Application of superconducting quantum interference devices to nuclear magnetic resonance Ya. S. Greenberg Novosibirsk State Technical University, 630092 Novosibirsk 92, Russia Nuclear magnetic resonance (NMR) provides information in low polarizing fields that is hard to obtain in high fields. A new generation of sensitive NMR detectors, the superconducting quantum interference device (SQUID), provides a fresh approach to low-field NMR studies. The SQUID is an ideal detector for low-field NMR, since its response does not depend on signal frequency as is the case of conventional NMR spectrometers. This review describes the experimental and theoretical studies in which SQUIDs have been used for the detection of NMR. Particular attention is paid to the calculation of the signal-to-noise ratio of SQUID NMR spectrometers with various input configurations as compared to that of conventional ones. The application of SQUIDs to nuclear thermometry and to absolute field measurements are also discussed. A SQUID directly measures the longitudinal nuclear magnetization M z and the review discusses extensively what we call M z spectroscopy. [S0034-6861(98)00701-6] CONTENTS I. Introduction 175 II. General principles of NMR 176 A. Magnetic properties of matter 176 B. Magnetic properties of nuclei 177 C. Nuclear susceptibility 177 D. NMR in a system of free spins 177 1. Pulse excitation 178 2. The influence of field inhomogeneity 178 3. Spin echoes 179 E. NMR in a system of interacting spins. The Bloch formulation 179 1. Adiabatic passage of the resonance 181 2. Pulse excitation. Free induction decay 182 3. The influence of field inhomogeneity 182 4. Spin echoes 183 F. Signal-to-noise ratio of conventional NMR spectrometers; relative sensitivity 183 III. SQUID application to NMR 185 A. SQUID basics 185 1. The rf SQUID; white noise 186 2. The dc SQUID 187 a. White noise 187 b. Low-frequency noise 188 3. The SQUID as a magnetometer 189 4. The dc SQUID as a radio-frequency amplifier 190 5. Flux-locked feedback circuit 191 B. Detection of NMR by SQUIDs 191 1. Noise considerations in SQUID NMR spectrometers 193 2. Relative sensitivity of SQUID NMR spectrometers 194 3. Comparison of noise in SQUID and conventional spectrometers 195 4. SQUIDs as transverse magnetization detectors 197 a. Noise in transverse SQUID NMR spectrometers 198 b. Resolution of the transverse SQUID NMR spectrometer with a nonsuperconducting flux transformer 200 5. Number of spins detectable 200 6. Technical problems 201 7. Application of the SQUID magnetometer to nuclear thermometry 202 8. The SQUID NMR spectrometer as an absolute field magnetometer 203 IV. Low-field NMR spectroscopy 205 A. Introduction 205 B. Couplings relevant to low-field NMR spectroscopy 205 C. Low-field NMR of dipolar coupled nuclei; low- field line narrowing 206 D. Zero-field M z spectrum of dipolar coupled nuclei 207 1. General formalism 207 2. Examples 208 E. Low-field quadrupolar NMR 208 1. Introduction 208 2. Quadrupolar spectroscopy of half-integer spin nuclei 209 a. Selective excitation 210 b. Fast field zeroing 211 3. Quadrupolar spectroscopy of integer spin nuclei 211 a. Fast field zeroing 211 b. Nonselective pulse excitation 211 c. Double-resonance technique 212 F. Low-field NMR of liquids 213 G. Low-field M z spectrum of liquids 215 V. Conclusion 216 A. Low-field NMR in solids 217 B. Spin multiplets in liquids 217 C. NMR imaging and medical diagnostics 217 D. Application to metrology 218 Acknowledgments 218 References 218 I. INTRODUCTION Nuclear magnetic resonance (NMR) is a powerful tool for investigating the internal structure of matter in many fields. NMR is widely applied in condensed-matter phys- ics, analytical chemistry, biology, and medicine. Measurements in NMR generally use strong polariz- ing magnetic fields (usually more than 0.5 T). The rea- son for this is very simple. The signal intensity of con- ventional NMR spectrometers is proportional to the 175 Reviews of Modern Physics, Vol. 70, No. 1, January 1998 0034-6861/98/70(1)/175(48)/$24.60 © 1998 The American Physical Society