift
Data.............................................120
4.1.2 ASimpleModelTheoryofSpinDynamicsforYBCO6.63126
4.1.3 INS Data for the Pseudogapof Underdoped YBCO....128
4.1.4 A Comprehensive T Data Set for YBCO6.63 .........130
1
4.2 Pseudogap Phenomenology with Other Probes ..............134
4.2.1 Pseudogap Effects in the Electronic Specific Heat......134
4.2.2 ARPES Studies of Pseudogapped Cuprates ...........136
4.3 Pseudogap Behavior of YBa Cu O (Y248).................138
2 4 8
4.3.1 NMR Shift and Relaxation Behavior in Y248 .........139
4.3.2 Measuring the Pseudogap Isotope Effect in Y248
with NMR........................................143
4.3.3 Theory of the Pseudogap by Varma. .................146
4.3.4 Effect of Zn impurities on the Pseudogap in Y248 .....147
4.4 “Pseudogap-like”Effects in La2−xSrxCuO4 (LSCO:x) ........148
4.4.1 Spin Susceptibility Scaling for La2−xSrxCuO4. ........149
4.4.2 Behavior of the 17O and 63Cu NMR Shifts in LSCO:x. .152
4.4.3 63Cu NQR spectra and Contrasting T Behaviors
1
in LSCO:x. .......................................153
References ..................................................156
5 Relaxation Models for Cuprate NMR......................159
5.1 The Uldry-Meier ParameterizationModel...................160
5.1.1 Basic Formulation of the UM Analysis ...............161
5.1.2 The Uldry-Meier Analysis of YBCO7 ................163
5.1.3 The Uldry-Meier Analysis of YBCO6.63..............167
5.1.4 The Uldry-Meier Analysis of YBa Cu O (Y248)......169
2 4 8
5.2 The Millis, Monien, and Pines Model for T in Cuprates .....172
1
5.3 T Model for YBCO Using INS Data for χ(cid:2)(cid:2)(q,ω)............179
1
5.3.1 The Gaussian Model Susceptibility ..................180
5.3.2 Comparison with the UM Analysis Results for YBCO7.184
5.4 A Small-U Hubbard Model of Cuprate Spin Dynamics .......187
5.4.1 Basic Formulation of the Dynamic Susceptibility ......187
5.4.2 Remarks on the Hubbard Model Calculations .........189
5.5 The Large-U Hubbard Model of Si, Levin et al ..............192
5.6 Relaxation via Orbital Currents proposed by Varma .........195
5.7 Relaxation of Planar 63Cu and 17O at T<T ...............199
c
5.7.1 χ(cid:2)(cid:2)(q, ω) for the Small-U Hubbard Model at T<T ...201
c
5.7.2 T and Spin-Spin Correlations below T : The UM
1 c
Analysis..........................................207
References ..................................................210