Table Of ContentConversion of Gaussian to Sf Units
Fundamental Gaussian SI Ratio·
quantity
SI
Symbol Units Symbol Units
Gaussian
Magnetization 41tM G M A/m 103/41t
Permeability of - - Jlo=41t X 10-7 Wb/Am 41tx 10-7
free space
Anisotropy K erg/cm3 K J/m3 10-1
Exchange A erg/cm A J/m 10-5
Gyromagnetic ratio y (s·Oe)-1 y (s·A/m)-1 '41t/103
Gilbert parameter a - a - 1
Parameter Defining Units Defining Units Ratio·
formula formula
Magnetic field H JH ·d'=41tNI/1O Oe JH.d'=NI A/m 103/41t
strength
Magnetic induction B B=H+41tM G B=Jlo(H+M) Wb/m2 10-4
Flux 4> 4>=JB.dA Mx 4>=JB.dA Wb 10-8
Energy product BHf81t~MH/2 erg/cm3 BH /2 ~ JloM H /2 J/m3 10-1
Demagnetization N Hd=-NM - Hd=-NM - 1/41t
factor
Volume X,K X=dM/dH - K=dM/dH - 41t
susceptibility
Permeability Jl Jl=dB/dH - Jl=dB/dH - 41t x 10-7
= 1 +41tX =Jlo(1 +K) =Jlo
Anisotropy field H" H,,=2K/M Oe H" = 2K/JloM A/m 103/41t
Stability factor Q Q=H,,/41tM - Q=H,,/M - 1
Wall energy (J (J=4VAJ( erg/cm2 (J=4VAJ( J/m2 10-3
density
Characteristic I 1= (J/41tM2 cm 1= (J/JloM2 m 10-2
length
Wall mobility Jl~ Jl~=l~ cm/s·Oe Jl~=l~ m2/s·A 41tx 10-5
a K a K
m meter s second A Ampere Oe Oersted G Gauss
cm centimeter N number of turns J Joule Wb Weber Mx Maxwell
• To obtain values in SI units mUltiply value in Gaussian units by the respective ratio
1
Springer Series in Solid-State Sciences
Edited by Peter Fulde
Springer-Verlag Berlin Heidelberg GmbH
Springer Series in Solid-State Sciences
Editors: M. Cardona P. Fulde K. von Klitzing H.-J. Queisser
Managing Editor: H. K.V. Lotsch Volumes 1-89 are listed at the end of the book
90 Earlier and Recent Aspects of 108 Site Symmetry in Crystals Theory and
Superconductivity Applications By R. A. Evarestov and
Editors: J. G. Bednorz and K. A. MUller V.P.Smirnov
91 Electronic Properties of ConJugated 109 Transport Phenomena in Mesoscopic
Polymers m Basic Models and Applications Systems Editors: H. Fukuyama and T. Ando
Editors: H. Kuzmany. M. Mehring. and S. Roth 110 Superlattices and Other Heterostructures
92 Physics and Engineering AppUcations of Symmetry and Optical Phenomena
Magnetism Editors: Y. Ishikawa and N. Miura By E. L. Ivchenko and G. E. Pikus
93 Quasicrystals Editors: T. Fujiwara and T. Ogawa 111 Low-Dimensional Electronic Systems
94 Electronic Conduction in Oxides New Concepts
By N. Tsuda. K. Nasu. A. Yanase, and K.Siratori Editors: G. Bauer. F. Kuchar, and H. Heinrich
95 Electronic Materials 112 Phonon Scattering in Condensed Matter VII
A New Era in MaterialsScience Editors: M. Meissner and R. O. Pohl
Editors: J. R. Cbelikowsky and A. Franciosi 113 Electronic Properties of rugh-Tc
96 Electron Liquids By A. Isibara Superconductors
97 Localization and Confinement of Electrons in Editors: H. Kuzmany. M. Mebriog. and J. Fink
Semiconductors 114 Interatomic Potential and Structural Stability
Editors: F. Kuchar. H. Heinrich. and G. Bauer Editors: K. Terakura and H. Akai
98 Magnetism and the Electronic Structure of 115 Ultrafast Spectroscopy of Semiconductors and
Crystals By V.A.Gubanov. A.I. liechtenstein. Semiconductor Nanostructures By J. Shah
and A.V. Postnikov 116 Electron Spectrum of Gapless Semiconductors
99 Electronic Properties of rugh-Tc By J. M. Tsidilovski
Superconductors and Related Compounds 117 Electronic Properties of Fnllerenes
Editors: H. Kuzmany. M. Mehring. and J. Fink Editors: H. Kuzmany, J. Fink. M. Mehring,
andS. Roth
100 Electron Correlations In Molecnlea and
Solids 3rd Edition By P. Fulde 118 Correlation Effects in Low-DImensional
101 High Magnetic Fields in Semlcondnctor Electron Systems
Editors: A. Okiji and N. Kawakami
Physics III Quantum Hall Effect. Transport and
Optics By G. Landwehr 119 Spectroscopy of Mott Insulators
and Correlated Metals
102 ConJugated Conducting Polymers
Editors: A. Fujimori and Y. Tokura
Editor: H. Kiess
120 Optical Properties 01111-V Semiconductors
103 Molecular Dynamics Simulations
The Influence of Multi-Valley Band Structures
Editor: F. Yonezawa
ByH. Kalt
104 Products of Random Matrices io Statistical
Physics By A. Crisanti, G. Paladin. and
A. Vulpiani
105 Self-Trapped Exdtons
2nd Edition By K. S. Song and R. T. Williams
106 Physics of rugh-Temperature
Superconductors
Editors: S. Maekawa and M. Sato
107 Electronic Properties of Polymers
Orientation and Dimensionality of Conjugated
Systems Editors: H. Kuzmany. M. Mehring,
and S. Roth
C.p. Slichter
Principles of
Magnetic Resonance
Third Enlarged and Updated Edition
With 185 Figures
Springer
Professor Charles P. Slichter, Ph. D.
Oepartment of Physics, University of lllinois at Urbana-Champaign
Urbana, IL 61801, USA
Series Editors:
Professor Dr., Dres. h. c. Manuel Cardona
Professor Dr., Dres. h. c. Peter Fulde*
Professor Dr., Dres. h. c. Klaus von Klitzing
Professor Dr., Dres. h. c. Hans-Joachim Queisser
Max-Planck-Institut ftir Festkorperforschung, Heisenbergstrasse 1,0-70569 Stuttgart, Germany
* Max-Planck-Institut fdr Physik komplexer Systeme, Bayreuther StraBe 40, Haus 16,
0-01187 Oresden, Germany
Managing Editor:
Dr.-Ing. Helmut K. V. Lotsch
Springer-Verlag, Tiergartenstrasse 17,0-69121 Heidelberg, Germany
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
SlIchter, Charles P.:
Principles of magnetic resonance / C. P. Slichter. - 3., enl. and
updated ed., corr. 3. printing.
(Springer series in solid-state sciences ; 1)
ISBN 978-3-642-08069-2 ISBN 978-3-662-09441-9 (eBook)
DOI 10.1007/978-3-662-09441-9
NE:GT
Tbe original edition Principles of Magnetic Resonance with Examples from Solid State Physics
was published in 1963 by Harper & Row Publishers, New York, Evanston, and London.
3rd Enlarged and Updated Edition 1990
Corrected 3rd Printing 1996
ISBN 978-3-642-08069-2
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed,
specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on
microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted
only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission
for use must always be obtained from Springer-Verlag Berlin HeideIberg GmbH. Violations are liable for prosecution
under the German Copyright Law.
I© Springer-Verlag Berlin Heidelberg 1978, 1990
Originally published by Springer-Verlag Berlin Heidelberg New York in 1990
Softcover reprint ofthe hardcover 3rd edition 1990
Tbe use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even
in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations
and therefore free for general use.
JYpesetting: Springer TE X in-house system
SPIN: 11347132 54/3111-54 -Printedonacid-freepaper
Preface to the Third Edition
The first edition of this book was written in 1961 when I was Morris Loeb
Lecturer in Physics at Harvard. In the preface I wrote: "The problem faced by
a beginner today is enormous. If he attempts to read a current article, he often
finds that the first paragraph refers to an earlier paper on which the whole article
is based, and with which the author naturally assumes familiarity. That reference
in turn is based on another, so the hapless student finds himself in a seemingly
endless retreat.
I have felt that graduate students or others beginning research in magnetic
resonance needed a book which really went into the details of calculations, yet
was aimed at the beginner rather than the expert."
The original goal was to treat only those topics that are essential to an
understanding of the literature. Thus the goal was to be selective rather than
comprehensive. With the passage of time, important new concepts were becoming
so all-pervasive that I felt the need to add them. That led to the second edition,
which Dr. Lotsch, Physics Editor of Springer-Verlag, encouraged me to write and
which helped launch the Springer Series in Solid-State Sciences. Now, ten years
later, that book (and its 1980 revised printing) is no longer available. Meanwhile,
workers in magnetic resonance have continued to develop startling new insights.
There are new topics which are so important that they must be included in a
book that is intended to be an introductory text. The original course was one
semester - the book had more topics than I taught in that amount of time. The
new edition clearly would need a full year.
Throughout the history of this book, I have considered it as a textbook.
Thus the aim was to explain in a rigorous but physical manner concepts which
are essential for the student of magnetic resonance. Rather than giving an ex
haustive treatment of anyone topic, my intention has been to help prepare a
student to read the literature on that topic. The main additions include an en
largement and modest rewrite of the topic of double resonance, explanations of
one- and two-dimensional Fourier transform methods, of coherence transfer, of
multiple quantum coherence, and of important topics related to dipolar coupling
that underlie the method of spin-flip line narrowing. In the earlier editions, the
chapter on the density matrix focused almost exclusively on its use in analyzing
relaxation processes. The new edition explains its use in analyzing the effect· of
rf fields.
v
The first edition of this book came out shortly after the publication of Ana
tole Abragam's classic-ta-be Principles 0/ Nuclear Magnetic Resonance. There
were not many other books on the market. Today there are many books on mag
netic resonance, a large fraction written by some of the most illustrious founders
of the field and practitioners of the art. The styles of these books are as varied as
the scientific styles of their authors. As I have explored these marvellous books,
I have been struck by the opportunity that exists today to get the flavor of the
scientific thought of these great scientists.
When I wrote the first edition of this book at Harvard, I had no duties other
than preparing and giving the lectures. The third edition has been written on
evenings and weekends while I tried to carry on my normal activities. It would
not have been possible without the expert, dedicated, and always cheerful support
of my secretary, Ann Wells. Her association with the book has been long, since
she helped type the original edition. I am also grateful for the help of Jamie
Froman in the final stages.
Urbana, lllinois
June 1989 Charles P. Slichter
VI
Contents
1. Elements of Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction ........................................ 1
1.2 Simple Resonance Theory ............................. 2
1.3 Absorption of Energy and Spin-Lattice Relaxation ......... 4
2. Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Motion of Isolated Spins-Classical Treatment ............ 11
2.2 Quantum Mechanical Description of Spin in a Static Field .. 13
2.3 Equations of Motion of the Expectation Value ............ 17
2.4 Effect of Alternating Magnetic Fields . . . . . . . . . . . . . . . . . . . 20
2.5 Exponential Operators ................................ 25
2.6 Quantum Mechanical Treatment of a Rotating Magnetic Field 29
2.7 Bloch Equations ..................................... 33
2.8 Solution of the Bloch Equations for Low HI .. . . . . . . . . . . . 35
2.9 Spin Echoes ........................................ 39
2.10 Quantum Mechanical Treatment of the Spin Echo ......... 46
2.11 Relationship Between Transient and Steady-State Response
of a System and of the Real and Imaginary Parts
of the Susceptibility .................................. 51
2.12 Atomic Theory of Absorption and Dispersion ............. 59
3. Magnetic Dipolar Broadening of Rigid Lattices . . . . . . . . . . . . . . . . . 65
3.1 Introduction ........................................ 65
3.2 Basic Interaction .................................... 66
3.3 Method of Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4 Example of the Use of Second Moments ................. 80
4. Magnetic Interactions of Nuclei with Electrons . . . . . . . . . . . . . . . . . 87
4.1 Introduction ........................................ 87
4.2 Experimental Facts About Chemical Shifts ............... 88
4.3 Quenching of Orbital Motion .......................... 89
4.4 Formal Theory of Chemical Shifts ...................... 92
4.5 Computation of Current Density ........................ 96
4.6 Electron Spin Interaction .............................. 108
4.7 Knight Shift ........................................ 113
VII
4.8 Single Crystal Spectra ................................ 127
4.9 Second-Order Spin Effe.cts-Indirect Nuclear Coupling 131
S. Spin-Lattice Relaxation and Motional Narrowing
of Resonance Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.1 Introduction ........................................ 145
5.2 Relaxation of a System Described by a Spin Temperature ... 146
5.3 Relaxation of Nuclei in a Metal ........................ 151
5.4 Density Matrix-General Equations ..................... 157
5.5 The Rotating Coordinate Transfonnation ................. 165
5.6 Spin Echoes Using the Density Matrix ................... 169
5.7 The Response to a c5-Function .......................... 174
5.8 The Response to a 7r /2 Pulse: Fourier Transfonn NMR ..... 179
5.9 The Density Matrix of a Two-Level System .............. 186
5.10 Density Matrix-An Introductory Example ............... 190
5.11 Bloch-Wangsness-Redfield Theory ...................... 199
5.12 Example of Redfield Theory ........................... 206
5.13 Effect of Applied Alternating Fields ..................... 215
6. Spin Thmperature in Magnetism and in Magnetic Resonance 219
6.1 Introduction ........................................ 219
6.2 A Prediction from the Bloch Equations .................. 220
6.3 The Concept of Spin Temperature in the Laboratory Frame
in the Absence of Alternating Magnetic Fields ....... ,'.... 221
6.4 Adiabatic and Sudden Changes ......................... 223
6.5 Magnetic Resonance and Saturation ..................... 231
6.6 Redfield Theory Neglecting Lattice Coupling ............. 234
6.6.1 Adiabatic Demagnetization in the Rotating Frame ... 235
6.6.2 Sudden Pulsing ............................... 237
6.7 The Approach to Equilibrium for Weak HI ............... 239
6.8 Conditions for Validity of the Redfield Hypothesis ......... 241
6.9 Spin-Lattice Effects .................................. 242
6.10 Spin Locking. TIll' and Slow Motion .................... 244
7. Double Resonance ........................................ 247
7.1 What Is Double Resonance and Why Do It? .............. 247
7.2 Basic Elements of the Overhauser-Pound Family
of Double Resonance ................................. 248
7.3 Energy Levels and Transitions of a Model System ......... 250
7.4 The Overhauser Effect ................................ 254
7.5 The Overhauser Effect in Liquids: The Nuclear
Overhauser Effect ................................... 257
7.6 Polarization by Forbidden Transitions: The Solid Effect ..... 264
7.7 Electron-Nuclear Double Resonance (ENOOR) ............ 266
VIII
7.8 Bloembergen's Three-Level Maser ...................... 269
7.9 The Problem of Sensitivity ............................ 270
7.10 Cross-Relaxation Double Resonance .................... 271
7.11 The Bloembergen-Sorokin Experiment ................... 275
7.12 Hahn's Ingenious Concept ............................. 277
7.13 The Quantum Description ............................. 279
7.14 The Mixing Cycle and Its Equations .................... 283
7.15 Energy and Entropy .................................. 287
7.16 The Effects of Spin-Lattice Relaxation ................... 289
7.17 The Pines-Gibby-Waugh Method of Cross Polarization ..... 293
7.18 Spin-Coherence Double Resonance-Introduction .......... 295
7.19 A Model System-An Elemen~ary Experiment:
The S-Hip-Only Echo ................................ 296
7.20 Spin Decoupling ..................................... 303
7.21 Spin Echo Double Resonance .......................... 311
7.22 Two-Dimensional Ff Spectra-The Basic Concept ......... 319
7.23 Two-Dimensional Ff Spectra-Line Shapes .............. 324
7.24 Fonnal Theoretical Apparatus I - The Time Development
of the Density Matrix ................................ 325
7.25 Coherence Transfer .................................. 331
7.26 Fonnal Theoretical Apparatus II - The Product Operator
Method .................. .......................... 344
7.27 The Jeener Shift Correlation (COSY) Experiment .......... 350
7.28 Magnetic Resonance Imaging .......................... 357
8. Advanced Concepts in Pulsed Magnetic Resonance . . . . . . . . . . . . . . 367
8.1 Introduction ........................................ 367
8.2 The Carr-Purcell Sequence ............................ 367
8.3 The Phase Alternation and Meiboom-Gill Methods ......... 369
8.4 Refocusing Dipolar Coupling .......................... 371
8.5 Solid Echoes ........................................ 371
8.6 The Jeener-Broekaert Sequence for Creating Dipolar Order .. 380
8.7 The Magic Angle in the Rotating Frame-
The Lee-Goldburg Experiment ......................... 384
8.8 Magic Echoes ....................................... 388
8.9 Magic Angle Spinning ................................ 392
8.10 The Relation of Spin-Hip Narrowing to Motional Narrowing 406
8.11 The Fonnal Description of Spin-Hip Narrowing ........... 409
8.12 Observation of the Spin-Hip Narrowing ................. 416
8.13 Real Pulses and Sequences ............................ 421
8.13.1 Avoiding a z-Axis Rotation ..................... 421
8.13.2 Nonideality of Pulses .......................... 422
8.14 Analysis of and More Uses for Pulse Sequence ........... 423
IX
