Theory of nuclear spin relaxation in a two-dimensional disordered HTcS in the normal state

The nuclear spin relaxation rateT ₁ ^–1 is calculated for a disordered two dimensional highcritical temperature superconductor taking into consideration the inelastic scattering of the electrons on the impurities. The deviation from the Korringa law of the formT ₁ ^–1 =AT+ B has been obtained if the quantum correction to the transport is dominated by the magnetic correlations.     

3He-CMN boundary resistance

The boundary resistance between liquid and solid³He and CMN is calculated taking the coupling to be due to the nuclear spin-electron spin dipolar interaction. The boundary resistance is calculated using a relationship betweenR _K ^–1 and the longitudinal relaxation timeT ₁. We find qualitative agreement with the results of Leggett and Vuorio for the temperature dependence and impurity dependence ofR _K ^–1 . Quantitative agreement with experiment is possible using a number of plausible assumptions. An important insight emerges: the relative rates of motion of the spins in³He and CMN are crucial to their coupling. Solid³He at low pressure is in near synchronism with CNM. As a consequence its boundary resistance should be very low.Supported in part by the National Science Foundation and the A. P. Sloan Foundation.     

Relaxation times of molecular ions OH− in glasses at very low temperature

This paper presents a detailed study of the temperature dependence of the longitudinal relaxation time T ₁ and of the coherence time T ₂ of a population of ionic molecular impurities in silica glass. Electric dipolar echoes taken in a temperature range 4–22 mK and a frequency of 370 MHz show that T ₁ is governed by a one-phonon process; consequently T ₁ varies like T ^–1; experimental data show that T ₂ also varies like T ^–1 and this in contradiction with predictions which lead to T ^–2. The relaxation of the spontaneous and stimulated echoes shows that there is a wide distribution of relaxation times (T ₁ and T ₂) ; from the amplitude of the signal it is also possible to extract both the longitudinal and the transverse electric moment; the coupling constant of the impurities with the strain is found to be as large as 3 eV.     

Domain Wall Motion in the Presence of Nuclear Spins

We investigate the motion of a domain wall in the presence of a dynamical hyperfine field. At temperature T high compared to the hyperfine coupling, the nuclear spins create a spatially random potential landscape, with dynamics dictated by the nuclear relaxation time T ₂. The distribution of the domain wall relaxation times (both in the thermal and quantum regimes) can show a long tail, characteristic of stochastic processes where rare events are important. Here, these are due to occasional strong fluctuations in the nuclear spin polarisation.     

Susceptibility and relaxation measurements on rhodium metal at positive and negative spin temperatures in the nanokelvin range

We have measured the susceptibility of polycrystalline rhodium foils, down to nuclear spin temperaturesT = 280 pK and up toT = –750 pK. AtT > 0, the static susceptibility follows the antiferromagnetic Curie-Weiss law with = –1.8±0.3 nK. AtT < 0, the expected ferromagnetic behavior in the vicinity ofT = –0 changes into antiferromgnetic tendency around –6 nK. If only nearest and next nearest neighbor interactions are assumed, our data yieldJ _n/h = –17±3 Hz andJ _nnn/h = 10±3 Hz for the exchange interaction coefficients. We have also investigated the field and polarization dependence of the spin-lattice relaxation time ₁ at positive and negative nanokelvin temperatures; surprisingly ₁ is longer whenT< 0. Infields below 1 mT, the Korringa constant shows a strong decrease, which becomes more pronounced as the conduction electron temperature decreases. Observed behavior is consistent with conduction electrons scattering from magnetic impurities, provided that the impurity-induced contribution to spin-lattice relaxation is proportional to the inverse of the nuclear spin temperature in small fields.     

Electronic Inhomogeneity and Possible Pseudogap Behavior of Spin Susceptibility in the Electron-Doped Superconductor Sr0.93La0.07CuO2: 63Cu NMR Study

The magnetic susceptibility, NMR spectra, nuclear spin-lattice relaxation rate (T ₁ ^–1) and the echo-decay rate (T ₂ ^–1) of ⁶³Cu were measured for the electron-doped infinite-layer superconductor Sr_0.93La_0.07CuO₂/T _c ^onset = 42.4 K). The results obtained revealed a clear tendency toward frustrated phase separation in this nominally underdoped high-T _c material. Above T _c the ⁶³Cu Knight shift is found to decrease upon cooling giving an evidence for a pseudogap-like decrease of the spin susceptibility. It is shown that unusual anisotropy of the ⁶³Cu Knight shift in the electron-doped CuO₂ layer can be understood as a compensation effect between the isotropic hyperfine coupling, mediated by the 4s Fermi-contact and 3d core-polarization exchange interactions, and the anisotropic on-site spin-dipolar hyperfine interaction of the Cu nuclei with the itinerant carriers, whose states near the Fermi energy have a sizeable admixture of Cu(4p_z) and/or Cu(3d_z ²) orbitals.     

Effect of Berezinskii-Kosterlitz-Thouless vortex fluctuations on the nuclear spin relaxation rate

In this work we examine the influence of the diffusive motion of vortices in highly anisotropic high-T_c superconductors near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T _bkt on the spin-lattice relaxation rate T ₁ ^–1 .We find a jump in T ₁ ^–1 at the temperature T _bkt .     

Measurements of the nuclear spin-lattice relaxation times in BCC3He for high magnetic fields,high molar volumes,and low temperatures

Experimental studies of the nuclear spin-lattice relaxation times in BCC helium three are reported for high molar volumes and low temperatures close to the minimum in the melting curve. The results show the existence of a new relaxation mechanism at low temperatures with an approximately linear temperature dependence (T ₁ T ^–1). An analysis of the vacancy-induced relaxation shows that both the vacancy formation energy and the vacancy mobility decrease dramatically as a function of density on approaching the maximum possible molar volume (minimum density) of the solid. A possible interpretation of both the new relaxation mechanism and the vacancy properties is outlined.     

Interplay Between Vorticity and Chirality Inside the Vortex Core in Chiral p-Wave Superconductors

The vortex core in chiral p-wave superconductors exhibits various properties owing to the interplay between the vorticity and chirality inside the vortex core. In the chiral p-wave superconductors, the site-selective nuclear spin-lattice relaxation rate T ^–1 ₁ is theoretically studied inside the vortex core within the framework of the quasiclassical theory of superconductivity. T ^–1 ₁ at the vortex center depends on the sense of the chirality relative to the sense of the magnetic field. The effect of a tilt of the magnetic field upon T ^–1 ₁ is investigated. The effect of the anisotropy in the superconducting gap and the Fermi surface is then investigated. The result is expected to be experimentally observed as a sign of the chiral pairing state in a superconducting material Sr₂RuO₄.     

Concentration dependence ofD,T 1, andT 2 for dilute solutions of3He in solid4He

Measurements of the spin diffusion coefficientD and NMR relaxation timesT ₁ andT ₂ are reported for dilute solutions of³He in solid⁴He at two molar volumes, 20.95 and 20.7 cm³. The weakly interacting impuriton model, for whichD ^–1 is proportional to impurity concentration, is observed only at fractional impurity concentrationx ₃ below 3 × 10^–4. Forx ₃ around 10^–3,T ₁ andT ₂ are controlled by the formation and breakup of³He₂ molecules.     

Spatially-Resolved NMR Study on Antiferromagnetic Vortex Core in HTSC

Magnetism in the vortex core of nearly-optimal doped Tl₂Ba₂CuO₆₊ (T _c=85 K) is investigated by a spatially-resolved NMR. The NMR relaxation rate T ^–1 ₁ at ²⁰⁵Tl site provides a direct evidence of the significant enhancement of the AF spin correlations in the vortex core region and shows clearly a local AF ordering of the core region Cu spins at T _N=20 K. Above T _N the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T ^*–120 K), indicating that the pseudogap disappears within the vortex core.     

Electronic Theory for the Magnetic Anisotropy in Sr2RuO4

Using a three-band Hubbard Hamiltonian we calculated within the random-phase-approximation the spin susceptibility, χ(q, ω), and NMR spin-lattice relaxation rate 1/T ₁, in the normal state of the triplet superconductor Sr₂RuO₄, and obtained quantitative agreement with experimental data. Most importantly, we found that because of spin–orbit coupling the out-of-plane component of the spin susceptibility χ ^zz (q, ω) becomes two times larger than the in-plane one at low temperatures. We analyze in particular the role of the xy-band in the magnetic anisotropy.     

Model nuclear relaxation time of inhomogeneous fluids near a substrate: Liquid 3He in confined geometries or physisorbed molecular systems

We extend a previous analysis for the temperature dependence of the longitudinal nuclear spin relaxation time T ₁of pure liquid ³He in confined geometries to the case where the various walls are coated with a film of ⁴He. This leads us to consider relaxation not only of ³He spins on the walls as we did earlier, but also relaxation by coupling between the different layers of ³He of inhomogeneous structure. We characterize the inhomogeneous ³He as a sequence of layers of different densities and thus different static susceptibilities and different fluctuation frequencies. We suggest that the same idea might help to understand the behavior of T ₁(T) for adsorbed molecular fluids of BET type III, such as NH₃, where one adsorbed monolayer grows into islands of multilayers, for which we propose a model structure, varying with temperature, whose overall T ₁ bears much resemblance to that of ³He near a wall. We believe that both cases illustrate the more general behavior of T ₁(T) in an inhomogeneous fluid; here the inhomogeneous density has its source in the attraction to the substrate, but any density gradient could in principle yield the same effect. Our phenomenological model is compared with existing data and further experiments are suggested.Work supported in part by NATO grant No. 1196.Laboratoire associé au CNRS.     

63,65Cu NQR Evidence for Low-Temperature Charge Ordering in the Superconducting State of YBa2Cu3O7?δ

Measurements of the nuclear quadrupole resonance (NQR) transverse relaxation rate and of the NQR spectral linewidths of ^63,65Cu in the superconducting state of YBa₂Cu₃O_7– reveal unusual features below T = 35 K. A narrow peak in the transverse relaxation rate and an increased quadrupolar line broadening with decreasing temperature are attributed to a charge density wave (CDW) ordered state below T = 35 K.     

Ferromagnetic Correlations in Ca-Doped Sr2RuO4: 87Sr NMR Study

Magnetic properties on Sr_2–x Ca _x RuO₄ have been investigated by a microscopic probe of ⁸⁷Sr-NMR in order to understand the magnetic character on spin-triplet superconductor of Sr₂RuO₄, which has multibands on the Fermi surface. With substituting Ca for Sr which gives rise to crystal distortion, the Knight shift (K) and the nuclear spin-lattice relaxation rate divided by temperature (1/T _{1 T}) increases progressively up to x=1.5. The Korringa relation from K and 1/T ₁ T becomes smaller, indicative of development of ferromagnetic fluctuations with increasing Ca content. This suggests that the q-independent spin fluctuations originating from the 2-dimensional band are changed to the ferromagnetic ones by the Ca doping.     

NMR of 89Y in T′-Phase La1.5 Y0.5CuO4

We report measurements of NMR spin-lattice (T ₁ ) and spin-spin (T ₂ ) relaxation times for ₈₉ Y in the parent structure of the electron–doped copper–oxide superconductors. T ₁ data exhibit non–exponential recovery with T ₁ 20 s. T ₂ decreases rapidly with temperature above the Néel temperature, but remains constant above 425 K. We discuss these behaviors by considering fluctuating antiferromagnetic spin clusters associated with oxygen defects.     

Short Time Quantum AC Response of a System of Nanomagnets

We calculate the magnetization relaxation in the short-time regime for an ensemble of nanornagnets in the presence of a low frequency external AC biasing field at temperatures lower than the magnetic anisotropy energy of the individual nanornagnets. It is found that the relaxation is strongly affected by AC fields with amplitude larger than that of the T ₂ fluctuations in the nuclear field. This will allow experimental probing of the nuclear spin relaxation mechanism.     

Study of surface relaxation mechanism of liquid3He in porous glass by using SQUID NMR

Nuclear spin relaxation of liquid³He in porous glass has been studied. In addition to measurements of the longitudinal spin relaxation timeT ₁ by a usual pulsed SQUID NMR, measurements of the transverse spin relaxation timeT ₂ have been performed by using a newly developed SQUID NMR method to observe a spin echo signal. Temperature and frequency dependences ofT ₁ andT ₂ have been measured. A simple model is proposed which explains the main features of the experimental results.     

Longitudinal spin relaxation in a dilute,degenerate Fermi gas at arbitrary polarization

We calculate the longitudinal magnetic relaxation timeT ₁ ^–1 for a dilute, polarized Fermi gas with short range interactions at low temperatures. In the limit of small polarizationsT ₁ ^–1 is proportional toT ^–2 in agreement with earlier predictions, while in the opposite caseT ₁ ^–1 is strongly affected by polarization, and in the limit of large polarizations becomes proportional to the square of the energy separation between the Fermi surfaces for up and down spins. The possibility of measuringT ₁ in dilute solutions of ³ He in superfluid ⁴ He is investigated.     

Nuclear spin-lattice relaxation measurements in small superconducting aluminum particles

The ²⁷Al nuclear spin-lattice relaxation times T ₁ have been measured in the normal and superconducting states of small aluminum particles with average particle diameters ranging from 170 to 750 ». Experiments were performed in magnetic fields between 0 and 1200 Oe and at temperatures between 0.5 and 4.2 K. The nuclear spin-lattice relaxation rate 1/T ₁ at zero and low magnetic fields is characterized by a sum of a Korringa rate (due to conduction-electron spin-flip scattering) and an additional rate, which is attributed to a cross-relaxation process involving nuclei near the particle surfaces. At the highest field (1200 Oe), where the Zeeman energy either dominates in larger particles or plays an important role in smaller particles, measured rates for all three samples are in good agreement with the microscopic theory of Sone. At low fields (H 150 Oe) our T ₁ results, which show a strong field dependence and less effect of superconducting fluctuations near T _c, are in disagreement with Sone. We suggest that the theory has overestimated the effects of fluctuations on quasiparticle excitations at these low fields.