Temperature dependence of nuclear spin-lattice relaxation in the heavy-fermion superconducting state

Some features of the experimental data on nuclear spin relaxation time T₁ in the heavy-fermion superconducting state can be explained by taking into account the effect of the electron Zeeman energy. It is found that at intermediate temperatures the usual quasiparticle spin-flip scattering dominates, while at very low temperatures a new process, pair creation (annihilation), dominates and gives T^-1₁ ∝ T.     

Temperature dependence of the spin-lattice relaxation time for quadrupole nuclei under conditions of NMR line saturation

The contributions of different mechanisms of nuclear spin-lattice relaxation are experimentally separated for ⁶⁹Ga and ⁷¹Ga nuclei in GaAs crystals (nominally pure and doped with copper and chromium), ²³Na nuclei in a nominally pure NaCl crystal, and ²⁷Al nuclei in nominally pure and lightly chromium-doped Al₂O₃ crystals in the temperature range 80–300 K. The contribution of impurities to spin-lattice relaxation is separated under the condition of additional stationary saturation of the nuclear magnetic resonance (NMR) line in magnetic and electric resonance fields. It is demonstrated that, upon suppression of the impurity mechanism of spin-lattice relaxation, the temperature dependence of the spin-lattice relaxation time T₁ for GaAs and NaCl crystals is described within the model of two-phonon Raman processes in the Debye approximation, whereas the temperature dependence of T₁ for corundum crystals deviates from the theoretical curve for relaxation due to the spin-phonon interaction.     

Temperature dependence of the spin-lattice relaxation time in local triplet-excited states of a doped C60 fullerene crystal

The temperature dependence of the spin-lattice relaxation time of triplet-excited impurity centers of a C₆₀ fullerene crystal is investigated within the framework of the spin-phonon coupling mechanism which arises as a result of the admixture of rotational to translational motions of the molecules due to acoustic lattice vibrations. General expressions are obtained for the transition probabilities for the direct single-phonon and Raman two-phonon processes. The method of atom-atom potentials is used to carry out a concrete calculation of the spin-lattice relaxation time for an isotopic impurity in a C₆₀ crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1699–1702 (September 1997)     

Temperature dependence of nuclear magnetization and relaxation

The temperature dependences of nuclear magnetization and relaxation rates are reviewed theoretically and experimentally in order to quantify the effects of temperature on NMR signals acquired by common imaging techniques. Using common sequences, the temperature dependences of the equilibrium nuclear magnetization and relaxation times must each be considered to fully understand the effects of temperature on NMR images. The temperature dependence of the equilibrium nuclear magnetization is negative because of Boltzmann's distribution for all substances at all temperatures, but the combined temperature dependences of the equilibrium magnetization and relaxation can be negative, weak or positive depending on the temperature (T), echo time (T(E)), repetition time (T(R)), and the temperature dependences of the relaxation times T(1)(T) and T(2)(T) in a pulse sequence. As a result, the magnitude of the NMR signal from a given substance can decrease, increase or stay somewhat constant with increasing temperature. Nuclear thermal coefficients are defined and predictions for spin echo and other simple sequences are verified experimentally using a number of substances representing various thermal and NMR properties.     

Spin-wave contribution to the nuclear spin-lattice relaxation in triplet superconductors

We discuss collective spin-wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons, we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be 1 and 20 GHz, respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin-lattice relaxation rate. We find that, in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1/T1 with temperature. For two- and three-dimensional systems, the scaling exponents are 3 and 5, respectively. We discuss experimental manifestations of the spin-wave mechanism of the nuclear spin-lattice relaxation.     

Influence of moving dislocations on the nuclear spin-lattice relaxation time in the rotating frame

Dislocation motion at various velocities in Na²³Cl single crystals was studied using the spin-locking technique. The resulting spin-lattice relaxation time in the rotating frame, T_1?, is strongly dependent on the plastic deformation rate ?e, but not on the plastic strain ?. The experimental results are in accord with a theoretical expression for T_1? based on the relaxation model of Rowland and Fradin for atomic diffusion.     

Mechanism of nuclear spin-lattice relaxation and its field dependence for ultraslow atomic motion

The contribution of ultraslow self-diffusion of polycrystalline benzene molecules to the spin-lattice relaxation of protons is studied as a function of effective magnetic field H ₂ in a doubly rotating frame (DRF). Proton relaxation time T _1ρρ is measured by direct recording of NMR in a rotating frame (RF). The effective fields have a “magic” orientation corresponding to angles arccos(1/√3) in the RF and π/2 in the DRF so that the secular part of the dipole-dipole interactions of protons is suppressed in two orders of perturbation theory, while the nonsecular part becomes predominant. It is found that the diffusion contribution of benzene molecules to proton relaxation time T _1ρρ is a linear function of the square of field H ₂ and exhibits all peculiarities typical of the model of strong collisions generalized to only fluctuating nonsecular dipole interactions in fields exceeding the local field. This means that the model can also be employed in the given conditions. It is shown that perfect agreement with such a dependence can also be obtained in the model of weak collisions if we take into account the concept of the locally effective quantization field, whose magnitude and direction are controlled by the vector sum of field H ₂, and the nonsecular local field perpendicular to it.     

Field dependence of spin-lattice relaxation in paramagnetic salts

The field dependence of the Raman SLR rate is determined for H₀ of the order of the local field. Both S-state and non S-state transition salts are investigated when (i)H_dip > H_exch and (ii) H_exch > H_dip. Measurements are obtained from the response of the longitudinal magnetization to an amplitude modulated microwave field. The observed dependences agree with Orbach-Huang calculations.     

Angular dependence of the Knight shift, electric field gradient, and spin-lattice relaxation time of 9Be NMR in beryllium metal

Angular dependences of ⁹Be NMR (±1/2) and (±1/2 ? ±3/20 transition frequencies are measured in a single-crystal beryllium metal plate in a field of 7.04T. The isotropic K _iso and anisotropic K _aniso components of the Knight shift are determined. The measured values of K _iso and T ₁ are considered in terms of the contact, polarization, and orbital contributions.     

Electric quadrupolar contribution to the nuclear spin-lattice relaxation of Ir in Fe

We report on the first quantitative determination of the electric quadrupolar contribution to the nuclear spin-lattice relaxation in a transition metal. For 186Ir and 189Ir in Fe we have determined the magnetic and the electric quadrupolar part of the relaxation for magnetic fields between 0.01 and 2 T. The quadrupolar part gives information on the role of the orbital motion of the electrons for the relaxation process. Our results prove that the unexpected high relaxation rates in Fe and their magnetic field dependence are due to a nonorbital relaxation mechanism.     

Proton spin-lattice relaxation time of hydrated gelatin

In this work we obtain a model to describe the relaxativity of water molecules, adsorbed on macromolecules, as a function of the concentration. Excellent agreement with experimental data was obtained. The model allows us to estimate the adsorption energy of water molecules on different sites of the macromolecules.     

Random distribution of paramagnetic centers in the nuclear spin-lattice relaxation

A numerical solution is presented for the differential equation governing the nuclear spin-lattice relaxation via paramagnetic centers for spherically symmetric spin-diffusion constantD and direct relaxation transition probabilityC in the one-paramagnetic-center approximation. An interpolation function is given which reproduces the computedT ₁ values within ±5% for both the rapid diffusion and diffusion-limited cases. The introduction of a random distribution of the paramagnetic centers over the sample causes the relaxation to occur as exp(?at ^h ) with 0.5<h<1.0 forβ=(C/D)^1/4<R _av=the average radius of the influence spheres. This differs from the experimentally observed exp(?a ₁ t) behaviour. However, the random distribution seems to explain the difference between the theoretically calculated fluorine spin-diffusion in CaF₂ and that extracted from experimental NMR data by using the uniform-distribution model.     

Temperature dependence of the relaxation time of the superconducting order parameter

We have measured the temperature dependences of the relaxation time of the superconducting order parameter and of the equilibrium energy gap close to the transition temperature in very clean films of aluminum. The results are only consistent with the temperature and energy gap dependence predicted by Schmid and Schön. We also show that the magnitude and mean free path dependence of the electron inelastic collision time is in good agreement with calculations.     

Electronic spin-lattice relaxation time in TTF-TCNQ and Rb-TCNQ

Measurements at room temperature of the electronic spin lattice relaxation time in tetrathiafulvalene tetracyanoquinodimethan (TTF-TCNQ) and rubidium-TCNQ (II) are reported. A tentative discussion of the experimental results is given.     

Proton spin-lattice relaxation in deuterated diluted copper tutton salts

The spin-lattice relaxation time, T_1I, of the protons in (Cu,Zn)Cs₂(SO₄)₂·6(H,D)₂O was measured. The sample was 94% deuterated and contained 0.5% Cu²⁺ ions. The T_1I measurements were carried out at liquid helium temperatures and at fields in the region from 5–15 kOe. Under these conditions, T_1I shows a strong dependence on the direction of H₀ with respect to the crystal axes, in the magnetic K₁–K₃ plane. This angular dependence has been accurately determined close to the K₁ and K₃ axes, at 1.4K. Between the angular dependent behaviour of the proton relaxation time and the EPR spectrum of the Cu²⁺ ions exists a striking correlation: T_1I exhibits sharp minima at angles where the frequency distance between the EPR lines is about equal to the proton resonance frequency.The observed temperature dependence in the liquid helium region is weak and can very well be described with a factor (1−P²₀)⁻¹, where P₀ denotes the electron polarization. The field dependence of T_1I appears to be between H^1.0₀ and H^1.5₀.