Low-field relaxation and the study of ultraslow atomic motions by magnetic resonance

Journal ArticleConventional resonance enables one to study motion of atoms by measurement of line width when the mean time r between jumps is less than 1/Aco, where Aa> is the rigid lattice line width, or by measurement of the spin-lattice relaxation time, Ti, when r ^ l / coo , where coo is the Larmor frequency. We describe a new technique applicable when T<TI. It is therefore applicable to the study of very slow motion. The method is analogous to measuring T\ with coo = 0. However, we are able to keep cu0 in the megacycle region by performing the experiments in the reference frame rotating at the Larmor frequency. Analysis of the technique requires solution of the problem of the effect of infrequent motion on the nuclear relaxation time when the applied static field is comparable to the local field. The relaxation time is then comparable to r, indicating that jumps are strong "collisions" for the spins. The case of strong "collisions" is not treated in the conventional treatment of Bloembergen, Purcell, and Pound. We solve the problem by use of the concept of spin temperature and the sudden approximation. Explicit formulas are given for the nuclear relaxation in the laboratory for weak static fields, and in the rotating frame for alternating fields of the order of or less than the local field. We treat both diffusional motion and molecular reorientation

79Br nuclear-quadrupole-resonance lineshape and Raman-induced spin-lattice relaxation in the incommensurate phase of β- ThBr4

Journal ArticleWe performed 7 9Br nuclear-quadrupole-resonance (NQR) line-shape and spin-lattice relaxation time measurements in the incommensurate (D system j8-ThBr4 over the temperature range 293-2.5 K. In addition, we extended the theory of the effects of Raman processes on amplitudon and phason spin-lattice relaxation in incommensurate systems by obtaining general expressions for the spectral densities and phason gap A^ that are valid at all temperatures in the / phase. By measuring Tx selectively for the different parts of the broadened NQR line in /3-ThBr4, we separately obtained the phason and amplitudon contributions, and TXA, respectively. A comparison between theory and the experimental data shows excellent agreement and demonstrates that spin-lattice relaxation in /?-ThBr4 is dominated by Raman processes. The phason gap A^ was determined to be 0.072+0.020 THz

Study of utraslow atomic motions by magnetic resonance

Journal ArticleMagnetic resonance has been widely used to study phenomena such as atomic diffusion and molecular reorientation. It is applicable when the mean time, r, between atomic jumps is either (a) sufficiently short to narrow the resonance line width or (b) of the correct magnitude to produce spin-lattice relaxation. Case (a) occurs when r is less than 1/Aco where Au> is the rigid lattice linewidth. Case (b) occurs when T is of the order of l/co0 , where oo0 is the Larmor frequency. Typically, case (a) is found when r < 100 /isec, case (b) when r ~ 10 ~ 8 sec. In this Letter we report a new, experimentally simple technique which enables us to study motions of a much slower rate, the criterion being roughly T < T 1 where T1 is the spin-lattice relaxation time

Observation of ultraslow translational diffusion in metallic lithium by magnetic resonance

Journal ArticleThe theory of a new magnetic-resonance technique for studying the ultra slow motion of atoms was presented in a previous paper. In this paper, we present its experimental confirmation for the case of translational diffusion in lithium metal. By this technique the mean time between atomic jumps r can be measured provided that r is less than the spin-lattice relaxation time Ti, permitting study of much slower rates of motion than previously has been possible using magnetic resonance. For lithium metal we have measured over nine orders of magnitude from r = 10- 9 sec to T = 1 sec, thereby extending by nearly five decades the results previously obtained by Holcomb and Norberg using conventional techniques. We have applied a new spin-temperature theory to the analysis of our low-temperature results in the range of its validity, TI>T>T2. By studying the variation of our relaxation time with the rf field strength Hi, we have unambiguously demonstrated the validity of the spin-temperature theory and the invalidity of perturbation theories in describing relaxation due to infrequent atomic motions in weak applied fields

31P NMR spin-lattice relaxation: structural glass dynamics in Rb1-x(ND4)xD2PO4

Journal ArticleWe performed 3 1P NMR measurements of the temperature-dependent spin-lattice relaxation time in several mixed single crystals of Rbi_x(ND4 ) xD2P04 [DRADP] having different ammonium concentration x (x =0.22, 0.44, 0.78) as well as in three pure single crystals (ND4)D2P04 [DADP], (NH4)H2P04 [ADP], and RbH2P04 [RDP]. The 3 1P NMR spin-lattice relaxation-time measurements in mixed crystals show that the phosphorus nuclei are strongly influenced by the gradual slowing down of the motions of protons in the nearby O-D • • • O acid bonds in the structural spin-glass states. In addition to a common Tl minimum observed in all ammonium-containing systems, a second Tl minimum is observed in the temperature region of the glass transition in mixed spin-glass systems but not in pure ADP, DADP, or RDP. We attribute this lower temperature Tx minimum to the extreme slowing down of the O-D • • • O intrabond motion, which is unique to the glass system. In addition, the correlation times and activation energies for the Tx minima in all samples were determined. A comparison between the pure and mixed systems reveals that the mixed system 7^ minimum must be fit to a distribution of correlation functions but that each pure system requires only a single correlation function. Furthermore, measurements on systems having x =0.78 and 0.22 show that 3 1P NMR can be used to determine the threshold concentrations that characterize the glass phase

Commensurability and defect-induced phason gaps in incommensurate systems

Journal ArticleThe phason energy gap has been observed to increase on going from the incommensurate to higher-order commensurate phases in the "devil's staircase" compound [N(CH3)4]2ZnCl4. The gap was determined via the phason-induced 1 4N spin-lattice relaxation contribution, which was obtained from the variation of the effective spin- lattice relaxation rate over the inhomogeneous incommensurate frequency distribution. Here, as well as in Rb2ZnCl4 and Rb2ZnBr4 , the phason gap in the incommensurate phase is defect induced

Dynamics of the pinned modulation wave in incommensurate bis (4-chlorophenyl) sulfone (BCPS)

Journal ArticleWe show that both the anomalously huge resonance-frequency dependence of the 3 5Cl nuclear quadrupole resonance (NQR) spin-lattice relaxation time in BCPS, reported here for the first time, and its anomalous temperature dependence can be explained by large-scale fluctuations of the pinned modulation wave instead of small-scale fluctuations (phasons and amplitudons). The results were obtained by measuring the laboratory (T1Q ) and rotating frame ( T 1QP ) 3 5Cl relaxation times. This is the first time that an effective resonance frequency dependence of the spin-lattice relaxation rate was measured in pure NQR

Nature of the incommensurate-paraelectric transition: a two dimensional exchange-difference NMR study

Journal Article87Rb two-dimensional exchange-difference NMR was used to study collective motions in the incommensurate (I) and paraelectric (P) phases of Rb2ZnCl4, which elucidate the nature of the I-P transition. We measured the cross-peak frequency displacement vs mixing time and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. The P phase results are identified as normal modes arising from simultaneous displacement of the Rb ions and rotations of the ZnCl4 between two sites, and these modes freeze out in the I phase to become the modulation wave

Thermal fluctuations and NMR spectra of incommensurate insulators

Journal ArticleThe effects of thermal order-parameter fluctuations on the NMR line shape of incommensurate systems are evaluated within the mean-field Landau theory and the results are compared with the 8 7Rb and 3 9K 1/2 -1/2 NMR spectra of Rb2ZnCl4 and K2Se04 just below the paraelectric-incommensurate transitions. We show that thermal fluctuations do not only reduce the effective incommensurate splitting as compared to the static case but also change the shape of the spectrum. In particular they remove the 8- function-like form of the two edge singularities in analogy to the Debye-Waller factor in x-ray scattering. Two-dimensional NMR separation techniques allow for a separate observation of static and dynamic incommensurate line shapes close to the paraelectric-incommensurate transition temperature Tj. The static inhomogeneously broadened NMR line shape results from the static distribution of quadrupole perturbed Zeeman frequencies, reflecting the frozen-out incommensurate modulation wave. The dynamic line shape reflects the time-dependent part of the electric quadrupole interaction resulting from phason and amplitudon thermal fluctuations of the modulation wave. Close to Tl these fluctuations become so low in frequency that they influence the line shape. A precise determination of 77 can be obtained from the maximum in the width of the dynamic line shape

NMR spectra and relaxation in incommensurate systems in the presence of a devil's staircase

Journal ArticleThe possibility of discriminating true incommensurate phases from long period commensurate phases via NMR lineshape and spin-lattice relaxation measurements is discussed. The theoretical results are compared with experimental data in Rb2ZnCl4, Rb2ZnBr4, and [N(CH3)4]2ZnCl4. Devil's staircase effects seem to be in the majority of cases masked by defects