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Journal of the Physical Society of Japan

Effects of Magnetic Dipolar Interaction on Two-Quantum Free Decay in a Solid

Hiroshi Hatanaka, Tsuneo Hashi

Published Nov 1, 1981• 7 citations
Publisher

Abstract

Effects of magnetic dipolar interaction between like nuclei on two-quantum (TQ) free decay were examined in a multi-level NMR system, Al in Al 2 O 3 . TQ free decay was observed using a TQ π/2-pulse followed by a probe pulse. The effect of probe pulse was carefully examined to deduce the intrinsic decay time of the TQ coherence. The second moments for two- and three-quantum transitions were calculated. The observed decay time is in good agreement with that obtained from the calculated second moment by assuming Gaussian decay. Basic equations for TQ resonance are also presented.

DOI
10.1143/jpsj.50.3629

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Effects of magnetic dipolar interaction between like nuclei on two-quantum (TQ) free decay were examined in a multi-level NMR system, Al in Al 2 O 3 . TQ free decay was observed using a TQ π/2-pulse followed by a probe pulse. The effect of probe pulse was carefully examined to deduce the intrinsic decay time of the TQ coherence. The second moments for two- and three-quantum transitions were calculated. The observed decay time is in good agreement with that obtained from the calculated second moment by assuming Gaussian decay. Basic equations for TQ resonance are also presented.
The phenomenon of transfer of coherence and the effect of level shift caused by two-quantum (TQ) excitation were studied on 27Al^{27}\mathrm{Al}27Al nuclei in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​. Transfer of coherence between two single-quantum (SQ) transitions and that between SQ and three-quantum transitions were examined. It was observed that the coherences transfer periodically with frequency equal to one-half the TQ transient nutation frequency accompanied by phase shifts caused by the level shift. Experimental results are in good agreement with theoretical predictions. The effect of magnetic dipole interaction was also studied. A precise measurement was made on the shift of TQ resonance frequency and it was confirmed that no shift exists on the TQ resonance frequency contrary to the prediction based on the three-level model.
Abstract In the past decade, nuclear magnetic resonance (NMR) has been actively used to study the basic principles of quantum computers. It is assumed that quantum correlations play a significant role in their performance. They exist at both low and high temperatures. At the same time, the time correlation functions of nuclear spin systems of solids determine the observed signals in traditional NMR implementations. The separation of such signals into quantum and classical components has not previously been carried out and will be performed in this study for the most important of the correlational functions observed in magnetic resonance: the free induction decay (FID).
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
A change in the time dependence of the second moment of the distribution of intensities of coherences with various orders in the spectrum of multiple-quantum NMR in a solid at the inclusion of an inhomogeneous magnetic field in the effective interaction is studied. Both the secular dipole–dipole and nonspecular twoquantum interactions are considered as nucleus–nucleus interactions, which correspond to traditional experimental realizations. It is shown that, with an increase in the magnitude of the inhomogeneous field, an exponential increase in the second moment of multiple-quantum NMR with time changes to a power-law increase. The results obtained in this work indicate that this second moment, which determines the average number of dynamically correlated spins, can be used as a convenient characteristic for studying a transition to a many-body localized state.
Two-quantum rotary echoes predicted by Bloch like equations for two-quantum transition have been observed in a multi-level NMR system of 27 Al nuclei in Al 2 O 3 . An rf field exactly at resonance to the two-quantum transition ( Δ m =2) was turned on at t =0 and its phase was shifted by 90° at t =τ. The echo at t =2τ was observed by using the technique of transfer of coherence reported previously. Characteristic dependence of the echo width upon inhomogeneity of rf field amplitude was confirmed experimentally.