Spin-lattice relaxation in cuprate superconductors

This presentation gives a personal review of nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spin-lattice relaxation studies in cuprate superconductors mainly dealing with the YBa₂Cu₄O₈ compound with many examples from the Zürich laboratory. The studies were performed in both the normal and the superconducting state with various NMR isotopes (e.g.,¹⁷O,^63,65Cu,^135,137Ba). The relatively broad signals were mostly obtained by a phase-alternating add-subtract spin-echo technique. We will discuss the general behavior of spin-lattice relaxation in the normal state and the calculation of the dynamic spin including an approach (on the basis of thet-J model) to calculate the relaxation for plane copper, oxygen, and yttrium. An application of the Luttingerliquid model to the relaxation of chain copper in YBa₂Cu₃O₇ and YBa₂Cu₄O₈ is also given. We then will deal with characteristic features of the YBa₂Cu₄O₈ structure: the spin gap, an electronic crossover in the normal state, the single-spin fluid model, and the d-wave pairing.     

Spin-lattice relaxation measurements in lithium acetate revisited

The Zeeman spin-lattice relaxation is measured in a single crystal and in powdered samples of lithium acetate (CH₃COOLi·2D₂O). Measurements have also been performed in powdered samples of lithium acetate which contain 50% and 95% of CD₃-groups besides the CH₃-groups. A non-exponential behaviour, i.e. time dependence, of the Zeeman spin-lattice relaxation is clearly observed at temperatures above the T₁-minimum in all samples. The results are explained within the framework of the symmetry-restricted spin-diffusion model of Emid and Wind.     

Spin-lattice relaxation of nearest neighbor ortho-hydrogen pairs

Specially chosen pulse sequences have been used to isolate the contribution to the nuclear magnetic resonance signal from nearest neighbor oH₂ molecules. Measurements of the rotational diffusion were shown to be consistent with earlier measurements where only oH₂ pairs or only isolated singles could be observed. It was found that the pair magnetization so obtained did not relax exponentially.     

Spin-lattice relaxation and dynamic polarization of protons in ethyleneglycol-methanol samples

We report measurements of nuclear spin-lattice relaxation and dynamic polarization of protons in ethyleneglycol-alcohol mixtures at 9 kG and 4·2 K and 1·3 K. Comparison of experimental results with a proposed model of spin-lattice relaxation indicates that the role of dipolar and exchange reservoirs of paramagnetic ions in nuclear relaxation is not necessarily negligible, particularly in the presence of high concentration of paramagnetic impurities. The influence of methanol is to enhance the dynamic polarization of protons compared to pure ethyleneglycol, in the most favourable cases by almost 50% in our experimental conditions.     

Spin-lattice relaxation of Fe nuclei in yttrium iron garnet

Pulse measurements of T₁ for ⁵⁷Fe nuclei in very pure, single crystals of YIG are reported. The temperature was varied from 2° to 292°K, and the externally applied field ranged from 0 to 6000 Oe. The temperature variation of T₁ is quite strong, being three orders of magnitude in the range 2°–40°K. At constant temperature, T₁ changed approximately one order of magnitude between saturation field and 6000 Oe. The data are compared with the results of a calculation by Beeman and Pincus, in which a second-order Raman process and the three-magnon process are assumed to predominate below 50°K. Agreement is only qualitative, the experimental values of T₁ being larger than predicted. At 4.2°K in zero field, it is found that a polycrystalline sample containing particles of ≈ 5 × 10⁻⁴ cm dia. has a value of 1/T₁ which is some two orders of magnitude larger than for a macroscopic crystal. The presence of a relaxation mechanism associated with surface effects is suggested.     

19F Spin-lattice relaxation and stable radicals in radiation-modified fluoropolymers

Fluorine-19 spin-lattice relaxation of electron-beam-irradiated poly(tetrafluoroethylene) (PTFE) has been investigated in the temperature range from 250 to 315 K. As shown before, in the initial step, radicals are produced by the electron-beam irradiation and chain scission takes place. The concentrations of radicals and chain end groups after irradiation of PTFE strongly depend on the irradiation conditions. Radicals like other paramagnetic species decrease the spin-lattice relaxation times. In addition, decreased polymer chain lengths shift theT ₁ minimum to lower temperatures. Tetrafluorosuccinic acid in solution was used as a model system and paramagnetic copper sulphate CuSO₄ added to quantify the effect on the relaxation times. The shift of the minima inT ₁ versus temperature in PTFE are compared with the chain length determined from high-resolution solid-state nuclear magnetic resonance spectra and with the concentration of paramagnetic species.     

Spin-lattice relaxation times of rare earth ions in binary nitrates

The Van Vleck method is used with the point-charge model to calculate the spin-lattice relaxation times of the Ce³⁺ ion in binary nitrates. Normal coordinates are found for the icosahedral XY₁₂ complex containing the paramagnetic ion and its nearest neighborhood. The theoretical transition probabilities for the purely ionic model turn out to be slightly above the experimental results, so covalent effects are important.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 8, pp. 31–37, August, 1969.The author thanks L. K. Aminov for supervision of and assistance in this study.     

Spin-lattice relaxation in solid 3He in weak magnetic fields

Spin-lattice relaxation times T ₁ were measured for solid ³He at temperatures of 0.22 to 0.73 K in a 44-Oe magnetic field. An increase in T ₁ at temperatures higher than approximately 0.4 K was related to switching on the vacancy mechanism of atomic mobility in the crystal. At a melting curve minimum, in the region of predominance of exchange motions of atoms in the crystal, measurements of T ₁ were performed in magnetic fields of 2 to 71 Oe. The data obtained in fields higher than 5 Oe were in agreement with the Cowan-Fardis theory.     

Spin-lattice relaxation enhancement in liquid gallium confined within nanoporous matrices

Nuclear spin relaxation for liquid gallium embedded into nanoporous matrices was found to accelerate remarkably compared to the bulk melt. NMR measurements on two gallium isotopes showed that the dominant mechanism of relaxation was changed from magnetic to quadrupolar and the relation rate depended on the Larmor frequency. The correlation time of electric field gradient fluctuations was estimated using data for quadrupolar relaxation contribution and was found to increase drastically compared to bulk, which corresponded to slowing down mobility in confined liquid gallium.     

Spin-lattice relaxation and magnetization transfer in intracranial tumors in vivo: Effects of Gd-DTPA on relaxation parameters

Spin-lattice relaxation time T₁ and relaxation parameters in magnetization transfer (MT) imaging were measured in 11 intracranial tumors before and after injection of Gd-DTPA at 0.1 T by using the inversion recovery method and the saturation transfer technique, respectively. Preinjection T₁ relaxation times of the tumors were longer than those of white matter, but after Gd-enhancement the relaxation times of most tumors were in the same range as those of white matter. Gd-DTPA shortened the apparent relaxation time in the presence of off-resonance saturation pulse (T_1α) due to marked shortening of the relaxation time of mobile water (T_1w). Gd-DTPA decreased the magnetization transfer contrast (MTC) but did not influence on the magnetization transfer rate (R_wm). The parameters MTC and R_wm differed clearly between Gd-enhanced tumors and normal brain, whereas the relaxation time T_1α was in many Gd-enhanced tumors in the same range as in normal brain.     

Spin-lattice relaxation by tunnelling motions of methyl groups in some organic compounds

The proton spin-lattice relaxation times, T₁, of methyl groups in (CH₃CO)₂O, CH₃COCl, CH₃ COBr and (CH₃)₂S₂ have been measured below melting points at 52 MHz. The observed T₁ minima display the presence of tunnelling rotation. From the fit of the experimental results the ground, the first excited state tunnelling frequencies and the energy difference between the ground and the first excited states of the compounds have been estimated.     

Spin-lattice relaxation of the O2 − molecule-ion in the potassium halides

An experimental and theoretical study of the spin-lattice relaxation (SLR) of the O₂ ^? molecule-ion in the potassium halides has been made. The SLR rate was measured by several methods between 1.32°K and 36°K with a 3 cm. ESR spectrometer. The results indicate a one phonon process with a large anisotropy dominates forT<2°K.T ₁ is much longer for the magnetic field parallel to the molecular axis. Detailed theoretical calculations indicate a new SLR process, namely phonon-induced libration of the molecular axis, can probably explain the field parallel case. The Van Vleck SLR process can account for the field-perpendicular case.     

Spin-lattice relaxation in hyperfine-coupled systems: Applications to interstitial diffusion and molecular dynamics

The solid state diffusion of hydrogen, or of its pseudo-isotope muonium, provides an interesting example of spin-lattice relaxation in a 2-spin, 4-level system. The local field experienced by the interstitial atom fluctuates as it moves, inducing transitions between the coupled electron and nuclear spin states. Rate equations governing the populations of these states may be solved numerically to simulate the different relaxation functions which would be displayed by ESR, ENDOR and μSR spectroscopies and to assist in extracting motional correlation times from the experimental data. Spin relaxation in molecular radicals may be treated similarly, with different selection rules for different mechanisms: this paper treats the spin rotation mechanism and perturbation to anisotropic or isotropic components of the hyperfine interaction, caused by inter or intra-molecular motion. Conventional magnetic resonance monitors the population differences appropriate to particular transitions; only in sufficiently high fields do these distinguish the electronic and nuclear response. Muon spin relaxation is remarkable in separating out the nuclear spin projection whatever the degree of mixing of the spin states,via the asymmetry in the muon radioactive decay. Experimentally it has the advantage that measurements can be made over a wide range of field, from null external field up to thelevel crossing where the relaxation rate exhibits a striking peak.     

Spin-lattice relaxation as a function of chain position in perdeuterated potassium palmitate

Using the quadrupolar echo Fourier transform technique (Davis et al., Chem. Phys. Lett.42, 390 (1976)), T₁ has been measured, in a sample of 70% potassium palmitate (d₃₁)/30% H₂O, as a function of chain position and temperature in the L_α liquid-crystalline phase. At temperatures near the transition from the liquid-crystal to the gel phase, T₁ is roughly constant for the first eight or nine chain positions but increases rapidly on moving further out along the chain. As the temperature is increased the relaxation times for all positions increase but those nearer the head group increase more rapidly, resulting, of temperatures above ∼100°C, in a minimum in the plot of T₁ versus chain position at the center of the chain (the 8 or 9 position). These results are in general accord with the temperature dependence of chain disorder (Davis and Jeffrey, Chem. Phys. Lipids20, 87 (1977) and offer some suggestions on the kind of model required to explain relaxation in these systems.     

Spin-lattice relaxation in HF and NH3 doped ice and the outdiffusion of impurities

T₁ measurements have been done on pure, NH₃ doped and HF doped ice crystals. Three relaxation processes can be distinguished: a low temperature process, an extrinsic and an intrinsic process at high temperatures with activation energies of 0.08 eV, 0.35 eV and 0.62 eV respectively. Vested vacancies are proposed as defects effective in the low temperature process. The extrinsic high temperature process is due to vacancies which are formed by shifting a HF molecule to an interstitial site. Schottky defects are responsible for the intrinsic high temperature relaxation mechanism. Outdiffusion of HF is found to occur in concentration steps and at high concentrations by an interstitial mechanism.