Relaxation (NMR)

About: Relaxation (NMR) is a research topic. Over the lifetime, 29342 publications have been published within this topic receiving 689851 citations.

Electron Spin Resonance: Elementary Theory and Practical Applications

Abstract: 1 Basic Principles of Electron Spin Resonance.- 1-1 Introduction.- 1-2 Energy of Magnetic Dipoles in a Magnetic Field.- 1-3 Quantization of Angular Momentum.- 1-4 Relation between Magnetic Moments and Angular Momenta.- 1-5 Interaction of Magnetic Dipoles with Electromagnetic Radiation.- 1-6 Characteristics of the g Factor.- Problems.- 2 Basic Instrumentation of Electron Spin Resonance.- 2-1 A Simple ESR Spectrometer.- 2-2 Choice of Experimental Conditions.- 2-3 Typical Spectrometer Arrangement.- 2-3a The Cavity System.- 2-3b The Source.- 2-3c The Magnet System.- 2-3d The Modulation and Detection Systems.- 2-4 Line Shapes and Intensities.- References.- Problems.- 3 Nuclear Hyperfine Interaction.- 3-1 Introduction.- 3-2 Origins of the Hyperfine Interaction.- 3-3 Energy Levels of a System with One Unpaired Electron and One Nucleus with I = 1/2.- 3-4 The Energy Levels of a System with S = 1/2 and I=1.- 3-5 Summary.- Problems.- 4 Analysis of Electron Spin Resonance Spectra of Systems in the Liquid Phase.- 4-1 Introduction.- 4-2 Energy Levels of Radicals Containing a Single Set of Equivalent Protons.- 4-3 ESR Spectra of Radicals Containing a Single Set of Equivalent Protons.- 4-4 ESR Spectra of Radicals Containing Multiple Sets of Equivalent Protons.- 4-5 Hyperfine Splittings from Other Nuclei with I = 1/2.- 4-6 Hyperfine Splittings from Nuclei with I > 1/2.- 4-7 Useful Rules for the Interpretation of Spectra.- 4-8 Other Problems Encountered in the ESR Spectra of Free Radicals.- 4-9 Second-order Splittings.- Problems.- 5 Interpretation of Hyperfine Splittings in ?-type Organic Radicals.- 5-1 Introduction.- 5-2 Molecular Orbital Energy Calculations.- 5-3 Unpaired Electron Distributions.- 5-4 The Benzene Anion and Its Derivatives.- 5-5 The Anions and Cations of the Polyacenes.- 5-6 Other Organic Radicals.- 5-7 Summary.- References-HMO Method.- Problems.- 6 Mechanism of Hyperfine Splittings in Conjugated Systems.- 6-1 Origin of Proton Hyperfine Splittings.- 6-2 Sign of the Hyperfine Splitting Constant.- 6-3 Extension of the Molecular Orbital Theory to Include Electron Correlation.- 6-4 Alkyl Radicals-A Study of Q Values.- 6-5 The Effect of Excess Charge on the Parameter Q.- 6-6 Methyl-proton Hyperfine Splittings-Hyperconjugation.- 6-7 Hyperfine Splitting by Nuclei Other than Protons.- Problems.- 7 Anisotropic Interactions in Oriented Systems with S = 1/2.- 7-1 Introduction.- 7-2 A Simple Example of Anisotropy of g.- 7-3 Systems with Orthorhombic or Lower Symmetry.- 7-4 Experimental Determination of the g Tensor in Oriented Solids.- 7-5 Anisotropy of the Hyperfine Coupling.- 7-6 Origin of the Anisotropic Hyperfine Interaction.- 7-7 Determination of the Elements of the Hyperfine Tensor.- 7-8 Corrections to Hyperfine Tensor Elements.- 7-9 Line Shapes in Nonoriented Systems.- 7-9a Line Shapes for Systems with Axial Symmetry.- 7-9b Hyperfine Line Shapes for an Isotropic g Factor, S = 1/2 and One Nucleus with I = 1/2.- Problems.- 8 Interpretation of the ESR Spectra of Systems in the Solid State.- 8-1 Generation of Free Radicals in Solids.- 8-2 ?-type Organic Radicals.- 8-2a Identification.- 8-2b Aliphatic Radicals.- 8-2c Radicals from Unsaturated Organic Compounds.- 8-3 ?-type Organic Radicals.- 8-4 Inorganic Radicals.- 8-4a Identification of Radical Species.- 8-4b Structural Information.- 8-5 Point Defects in Solids.- 8-5a Generation of Point Defects.- 8-5b Substitutional or Interstitial Impurities.- 8-5c Trapped-electron Centers.- 8-5d Trapped-hole Centers.- References.- Problems.- 9 Time-dependent Phenomena.- 9-1 Introduction.- 9-2 Spin-lattice Relaxation Time.- 9-3 Other Sources of Line Broadening.- 9-3a Inhomogeneous Broadening.- 9-3b Homogeneous Broadening.- 9-4 Mechanisms Contributing to Line Broadening.- 9-4a Electron Spin-Electron Spin Dipolar Interactions.- 9-4b Electron Spin-Nuclear Spin Interactions.- 9-5 Chemical Line-broadening Mechanisms.- 9-5a General Model.- 9-5b Electron-spin Exchange.- 9-5c Electron Transfer.- 9-5d Proton Exchange.- 9-6 Variation of Linewidths within an ESR Spectrum.- 9-6a Time-dependent Hyperfine Splitting for a Single Nucleus.- 9-6b Time-dependent Hyperfine Splittings for Systems with Several Nuclei.- 9-7 Spectral Effects of Slow Molecular Tumbling Rates.- 9-8 Spectral Effects of Rapid Molecular Tumbling Rates-Spin-rotational Interaction.- 9-9 Summary.- Problems.- 10 Energy-level Splitting in Zero Magnetic Field The Triplet State.- 10-1 Introduction.- 10-2 The Spin Hamiltonian for S = 1.- 10-3 State Energies for a System with S = 1.- 10-4 The Spin Eigenfunctions for a System with S=1.- 10-5 Electron Spin Resonance of Triplet-state Molecules.- 10-6 Line Shapes for Randomly Oriented Systems in the Triplet State.- 10-7 The "?MS = 2" Transitions.- 10-8 Triplet Ground States.- 10-9 Carbenes and Nitrenes.- 10-10 Thermally Accessible Triplet States.- 10-11 Biradicals Exchange Interaction.- 10-12 Systems with S > 1.- Problems.- 11 Transition-metal Ions. I..- 11-1 States of Gaseous Transition-metal Ions.- 11-2 Removal of Orbital Degeneracy in Crystalline Electric Fields.- 11-3 The Crystal Field Potential.- 11-4 The Crystal Field Operators.- 11-5 Crystal Field Splittings of States for P-, D- and F-state Ions.- 11-6 Spin-orbit Coupling and the Spin Hamiltonian.- 11-7 D- and F-state Ions with Orbitally Nondegenerate Ground States.- 11-7a D-state Ions 3d1(ttdl + ttgl) in 3d1(cubal + ttgl) 3d7(1s)(oct + ttgl) 3d9(oct + ttgl).- 11-7b F-state Ions 3d8(oct) 3d2(ttdl) 3d8(oct + ttgl) 3d2(ttdl + ttgl) 3d3(oct) 3d7(hs)(ttdl) 3d3(oct + ttgl).- 11-8 S-state Ions 3d5(hs)(oct) 3d5(hs)(oct + ttgl).- Problems.- 12 Transition-metal Ions. II. Electron Resonance in the Gas Phase.- 12-1 Ions in Orbitally Degenerate Ground States.- 12-1a D-state Ions 3d1(oct) 3d1(oct + ttgl), ? > > ? > > ? 3d1(oct + ttgl), ? > > ? ? ? 3d1(oct + trgl) 3d5(1s)(oct + ttgl) 3d9(ttdl + ttgl) 3d6(hs)(oct).- 12-1b F-state Ions 3d2(oct) 3d2(oct + trgl) 3d7(hs)(oct).- 12-1c Jahn-Teller Splitting 3d9(oct) 3d7(1s)(oct).- 12-2 Elements of the 4d and 5d Groups (Palladium and Platinum Groups).- 12-3 The Rare-earth Ions.- 12-4 The Actinide Ions.- 12-5 Deficiencies of the Point-charge Crystal Field Model Ligand-Field Theory.- 12-6 Electron Resonance of Gaseous Free Radicals.- 12-7 The Practical Interpretation of ESR Spectra of Ions in the Solid State.- Problems.- 13. Double-resonance Techniques.- 13-1 An ENDOR Experiment.- 13-2 Energy Levels and ENDOR Transitions.- 13-3 Relaxation Processes in Steady-state ENDOR.- 13-4 An ENDOR Example: The F Center in the Alkali Halides.- 13-5 ENDOR in Liquid Solutions.- 13-6 ENDOR in Powders and Nonoriented Solids.- 13-7 Electron-electron Double Resonance.- Problems.- 14. Biological Applications of Electron Spin Resonance.- 14-1 Introduction.- 14-2 Substrate Free Radicals.- 14-3 Flavins and Metal-free Flavoproteins.- 14-4 Photosynthesis.- 14-5 Heme Proteins.- 14-6 Iron-sulfur Proteins.- 14-7 Spin Labels.- Appendix A. Mathematical Operations.- A-1 Complex Numbers.- A-2 Operator Algebra.- A-2a Properties of Operators.- A-2b Eigenvalues and Eigenfunctions.- A-3 Determinants.- A-4 Vectors: Scalar, Vector, and Outer Products.- A-5 Matrices.- A-5a Addition and Subtraction of Matrices.- A-5b Multiplication of Matrices.- A-5c Special Matrices and Matrix Properties.- A-5d Dirac Notation for Wave Functions and Matrix Elements.- A-5e Diagonalization of Matrices.- A-6 Tensors.- A-7 Perturbation Theory.- A-8 Euler Angles.- Problems.- Appendix B. Quantum Mechanics of Angular Momentum.- B-1 Introduction.- B-2 Angular-momentum Operators.- B-3 The Commutation Relations for the Angular-momentum Operators.- B-6 Angular-momentum Matrices.- B-7 Addition of Angular Momenta.- B-8 Summary.- Problems.- C-1 The Hamiltonian for the Hydrogen Atom.- C-2 The Spin Eigenfunctions and the Energy Matrix for the Hydrogen Atom.- C-3 Exact Solution of the Determinant of the Energy Matrix (Secular Determinant).- C-4 Selection Rules for High-field Magnetic-dipole Transitions in the Hydrogen Atom.- C-5 The Transition Frequencies in Constant Magnetic Field with a Varying Microwave Frequency.- C-6 The Resonant Magnetic Fields at Constant Microwave Frequency.- C-7 Calculation of the Energy Levels of the Hydrogen Atom by Perturbation Theory.- C-8 Wave Functions and Allowed Transitions for the Hydrogen Atom at Low Magnetic Fields.- Problems.- Appendix D. Experimental Methods Spectrometer Performance.- D-1 Sensitivity.- D-2 Factors Affecting Sensitivity and Resolution.- D-2a Modulation Amplitude.- D-2b Modulation Frequency.- D-2c Microwave Power Level.- D-2d The Concentration of Paramagnetic Centers.- D-2e Temperature.- D-2g Microwave Frequency.- D-2h Signal Averaging.- D-3 Absolute Intensity Measurements.- Problems.- Table of Symbols.- Name Index.

Resonant Spin Amplification in n-Type GaAs

Abstract: Extended electron spin precession in $n$-type GaAs bulk semiconductors is directly observed by femtosecond time-resolved Faraday rotation in the Voigt geometry. Synchronous optical pumping of the spin system amplifies and sustains spin motion, exposing a regime where spin lifetimes increase tenfold at low fields and exceed 100 ns at zero field. Precise studies in field and temperature provide clues to the relevant electron relaxation mechanisms, indicating a strong dependence on doping concentration.

Strong exchange and magnetic blocking in N₂³⁻-radical-bridged lanthanide complexes.

Abstract: Single-molecule magnets approach the ultimate size limit for spin-based devices. These complexes can retain spin information over long periods of time at low temperature, suggesting possible applications in high-density information storage, quantum computing and spintronics. Notably, the success of most such applications hinges upon raising the inherent molecular spin-inversion barrier. Although recent advances have shown the viability of lanthanide-containing complexes in generating large barriers, weak or non-existent magnetic exchange coupling allows fast relaxation pathways that mitigate the full potential of these species. Here, we show that the diffuse spin of an N(2)(3-) radical bridge can lead to exceptionally strong magnetic exchange in dinuclear Ln(III) (Ln = Gd, Dy) complexes. The Gd(III) congener exhibits the strongest magnetic coupling yet observed for that ion, while incorporation of the high-anisotropy Dy(III) ion gives rise to a molecule with a record magnetic blocking temperature of 8.3 K at a sweep rate of 0.08 T s(-1).

A N23– Radical-Bridged Terbium Complex Exhibiting Magnetic Hysteresis at 14 K

Abstract: The synthesis and magnetic properties of three new N23– radical-bridged dilanthanide complexes, {[(Me3Si)2N]2(THF)Ln}2(μ-η2:η2-N2)− (Ln = Tb, Ho, Er), are reported. All three display signatures of single-molecule-magnet behavior, with the terbium congener exhibiting magnetic hysteresis at 14 K and a 100 s blocking temperature of 13.9 K. The results show how synergizing the strong magnetic anisotropy of terbium(III) with the effective exchange-coupling ability of the N23– radical can create the hardest molecular magnet discovered to date. Through comparisons with non-radical-bridged ac magnetic susceptibility measurements, we show that the magnetic exchange coupling hinders zero-field fast relaxation pathways, forcing thermally activated relaxation behavior over a much broader temperature range.

A Stable Pentagonal Bipyramidal Dy(III) Single-Ion Magnet with a Record Magnetization Reversal Barrier over 1000 K.

Abstract: Single-molecule magnets (SMMs) with a large spin reversal barrier have been recognized to exhibit slow magnetic relaxation that can lead to a magnetic hysteresis loop. Synthesis of highly stable SMMs with both large energy barriers and significantly slow relaxation times is challenging. Here, we report two highly stable and neutral Dy(III) classical coordination compounds with pentagonal bipyramidal local geometry that exhibit SMM behavior. Weak intermolecular interactions in the undiluted single crystals are first observed for mononuclear lanthanide SMMs by micro-SQUID measurements. The investigation of magnetic relaxation reveals the thermally activated quantum tunneling of magnetization through the third excited Kramers doublet, owing to the increased axial magnetic anisotropy and weaker transverse magnetic anisotropy. As a result, pronounced magnetic hysteresis loops up to 14 K are observed, and the effective energy barrier (Ueff = 1025 K) for relaxation of magnetization reached a breakthrough among the SMMs.