What does NMR tell us about the electronic state of high-T c superconductors?

An introduction to the models which are usually applied, when interpreting the NMR (nuclear magnetic resonance) parameter Knight shift (K _s) and spin-lattice relaxation rate 1/T ₁ in the normal and the superconducting state of high-temperature superconductors, is given. The different hyperfine interaction parameters involved, as well as the static and dynamic susceptibility χ(q,ω) will be discussed. I will point at those highlights as antiferromagnetic correlations, spin gap and vortex lattice dynamics which have emerged from the analysis of the NMR data.     

Nuclear magnetic resonance measurements and the energy band structure of PtSn

Nuclear magnetic resonance measurements of the Knight shift and spin-lattice relaxation time for ¹⁹⁵Pt and ¹¹⁹Sn in PtSn are reported. The energy band structure as determined by the relativistic orthogonalized plane wave method is also presented. The band model developed has holes in the Pt d-band but does not have a large density of states associated therewith.     

High-temperature behaviour of spin-lattice relaxation and Knightshift of Te125 in tellurium

The Knightshift and the nuclear spin-lattice relaxation time of Te¹²⁵ in enriched (94% Te¹²⁵) polycrystalline tellurium have been studied from room temperature to the melting point (725 K). Over the whole temperature range, the shift is governed by an Arrhenius law with an activation energy of about 0.3 eV in agreement with the gap energy of tellurium at higher temperatures. Below 420 K, the relaxation time is caused by the conduction electrons, whereas in the high-temperature region the relaxation process is due to translational atomic diffusion. In this region, the relaxation mechanism is found to be determined by the chemical shift anisotropy of Te¹²⁵.     

NMR: hyperfine interactions in MoO3, MoS2, MoSe2 Mo3Se4, MoSi2 and Mo2C

Nuclear hyperfine interactions have been obtained by nuclear magnetic resonance (NMR) for in a number of binary Mo compounds, both insulators and metals, which illustrate the interplay between nuclear quadrupole and chemical (Knight) shift terms. The insulating phases are characterised by nuclear spin lattice relaxation times greater than 100 s, demonstrating the ineffectiveness of indirect phonon Raman relaxation for these compounds.     

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.     

Superconductivity and magnetic fluctuations in Cd(2))Re(2)O(7) via Cd nuclear magnetic resonance and re nuclear quadrupole resonance

We report Cd nuclear magnetic resonance (NMR) and Re nuclear quadrupole resonance (NQR) studies on Cd(2)Re(2)O(7), the first superconductor among pyrochlore oxides (T(c) approximately 1 K). The Re NQR spectrum at zero magnetic field below 100 K rules out any magnetic or charge order. The spin-lattice relaxation rate below T(c) exhibits a pronounced coherence peak and follows the weak-coupling BCS theory with nearly isotropic energy gap. The results of Cd NMR point to a moderate ferromagnetic enhancement at high temperatures followed by a rapid decrease of the density of states below the structural transition temperature of 200 K.     

27Al pulsed nuclear magnetic resonance study of CeAl2

The magnetic properties and the electronic structures of a rare-earth aluminum intermetallic compound CeAl₂ are investigated by magnetic susceptibility measurements and ²⁷Al pulsed nuclear magnetic resonance (NMR) techniques. The magnetic susceptibility is strongly temperature-dependent, following a Curie–Weiss law down to ∼12 K, and shows an antiferromagnetic transition at 4 K. The ²⁷Al NMR spectra show a typical powder pattern for a nuclear spin I of 5/2 with the second-order nuclear quadrupole interaction at high temperature and an additional large dipolar broadening between the 4f electron spins of cerium and the ²⁷Al nuclear spins at low temperature. The ²⁷Al NMR Knight shift follows the same temperature dependence as the magnetic susceptibility, suggesting that the ²⁷Al NMR Knight shift originates from the transferred hyperfine field of the Ce 4f electron spins with the hyperfine coupling constant of A = +5.7 kOe/μ_B. The spin-lattice relaxation rate 1/T₁ is roughly proportional to temperature, as with most non-magnetic metals at high temperature, and then strongly temperature-dependent, increasing rapidly with a peak near the antiferromagnetic transition temperature and decreasing at lower temperature. The temperature dependence of the Korringa ratio K, however, suggests that the antiferromagnetic spin fluctuation signature, which is an enhancement in the Korringa ratio, is washed out owing to the geometrical cancellation of Ce 4f fluctuations at the Al sites.     

Anisotropic spin fluctuations and superconductivity in "115" heavy fermion compounds: ⁵⁹Co NMR study in PuCoGa₅

We report results of ??Co nuclear magnetic resonance measurements on a single crystal of superconducting PuCoGa? in its normal state. The nuclear spin-lattice relaxation rates and the Knight shifts as a function of temperature reveal an anisotropy of spin fluctuations with finite wave vector q. By comparison with the isostructural members, we conclude that antiferromagnetic XY-type anisotropy of spin fluctuations plays an important role in mediating superconductivity in these heavy fermion materials.     

Spin gap and Luttinger liquid description of the NMR relaxation in carbon nanotubes

Recent NMR experiments by Singer et al. [Singer, Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magnetic field and temperature dependent NMR 13C spin-lattice relaxation is given in the framework of the Tomonaga-Luttinger liquid. The low temperature properties are governed by a gapped relaxation due to a spin gap ( approximately 30 K), which crosses over smoothly to the Luttinger liquid behavior with increasing temperature.     

Spin density distribution of the conduction electrons in diperylene hexafluorophosphate analysed by high-resolution NMR

High-resolution ¹³C nuclear magnetic resonance with ¹H cross polarization and ¹H decoupling under magic angle spinning is measured for the quasi-one dimensional organic conductor diperylene hexafluorophosphate (including tetrahydrofurane solvent molecules) at temperatures between 160 K and 270 K. Ab initio molecular orbital calculations are used for chemical shift analysis and for assignment of Knight shifted lines and individual carbon positions. The coexistence of neutral perylene molecules and perylene radicals in the same radical cation salt is revealed. From Knight and chemical shifts we were able to distinguish two inequivalent perylene radicals within the conducting stack. The spin density distribution of the molecular electronic wave function is determined quantitatively for these radicals. Received 29 June 1999 and Received in final form 4 November 1999     

NMR probe of bulk electronic structures in H+ beam irradiated Bi2Te3 topological insulator

We report a nuclear magnetic resonance (NMR) study on H⁺ beam irradiated Bi₂Te₃ powdered single crystals. In this work, we demonstrate that the beam creates defects within its penetration range giving rise to delocalized charge carriers, thereby making further ¹²⁵Te NMR Knight shift and line broadening. Upon increasing temperature, the NMR line narrowing manifests the activated motions of thermally excited charge carriers in the irradiated sample. In contrast, it reveals that in the unirradiated sample the free-charge carriers at the Fermi level dominantly contribute to the Knight shift. Our results show that the orbital contribution to the Knight shift in the bulk state of Bi₂Te₃ becomes predominant in the system with the higher density of defects, as evidenced by modified electronic structures induced by the beam irradiation.     

Spin dynamics in iron-based layered superconductor (La0.87Ca0.13)FePO revealed by 31P and 139La NMR studies

We report 31P and 139La NMR studies of (La0.87Ca0.13)FePO, which is a family member of the recently discovered superconductor LaFeAs(O1-xFx). In the normal state, Knight shift and nuclear spin-lattice relaxation rate divided by T (1/T1T) show that a Fermi-liquid state with moderate ferromagnetic fluctuations emerges below 30 K. From 1/T1T of 31P and 139La, a quasi-two- dimensional electronic structure is suggested, in which the FeP layer is more conductive than the LaO layer. In the superconducting (SC) state, although a clear Meissner signal was observed, 1/T1T increases below Tc, in contrast to a decrease of 1/T1T due to the opening of a SC gap, suggesting that novel low-energy spin dynamics develop in the SC state.     

NMR studies of metal-nonmetal transition in lithium-methylamine solutions

The Knight shift and the spin-lattice relaxation time of ⁷Li and ¹H have been measured in Li-methylamine solutions, in which a transition from the metallic to the nonmetallic states occurs.     

Delocalized quasiparticles in the vortex state of an overdoped high-T(c) superconductor probed by 63Cu NMR

We report the spin Knight shift (K(s)) and the nuclear spin-lattice relaxation rate (1/T1) in the vortex state as a function of magnetic field (H) up to 28 T in the high-Tc superconductor TlSr2CaCu2O6.8 (Tc = 68 K). At low temperatures well below Tc, both K(s) and 1/T1 measured around the middle point between the two nearest vortices (saddle point) increase substantially with increasing field, which indicate that the quasiparticle states with an ungapped spectrum are extended outside the vortex cores in a d-wave superconductor. The density of states (DOS) around the saddle point is found to be kappaN(0)square root[H/H(c2)], with kappa = 0.5-0.7 and N0 being the normal-state DOS.     

Magnetic-like field inducing negative Dirac mass in graphene on hexagonal boron nitride

The tight-binding electrons in graphene grown on top of hexagonal boron nitride (h-BN) substrate are studied. The two types of surfaces on the h-BN substrate give rise to Dirac fermions having positive and negative masses. The positive and negative masses of the Dirac fermions lead to the gapped graphene to behave as a “pseudo” ferromagnet. A very large (pseudo) tunneling magnetoresistance is predicted when the Fermi level approaches the gap region. The energy gap due to the breaking of sublattice symmetry in graphene on h-BN substrate is analogous to magnetic-induced energy gap on surface of topological insulators. We point out that positive and negative masses may correspond to signs of magnetic-like field perpendicular to graphene sheet acting on pseudo magnetic dipole moment of electrons, leading to pseudo-Larmor precession and Stern–Gerlach magnetic force.     

Nuclear relaxation rates for 3He adsorbed on zeolite

Transient nuclear magnetic resonance measurements of spin-lattice and spin-spin relaxation times have been carried out as a function of temperature and pressure on ³He adsorbed on two types of commercial zeolite. In addition, the number of atoms adsorbed on unit weights of zeolite was determined by spin counting. Mechanisms for spin-spin relaxation were provided by dipole interactions among helium spins and spin-lattice relaxation was probably due to atomic motion.     

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.     

NMR study of Chevrel phase superconductor

The nuclear spin lattice relaxation time, T₁, the Knight shift and the spin echo decay time, T₂, of ²⁰⁷Pb and ⁷⁷Se were measured in Pb_1.125Mo₆Se_7.5 and Pb_1.125Mo₆S_7.5 at He temperatures. The temperature dependence of T₁ shows the existence of the energy gap of 3.5kT_c at both sites of Pb and Se. The Knight shift dose not change with temperature even below T_c. A remarkable decrease of T₂ below T_c is observed, which is opposite to the case in usual type II superconductor.     

NMR study of Na3−xRu4O9

Low-dimensional conductor Na_3−xRu₄O₉ has been studied by means of ²³Na nuclear magnetic resonance measurement in order to clarify the electronic state of this compound. The magnetic susceptibility χ is almost constant from 100 to 300 K, then increases with temperature, and shows a kink at 584 K. The temperature dependence of the Knight shift K is almost in proportion to χ. From the result of the temperature dependence of spin–lattice relaxation time, it has been found that this compound has an energy gap, Δ, which is closely correlated with the gap-like behavior of χ. Consequently, we consider that there exists a spin-singlet state in all or a part of RuO₆ chains in Na_3−xRu₄O₉.     

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.