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.     

La NMR and As NQR study of the As-based filled skutterudite LaOs4As12

We report experimental results of nuclear magnetic resonance (NMR) at the La site and nuclear quadrupole resonance (NQR) at the As site in the normal state of the superconducting compound LaOs₄As₁₂. Measurements have been performed on powder sample obtained from high quality single crystals. The temperature dependences of the nuclear spin-lattice relaxation rates, 1/T₁, of ⁷⁵As and ¹³⁹La nuclei were measured. No scaling between them was found indicating a local character of relaxation processes. The relaxation of ⁷⁵As nuclei can consistently be understood in terms of antiferromagnetic spin fluctuations, as deduced from the T-dependence of (1/T₁T)=C/(T−θ)^1/2.     

Spin gap, phase separation and d-wave pairing as revealed by electron spin-lattice relaxation in 123 and 124 YBaCuO systems doped with Gd3+

With an original modulation technique, the Gd³⁺ electron spin-lattice relaxation has been investigated in normal and superconducting states of YBa₂Cu₃O_6+x (123) and YBa₂Cu₄O₈ (124) compounds doped with 1% Gd. In the 123 sample withx = 0.9T _c = 90 K), theT ₁ behavior within 50 <T< 200 K reveals the [1 ? tanh²(Δ/2kT)]/T dependence typical of a spin gap opening with Δ ≈ 240 K. Below 50 K, the exponential slowing down ofT ₁ is limited by the Korringa-like behaviorT ₁ T = const); the same Korringa-like law is found in the 123 sample withx = 0.59 (T _c = 56 K) within the total 4.2–200 K temperature range. This is interpreted in terms of microscopic separation of the normal and superconducting phases allowing for the electron spin cross-relaxation between them. In the 124 sample (T _c = 82 K), the Gd³⁺ relaxation rate below 60 K is found to obey a power lawT _n with an exponentn ≈ 3. Such a behavior (previously reported for nuclear spin relaxation) is indicative of the d-wave superconducting pairing. Additional paramagnetic centers characterized by relatively slow spin-lattice relaxation are found in both 123 and 124 systems. A well-pronounced change in theT ₁ temperature dependence atTT* ≈ 180–200 K is observed for these slowly relaxing centers as well as for the conventional, fast-relaxing Gd³⁺ ions, suggesting microscopic phase separation and a change in the relaxation mechanism due to electronic crossover related with the opening of the spin gap. This hypothesis is supported by some “180 K anomalies” previously reported by other authors.     

Mechanical detection of nuclear spin relaxation in a micron-size crystal

A room temperature nuclear magnetic resonance force microscope (MRFM), fitted in a 1 tesla electromagnet, has been used to measure the nuclear spin relaxation of ¹H in a micron-size (70 ng) crystal of ammonium sulfate. NMR sequences, combining both pulsed and continuous wave radio-frequency fields, have allowed us to measure mechanically T₂ and T₁, the transverse and longitudinal spin relaxation times. Because two spin species with different T₁ values are measured in our 7 μm thick crystal, magnetic resonance imaging of their spatial distribution inside the sample section have been performed. To understand quantitatively the measured signal, we carefully study the influence of spin-lattice relaxation and non-adiabaticity of the continuous-wave sequence on the intensity and time dependence of the detected signal. Received 23 February 2000     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

NMR studies of magnetic superconductor RuSr2RECu2O8 (RE=Gd, Eu and Y)

We have carried out ^99/101Ru and ^63/65Cu nuclear magnetic resonance experiments in order to investigate magnetic and electronic properties of the magnetic superconductor RuSr₂RECu₂O₈ (RE=Gd, Eu and Y). The two kinds of ^99/101Ru signals were observed in the magnetically ordered state for each system, suggesting a charge segregation of Ru⁵⁺ (S=3/2) and Ru⁴⁺ (S=1) ions in the RuO₂ layers. The internal field at the Cu sites is revealed to be of the order of kilo Oe, indicating weak magnetic interactions between the CuO₂ and RuO₂ planes. The temperature dependence of nuclear spin-lattice relaxation time T₁ of ⁶³Cu in RE=Y shows a ‘spin gap’ like behavior, suggesting the system is under-doped.     

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.     

Hindered rotation of CH3 groups and phenyl ring in clofibric acid (drug) studied by35Cl-NQR and1H-NMR spectroscopy

The³⁵C1-NQR frequency (V_Q), nuclear quadrupole spin-lattice relaxation time (T_1Q),¹H-NMR second moment (M ₂), nuclear magnetic spin-lattice relaxation time (T ₁) and spin-lattice relaxation time in rotating frame (T _1p ) were measured for polycrystalline clofibric acid (drug) as a function of temperature. Hindered rotation of two dynamically inequivalent methyl groups and the phenyl ring was detected, the relevant activation energies were determined. The rotations are discussed in detail.     

NMR observation of critical dynamics in the (TMTSF)2PF6 organic superconductor

We have studied the organic superconductor (TMTSF)₂PF₆ using ¹H nuclear magnetic resonance. The spin-lattice (T₁) and the spin-spin relaxation time (T₂) measurements manifested a divergence associated with a structural phase transition at 160 K.     

Phase transition and relaxation processes by 87Rb and 39K nuclear magnetic measurements of RbKSO4 single crystals

⁸⁷Rb and ³⁹K nuclear magnetic resonance (NMR) spectra of RbKSO₄ single crystals were measured at room temperature. ⁸⁷Rb central line has the angular dependences of second-order quadrupolar shifts. From these results, the quadrupole coupling constant and the asymmetry parameter were determined at room temperature. In addition, the spin–lattice relaxation rate, 1/T₁, and the spin–spin relaxation rate, 1/T₂, were measured as a function of temperature. The values of 1/T₁ for the ⁸⁷Rb and ³⁹K nuclei were found to increase with increasing temperature, and 1/T₁ was determined to be proportional to Tⁿ. Therefore, for the ⁸⁷Rb and ³⁹K nuclei, Raman processes with n=2 are more significantly in nuclear quadrupole relaxation than direct processes.     

Distinct critical fluctuations and molecular motions manifest in a model biomembrane

Lattice dynamics in bis-(n-C₁₆H₃₇NH₃)₂SnCl₆, where the hydrocarbon part is analogous to lipid membrane, was investigated by means of 200 MHz ¹H nuclear magnetic resonance. As a result, critical fluctuations and molecular dynamics associated with the phase transitions, an order-disorder and a conformational phase transition, were distinguished in a wide temperature range. The dynamical origin of the critical fluctuations, observed in the long-chain compounds but not in the short-chain compounds, by the laboratory frame spin-lattice relaxation measurements, is revealed and discussed in this work.     

Proton NMR study of α-MnH0.06

Proton nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates for the solid solution α-MnH_0.06 have been measured over the temperature range 11-297 K and the resonance frequency range 20-90 MHz. A considerable shift and broadening of the proton NMR line and a sharp peak of the spin-lattice relaxation rate are observed near 130 K. These effects are attributed to the onset of antiferromagnetic ordering below the Néel temperature T_N≈130 K. The proton NMR line does not disappear in the antiferromagnetic phase; this suggests a small magnitude of the local magnetic fields at H-sites in α-MnH_0.06. The spin-lattice relaxation rate in the paramagnetic phase is dominated by the effects of spin fluctuations.     

19F nuclear spin relaxation and spin diffusion effects in the single-ion magnet LiYF4:Ho3+

Temperature and magnetic field dependences of the ¹⁹F nuclear spin-lattice relaxation in a single crystal of LiYF₄ doped with holmium are described by an approach based on a detailed consideration of the magnetic dipole-dipole interactions between nuclei and impurity paramagnetic ions and nuclear spin diffusion processes. The observed non-exponential long time recovery of the nuclear magnetization after saturation at intermediate temperatures is in agreement with predictions of the spin-diffusion theory in a case of the diffusion limited relaxation. At avoided level crossings in the spectrum of electron-nuclear states of Ho^{3 +} ions, rates of nuclear spin-lattice relaxation increase due to quasi-resonant energy exchange between nuclei and paramagnetic ions in contrast to the predominant role played by electronic cross-relaxation processes in the low-frequency ac-susceptibility.     

Spin autocorrelation of Ni in K2Mn0.975Ni0.025F4 studied by nuclear spin-lattice relaxation

From the nuclear spin-lattice relaxation of the out-of-layer ¹⁹F nuclei in magnetic fields perpendicular to the c-axis the low-frequency component of the autocorrelation function 〈S^z(t)S^z(O)〉 of Ni in ordered K₂Mn_0.975Ni_0.025F₄ is found to be substantially reduced relative to the Mn host. The experimental rates vs temperature are in accord with those for relaxation involving two spin excitations calculated with local Green's functions.     

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.     

Magnetic properties of Heisenberg triangular antiferromagnet V15 cluster studied by NMR

The magnetic properties of an s?=?1/2 Heisenberg triangular antiferromagnet V15 have been studied by proton nuclear magnetic resonance (NMR) at very low temperature down to 100 mK using a He³-He⁴ dilution refrigerator. In total spin S _T?=?3/2 ground state above 2.7 Tesla, proton spin-lattice relaxation rate (1/T₁) shows thermally activated behavior as a function of temperature. On the other hand, a temperature independent behavior of 1/T₁ at very low temperatures is observed in frustrated S _T?=?1/2 ground state below 2.7 Tesla. Possible origins for the peculiar behavior of 1/T₁ will be discussed in terms of magnetic fluctuations due to spin frustration.     

Enhancement of the B11 nuclear relaxation in CrB2 near the antiferromagnetic transition

Measurements of B¹¹ nuclear spin-lattice relaxation as a function of temperature in the itinerant antiferromagnet CrB₂ are reported. T^-1₁ shows a divergent behavior near T_N and it approaches a constant value well above T_N. The results are compared with the different theoretical predictions of Moriya and Ueda obtained either from the RPA or from the renormalized spin fluctuation approach.     

Critical nuclear relaxation in cobalt metal

Nuclear magnetic resonance of cobalt metal was investigated in the paramagnetic and ferromagnetic states and in the critical region below T_c. The Knight shift and spin lattice relaxation times were measured in the paramagnetic phase in the solid and liquid states from 1578 K to 1825 K. The resonant frequency, spin-lattice and spin-spin relaxation times were measured in the ferromagnetic phase from room temperature to 1385 K. The main part of (T₁T)^-1 results from fluctuating orbital moments in both phases except near T_c where this process forms the background for critical spin relaxation. The critical exponents for T^-1₁ and for the magnetization in the ferromagnetic state were found to be n' = 0.96 ± 0.07 and β = 0.308 ± 0.012, respectively.     

Some peculiarities of spin-lattice relaxation of impurity rare-earth ions in crystals caused by the structure defects

The spin-lattice relaxation times for Nd³⁺ ions in yttrium-aluminum garnets (YAG) and for Yb³⁺ ions in CaF₂ in the low-temperature range have been measured. For the first system the temperature dependence of the relaxation rate is determined to a great extent by the method of sample preparation. For samples grow by the method of the horizontally oriented crystallization the dependence is described asT ₁ ^?1 =AT ⁿ ,n ? 4.7, which is an evidence of an influence of local structure disordering on the relaxation. The temperature dependence of the relaxation rate in CaF₂:Yb is also “anomalous”:T ₁ ^?1 =AT ^3.3. The results are compared with the previous data on the relaxation in similar systems, and with other cases of observation of “anomalous” temperature dependences. Different manifestations of the local crystal defects in spin-lattice relaxation are discussed.     

199Hg and63,65Cu NMR studies of mercury based high-T c superconductors

Hg-oxide ceramic high temperature superconductors were studied by¹⁹⁹Hg and^63,65Cu NMR spectroscopy. Room temperature spectra, spin-spin and spin-lattice relaxation times of samples with different superconducting transition temperatures are presented. A spin-lattice relaxation time ofT ₁=35 msec and a spin-spin relaxation time ofT ₂=1.6 msec were found for the¹⁹⁹Hg NMR. All samples exhibit similar characteristic powder spectra caused by an axially symmetric¹⁹⁹Hg spin interaction. The isotropic value and the anisotropy of the tensor relative to solid HgCl₂ as a standard substance is estimated. Furthermore, results of^63,65Cu NMR measurements at a temperature of 4.2 K which exhibit a typical powder line shape (forI=3/2) are presented.