General Approach to the Line-Shape Problem in Nuclear-Magnetic-Resonance Spectra

Lado, F.; Memory, J. D.; Parker, G. W.

doi:10.1103/physrevb.4.1406

Cited by 93 publications

(19 citation statements)

References 22 publications

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“…This can be gleaned from a set of coupled linear differential equations governing (Liouvillian) evolution of multi-spin correlation functions, known for quite some time. 34 Crucially, these equations are completely specified by the moments of the NMR lineshape. 35 Unfortunately, these moments are not particularly well known beyond a few low orders, 36 so there is no closed form solution of this problem in the dipolar case of interest here.…”

Section: Resultsmentioning

confidence: 99%

Multispin correlations and pseudothermalization of the transient density matrix in solid-state NMR: Free induction decay and magic echo

2012

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Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately “rewind” the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analysis based on mean magnetization we use a phase encoding technique to measure the growth of spin correlations in the density matrix at different points in time following magic echoes of varied durations and compare the results to those obtained during a free induction decay (FID). While considerable differences are documented at short times, the long-time behavior of the density matrix appears to be remarkably universal among the types of initial states considered – simple low order multispin correlations are observed to decay exponentially at the same rate, seeding the onset of increasingly complex high order correlations. This manifestly athermal process is constrained by conservation of the second moment of the spectrum of the density matrix and proceeds indefinitely, assuming unitary dynamics.

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Section: Resultsmentioning

confidence: 99%

Multispin correlations and pseudothermalization of the transient density matrix in solid-state NMR: Free induction decay and magic echo

2012

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“…͑5͒ has n-spin correlations. There has been much theoretical effort [1][2][3][4][5][6][7][8] to predict the shape of the FID in calcium fluoride ͑CaF 2 ͒. Calcium fluoride is a standard test system for spin dynamics as the 19 F ͑spin-1 / 2͒ nuclei are 100% abundant and form a simple cubic lattice.…”

Section: ͑5͒mentioning

confidence: 99%

“…This is a classic problem in spin dynamics and has been well studied since the early days of NMR. [1][2][3][4][5][6][7][8][9][10][11] At the magnetic fields typically used in NMR experiments ͑Ͻ20 T͒, the spin system is highly mixed at room temperature, and its equilibrium state is represented by a thermal density matrix. If the external Zeeman field is much stronger than the internal dipolar fields of the sample, the normalized deviation density matrix in thermal equilibrium can be approximated as…”

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confidence: 99%

Multispin dynamics of the solid-state NMR free induction decay

et al. 2005

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We present a new experimental investigation of the NMR free induction decay ͑FID͒ in a lattice of spin-1 / 2 nuclei in a strong Zeeman field. Following a / 2 pulse, evolution under the secular dipolar Hamiltonian preserves the coherence number in the Zeeman eigenbasis, but changes the number of correlated spins in the state. The observed signal is seen to decay as single-spin, single-quantum coherences evolve into multiple-spin coherences under the action of the dipolar Hamiltonian. In order to probe the multiple-spin dynamics during the FID, we measured the growth of coherence orders in a basis other than the usual Zeeman eigenbasis. This measurement provides the first direct experimental observation of the growth of coherent multiple-spin correlations during the FID. Experiments were performed with a cubic lattice of spins ͑

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“…The line-shape of the NMR spectrum 115 arises from the variation of the local field at a given nucleus because of the interaction with nearby neighbors. The inhomogeneity of the applied magnetic field may also increase the width of the line.…”

Section: Host Nuclear Spin Diffusion In Dilute Alloysmentioning

confidence: 99%

Statistical Theory of Spin Relaxation and Diffusion in Solids

Kuzemsky

2006

J Low Temp Phys

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A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed.It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.

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General Approach to the Line-Shape Problem in Nuclear-Magnetic-Resonance Spectra

Cited by 93 publications

References 22 publications

Multispin correlations and pseudothermalization of the transient density matrix in solid-state NMR: Free induction decay and magic echo

Multispin correlations and pseudothermalization of the transient density matrix in solid-state NMR: Free induction decay and magic echo

Multispin dynamics of the solid-state NMR free induction decay

Statistical Theory of Spin Relaxation and Diffusion in Solids

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