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Topological properties of materials are of fundamental as well as practical importance1,2. Of particular interest are unconventional superconductors that break time-reversal symmetry, for which the superconducting state is protected topologically and vortices can host Majorana fermions with potential use in quantum computing3,4. However, in striking contrast to the unconventional A phase of superfluid 3He where chiral symmetry was directly observed5, identification of broken time-reversal symmetry of the superconducting order parameter, a key component of chiral symmetry, has presented a challenge in bulk materials. The two leading candidates for bulk chiral superconductors are UPt3 (refs. 6–8) and Sr2RuO4 (ref. 9), although evidence for broken time-reversal symmetry comes largely from surface-sensitive measurements. A long-sought demonstration of broken time-reversal symmetry in bulk Sr2RuO4 is the observation of edge currents, which has so far not been successful10. The situation for UPt3 is not much better. Here, we use vortices to probe the superconducting state in ultraclean crystals of UPt3. Using small-angle neutron scattering, a strictly bulk probe, we demonstrate that the vortices possess an internal degree of freedom in one of its three superconducting phases, providing direct evidence for bulk broken time-reversal symmetry in this material. Small-angle neutron scattering measurements show that the vortices of the heavy-fermion compound UPt3 possess an internal degree of freedom in one of its three superconducting phases, implying the breaking of time-reversal symmetry in the bulk.

A central question in a large class of strongly correlated electron systems, including heavy fermion compounds and iron pnictides, is the identification of different phases and their origins. It has been shown that the antiferromagnetic (AFM) phase in some heavy fermion compounds is induced by Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized moments, and that the competition between this interaction and Kondo effect is responsible for quantum criticality. However, conclusive experimental evidence of the RKKY interaction in pnictides is lacking. Here, using high resolution $^{23}\mathrm{Na}$ NMR measurements on lightly Cu-doped metallic single crystals of ${\mathrm{NaFe}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}\mathrm{As}$ $(x\ensuremath{\approx}0.01)$ and numerical simulation, we show direct evidence of the RKKY interaction in this pnictide system. Aided by computer simulation, we identify the $^{23}\mathrm{Na}$ NMR satellite resonances with the RKKY oscillations of spin polarization at Fe sites. Our $^{23}\mathrm{Na}$ spin-lattice and spin-spin relaxation data exhibit a signature of an itinerant and inhomogeneous AFM phase in this system, accompanied by a simulation of Cu-induced perturbation to the ordered moments on the Fe sites. Our NMR results indicate coexistence of local and itinerant magnetism in lightly Cu-doped ${\mathrm{NaFe}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}\mathrm{As}$.

The discovery of superfluidity in 3He in 1971, published in 1972, [1, 2] has influenced a wide range of investigations that extend well beyond fermionic superfluids, including electronic quantum ma- terials, ultra-cold gases and degenerate neutron matter. Observation of thermodynamic transitions from the 3He Fermi liquid to two other liquid phases, A and B-phases, along the melting curve of liquid and solid 3He, discovered by Osheroff, Richardson, and Lee, were the very first indications of 3He superfluidity leading to their Nobel prize in 1996. This is a brief retrospective specifically focused on the AB transition.

The interplay between unconventional superconductivity and quantum critical ferromagnetism in the U-Ge compounds represents an open problem in strongly correlated electron systems. Sample quality can have a strong influence on both of these ordered states in the compound UCoGe, as is true for most unconventional superconductors. We report results of a new approach at UCoGe crystal growth using a floating-zone method with potential for improvements of sample quality and size as compared with traditional means such as Czochralski growth. Single crystals of the ferromagnetic superconductor UCoGe were produced using an ultra-high vacuum electron-beam floating-zone refining technique. Annealed single crystals show well-defined signatures of bulk ferromagnetism and superconductivity at $T_c \sim$2.6 K and $T_s \sim$0.55 K, respectively, in the resistivity and heat capacity. Scanning electron microscopy of samples with different surface treatments shows evidence of an off-stoichiometric uranium rich phase of UCoGe collected in cracks and voids that might be limiting sample quality., 10 pages, 6 figures

CeCd$_3$As$_3$ is a rare-earth triangular-lattice antiferromagnet with large inter-layer separation. Our field-dependent heat capacity measurements at dilution fridge temperatures allow us to trace the field-evolution of the spin-excitation gaps throughout the antiferromagnetic and paramagnetic regions. The distinct gap evolution places strong constraints on the microscopic pseudo-spin model, which, in return, yields a close {\it quantitative} description of the gap behavior. This analysis provides crucial insights into the nature of the magnetic state of CeCd$_3$As$_3$, with a certainty regarding its stripe order and low-energy model parameters that sets a compelling paradigm for exploring and understanding the rapidly growing family of the rare-earth-based triangular-lattice systems., Main Text: 6 pages, 3 figures SM: 19 pages, 23 figures Some clarifications are made relative to previous version

In the high temperature cuprate superconductor, HgBa 2 CuO 4 + δ , it has been determined that the dopant oxygen, O δ , resides in the Hg-plane. Here we present a systematic investigation of the 199 Hg NMR spectrum as a function of dopant oxygen concentration, δ . At high doping levels we observe four distinct 199 Hg resonance peaks which follow a binomial distribution in δ corresponding to zero, one, two, and three nearest neighbor O δ atoms. Additionally, we have measured a linear dependence of the peak frequencies on doping and suggest that these measurements might be theoretically amenable.

Liquid $^3$He confined in low-density, highly porous random solids such as silica aerogel provides tuneable systems to study the effects of disorder and confinement on the properties of a quantum liquid. New superfluid phases result from the interplay between disorder, confinement and complex symmetry-breaking. An extended bibliography is appended. An edited and abbreviated version of this article appeared in Physics Today 71, 11, 30 (2018).

Neutron scattering measurements have demonstrated that the heavily Cu doped ${\mathrm{NaFe}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}\mathrm{As}$ compound behaves like a Mott insulator exhibiting both real-space Fe-Cu stripes and antiferromagnetism below a N\'eel temperature for $x\ensuremath{\lesssim}0.5$. We have investigated the evolution of structural and magnetic ordering using $^{23}\mathrm{Na}$ and $^{75}\mathrm{As}$ NMR for single crystals ($x$ = 0.39 and 0.48), confirming antiferromagnetism in the form of magnetic stripes. We show that end-chain defects in these stripes are the principal source of magnetic disorder and are responsible for cluster spin-glass transitions in both compounds, in the latter case coexistent with antiferromagnetism. Aided by our numerical simulation of the $^{75}\mathrm{As}$ spectra, we show that a staggered magnetization at the Fe sites is induced by nonmagnetic Cu dopants.

It is known that both magnetic and nonmagnetic impurities suppress unconventional superconductivity. Here we compare their effect on the paradigm unconventional superconductor, superfluid $^{3}\mathrm{He}$, using highly dilute silica aerogel. Switching magnetic to nonmagnetic scattering in the same physical system is achieved by coating the aerogel surface with $^{4}\mathrm{He}$. We find a marginal influence on the transition temperature itself. However, we have discovered that the $A$ phase, which breaks time reversal symmetry, is strongly influenced, while the isotropic $B$ phase is unchanged. Importantly, this occurs only if the impurities are anisotropically distributed on a global scale.

Recent neutron scattering measurements indicate that NaFe$_{1-x}$Cu$_{x}$As forms an antiferromagnetic stripe phase near $x\approx 0.5$ in a Mott insulating state. This copper concentration is well in excess of that required for superconductivity, $x < 0.04$. We have investigated the development of magnetism in this compound using $^{23}$Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation measurements performed on single crystals ($x$ = 0.13, 0.18, 0.24, and 0.39). We find multiple inequivalent Na sites, each of which is associated with a different number of nearest neighbor Fe sites occupied by a Cu dopant. We show that the distribution of Cu substituted for Fe is random in-plane for low concentrations ($x = 0.13$ and 0.18), but deviates from this with increasing Cu doping. As is characteristic of many pnictide compounds, there is a spin pseudo gap that increases in magnitude with dopant concentration. This is correlated with a corresponding increase in orbital NMR frequency shift indicating a change in valence from Cu$^{2+}$ to a Cu$^{1+}$ state as $x$ exceeds 0.18, concomitant with the change of Fe$^{2+}$ to Fe$^{3+}$ resulting in the formation of magnetic clusters. However, for $x\leq 0.39$ there is no evidence of long-range static magnetic order., 20 pages, 10 figures

The direction of the orbital angular momentum of the $B$ phase of superfluid $^{3}\mathrm{He}$ can be controlled by engineering the anisotropy of the silica aerogel framework within which it is imbibed. In this work, we report our discovery of an unusual and abrupt ``orbital-flop'' transition of the superfluid angular momentum between orientations perpendicular and parallel to the anisotropy axis. The transition has no hysteresis, warming or cooling, as expected for a continuous thermodynamic transition, and is not the result of a competition between strain and magnetic field. This demonstrates the spontaneous reorientation of the order parameter of an unconventional BCS condensate.

The pressure dependence of the order parameter in superfluid $$^3\hbox {He}$$ is amazingly simple. In the Ginzburg–Landau regime, i.e., close to $$T_\mathrm{c}$$ , the square of the order parameter can be accurately measured by its proportionality to NMR frequency shifts and is strictly linear in pressure. This behavior is replicated for superfluid $$^3\hbox {He}$$ imbibed in isotropic and anisotropic silica aerogels. The proportionality factor is constrained by the symmetry of the superfluid state and is an important signature of the corresponding superfluid phase. For the purpose of identifying various new superfluid states in the p-wave manifold, the order parameter amplitude of superfluid $$^3\hbox {He}$$ -A is a useful reference, and this simple pressure dependence greatly facilitates identification.

Superfluid 3He is an unconventional neutral superfluid in a p-wave state with three different superfluid phases each identified by a unique set of characteristic broken symmetries and non- trivial topology. Despite natural immunity of 3He from defects and impurity of any kind, it has been found that they can be artificially introduced with high porosity silica aerogel. Furthermore, it has been shown that this modified quantum liquid becomes a superfluid with remarkably sharp thermodynamic transitions from the normal state and between its various phases. They include new superfluid phases that are stabilized by anisotropy from uniform strain imposed on the silica aerogel framework and they include new phenomena in a new class of anisotropic aerogels consisting of nematically ordered alumina strands. The study of superfluid 3He in the presence of correlated, quenched disorder from aerogel, serves as a model for understanding the effect of impurities on the symmetry and topology of unconventional superconductors., Comment: 23 pages, 8 figures, accepted Annual Reviews Condensed Matter Physics

The symmetry properties of the order parameter characterize different phases of unconventional superconductors. In the case of the heavy-fermion superconductor UPt$_3$, a key question is whether its multiple superconducting phases preserve or break time-reversal symmetry (TRS). We tested for asymmetry in the phase shift between left and right circularly polarized light reflected from a single crystal of UPt$_3$ at normal incidence, finding that this so-called polar Kerr effect appears only below the lower of the two zero-field superconducting transition temperatures. Our results provide evidence for broken TRS in the low-temperature superconducting phase of UPt$_3$, implying a complex two-component order parameter for superconductivity in this system., 19 pages, 7 figures

Helium is non-renewable. It is used in many areas of scientific research but demand is fast outstripping supply. We must adapt, and quickly.

Superfluid 3He-A in a fully characterized stretched aerogel, used in previous work [1], has been studied for parallel and perpendicular orientations of the magnetic field relative to the anisotropy axis of the aerogel. Consistently, we find that an equal spin pairing state (ESP) is stabilized down to the lowest temperature. From our pulsed NMR frequency shifts as a function of temperature and tip angle, the orientation of the orbital angular momentum l has been determined. The aerogel anisotropy introduced by uniaxial stretching tends to align l in the axial state parallel to the strain axis, confirming the theory proposed by Sauls [2] and contrary to the prediction of Volovik [3] based on an impurity calculation of Rainer and Vuorio [4]., 3 pages, 3 figures

Measurements of the $^{17}\mathrm{O}$ nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ were performed over a range of magnetic fields from 6.4--30 T in the superconducting state. Oxygen-isotope-exchanged single crystals were investigated with doping corresponding to superconducting transition temperatures from 74 K underdoped, to 78 K overdoped. The apical oxygen site was chosen since its NMR spectrum has narrow quadrupolar satellites that are well separated from any other resonance. Nonvortex contributions to the spectra can be deconvolved in the time domain to determine the local magnetic field distribution from the vortices. Numerical analysis using Brandt's Ginzburg-Landau theory was used to find structural parameters of the vortex lattice, penetration depth, and coherence length as a function of magnetic field in the vortex solid phase. From this analysis we report a vortex structural transition near 15 T from an oblique lattice with an opening angle of ${73}^{\ensuremath{\circ}}$ at low magnetic fields to a triangular lattice with ${60}^{\ensuremath{\circ}}$ stabilized at high field. The temperature for onset of vortex dynamics has been identified from spin-spin relaxation. This is independent of the magnetic field at sufficiently high magnetic field similar to that reported for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ and is correlated with mass anisotropy of the material. This behavior is accounted for theoretically only in the limit of very high anisotropy.

Experiment and theory indicate that ${\mathrm{UPt}}_{3}$ is a topological superconductor in an odd-parity state, based in part from the temperature independence of the NMR Knight shift. However, quasiparticle spin-flip scattering near a surface, where the Knight shift is measured, might be responsible. We use polarized neutron scattering to measure the bulk susceptibility with $H\ensuremath{\parallel}c$, finding consistency with the Knight shift but inconsistency with theory for this field orientation. We infer that neither spin susceptibility nor a Knight shift are a reliable indication of odd parity.

The phase boundary between the quantum solid and the liquid phases of $^{4}\mathrm{He}$ is strongly modified in a porous material. However the phase diagram at very low temperatures remains unexplored. We have used a variable-volume experimental cell with optical access to visualize the crystallization of $^{4}\mathrm{He}$ in silica aerogels with independent control of the pressure and temperature. The onset of crystallization was investigated in two aerogel samples with differing porosity both by pressurization at constant temperature and by cooling at constant pressure. With isothermal pressurization we have established a low-temperature phase diagram for each aerogel, and we find that the equilibrium crystallization pressure is reduced with increasing aerogel porosity. Crystals also began to grow in the aerogel on cooling at fixed pressure below an onset temperature ${T}_{\mathrm{grow}}$. We found that below this temperature the crystallization rate increased with decreasing temperature. The aerogel in our cell was surrounded by bulk crystals of $^{4}\mathrm{He}$, and surprisingly ${T}_{\mathrm{grow}}$ was found to be widely distributed when the surrounding bulk crystals were repressurized. In this experimental arrangement, crystallization within the aerogel on cooling requires mass flow from these exterior bulk crystals and is strongly influenced by the disordered structure at the interface between the bulk solid and the helium within the aerogel.

We present nuclear magnetic resonance evidence that very slow $(\ensuremath{\le}1$ MHz) spin fluctuations persist into the overdoped regime of $\mathrm{Ba}({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Rh}}_{x}){}_{2}{\mathrm{As}}_{2}$ superconductors. Measurements of the $^{75}\mathrm{As}$ spin echo decay rate, obtained both with Hahn Echo and Carr Purcell Meiboom Gill pulse sequences, show that the slowing down of spin fluctuations can be described by short-range diffusive dynamics, likely involving domain walls motions separating $(\ensuremath{\pi}/a,0)$ from $(0,\ensuremath{\pi}/a)$ correlated regions. This slowing down of the fluctuations is weakly sensitive to the external magnetic field and, although fading away with doping, it extends deeply into the overdoped regime.

Various forms of spin and charge ordering have been identified in a wide range of cuprate superconducting materials, but whether these behaviors are ubiquitous phenomena is not established. In this work we focus on one of the simplest compounds, HgBa$_{2}$CuO$_{4+\delta}$ (Hg1201), a superconductor with a high transition temperature, 97 K, having only a single layer and tetragonal structure, in contrast to one of the most extensively studied materials, YBa$_{2}$Cu$_{3}$O$_{6+y}$ (Y123). Using nuclear magnetic resonance we have discovered a coherent spatial modulation of both spin and charge that is temperature and magnetic field independent, in competition with superconductivity similar to other cuprates. However, there is no evidence for the magnetic field and temperature induced charge order observed in Y123. Electronic instabilities are a common feature of cuprates as in the present work on Hg1201, but their manifestations are not universal., Comment: 5 pages, 6 figures, and supplementary materials

We have performed optical birefringence measurements on isotropic aerogel samples grown with varying amounts of ammonia catalyst to determine the relationship between stress, strain, and transmitted light intensity, focusing on the regime of relatively small axial strain. We find that our samples exhibit a delayed onset of birefringence at ∼3 % strain, beyond which the transmitted intensity increases linearly, with a faster rate of increase for samples prepared with larger catalyst concentrations. We have also calculated the sound velocity from the slope of the stress-strain curve, and found an approximately linear increase with catalyst solution pH for samples of similar density. Samples of similar density also appear to exhibit a universal relationship between applied stress and transmitted intensity. We are not able to identify the mechanism for this unique behavior.

The distinct distribution of local magnetic fields due to superconducting vortices can be detected with nuclear magnetic resonance (NMR) and used to investigate vortices and related physical properties of extreme type II superconductivity. This review summarizes work on high temperature superconductors (HTS) including cuprates and pnictide materials. Recent experimental results are presented which reveal the nature of vortex matter and novel electronic states. For example, the NMR spectrum has been found to provide a sharp indication of the vortex melting transition. In the vortex solid a frequency dependent spin-lattice relaxation has been reported in cuprates, including YBa2Cu3O7−x, Bi2SrCa2Cu2O8+δ, and Tl2Ba2CuO6+δ. These results have initiated a new spectroscopy via Doppler shifted nodal quasiparticles for the investigation of vortices. At very high magnetic fields this approach is a promising method for the study of vortex core excitations. These measurements have been used to quantify an induced spin density wave near the vortex cores in Bi2SrCa2Cu2O8+δ. Although the cuprates have a different superconducting order parameter than the iron arsenide superconductors there are, nonetheless, some striking similarities between them regarding vortex dynamics and frequency dependent relaxation.

It has been predicted that superconducting vortices should be electrically charged and that this effect is particularly enhanced for, high temperature superconductors.\cite{kho95,bla96} Hall effect\cite{hag91} and nuclear magnetic resonance (NMR) experiments\cite{kum01} suggest the existence of vortex charging, but the effects are small and the interpretation controversial. Here we show that the Abrikosov vortex lattice, characteristic of the mixed state of superconductors, will become unstable at sufficiently high magnetic field if there is charge trapped on the vortex core. Our NMR measurements of the magnetic fields generated by vortices in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$ single crystals\cite{che07} provide evidence for an electrostatically driven vortex lattice reconstruction with the magnitude of charge on each vortex pancake of $\mathbf{\sim 2}$x$\mathbf{10^{-3} e}$, depending on doping, in line with theoretical estimates.\cite{kho95,kna05}, Comment: to appear in Nature Physics; 6 pages, 7 figures

It may be possible to stabilize new superfluid phases of $^{3}$He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid $^{3}$He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical $\sim$98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to be $\sim90^\circ$ out of phase relative to that induced by strain. This has implications for the possible stabilization of superfluid phases with specific symmetry., Comment: 6 pages, 4 figures, submitted to Quantum Fluids and Solids (QFS) conference 2006

We have made precision measurements of the frequency of a collective mode of the superfluid 3He-B order parameter, the J=2- imaginary squashing mode. Measurements were performed at multiple pressures using interference of transverse sound in an acoustic cavity. Transverse waves propagate in the vicinity of this order parameter mode owing to off-resonant coupling. At the crossing of the sound mode and the order parameter mode, the sound wave is strongly attenuated. We use both velocity and attenuation measurements to determine precise values of the mode frequency with a resolution between 0.1% and 0.25%., 6 pages, 4 figures, submitted to proceedings of Quantum Fluids and Solids (QFS) Conference 2006; revised 9/26/06

It has been shown that the relative stabilities of various superfluid states of ^{3}He can be influenced by anisotropy in a silica aerogel framework. We prepared a suite of aerogel samples compressed up to 30% for which we performed pulsed NMR on ^{3}He imbibed within the aerogel. We identified A and B phases and determined their magnetic field-temperature phase diagrams as a function of strain. From these results, we infer that the B phase is distorted by negative strain forming an anisotropic superfluid state more stable than the A phase.

We report our results of shear acoustic impedance measurements performed on superfluid 3He in 98% porosity silica aerogel. Experiments in high porosity aerogel provide unique opportunity to study the influence of disorder on a p-wave superfluid and compare the behavior with that of the well understood pure bulk. Our experiment is designed to detect acoustic signatures from both bulk liquid and liquid in aerogel. In the past, experiments on 3He in aerogel have been conducted in zero or low magnetic fields (< 1 tesla). We made measurements in magnetic fields as high as 15 tesla at 28.4 and 33.5 bars and observed a new phase in aerogel induced by magnetic fields splitting the superfluid transition into two.

We describe methods for the measurement of translational diffusion in very large static magnetic field gradients by NMR. The techniques use a "hole-burning" sequence that, with the use of fringe field gradients of 42 T/m, can image diffusion along one dimension on a submicron scale. Two varieties of this method are demonstrated, including a particularly efficient mode called the "hole-comb," in which multiple diffusion times comprising an entire diffusive evolution can be measured within the span of a single detected slice. The advantages and disadvantages of these methods are discussed, as well as their potential for addressing non-Fickian diffusion, diffusion in restricted media, and spatially inhomogeneous diffusion., 8 pages, 6 figures

Discovery of impurity phases of superfluid 3 He , produced by silica aerogel, provides a new approach to investigate the effect of disorder on unconventional pairing. A simple model that assumes homogeneous, isotropic scattering is in agreement with experiment including suppression of the superfluid transition temperature, the amplitude of the order parameter, and phase diagram of magnetic field, temperature, and pressure, with the feature that the polycritical point vanishes in a 98% porous aerogel. We also find a metastable equal-spin-pairing state in zero field although such a phase does not exist in equilibrium.

Combined theoretical and experimental studies are reported on alkali ion–cryptand interactions which affect charge transport in liquid electrolytes. Encapsulation of the cation by a cryptand cage can significantly improve the ionic conductivity, by reducing the fraction of time in which the cation is bound to its counterion. Comparison between experimental conductivities and NMR measurements of diffusion rates of Li and F in the amorphous LiMPSA electrolyte suggest that in the presence of the C222 cryptand, Li is bound to MPSA about 75% of the time. A hybrid classical/quantum methodology is used to model dynamics and electronic structure of a number of cryptand–alkali ion–MPSA and cryptand–ion–cryptand systems in an effort to extract general features which may be useful in designing electrolytes with improved performance.

We report on a solution to the problem of phase noise in nuclear magnetic resonance (NMR) experiments. Phase noise refers to the variation in the phases of NMR signals from successive acquisitions due to an unstable applied field. Such a situation exists in high-field resistive Bitter magnets and, for sufficiently long timescales, can cause serious signal degradation upon signal averaging. An inductive shield, formed by a highly conducting metal tube placed around the sample and along the applied field, provides screening of the AC components of the applied field and thereby retains phase coherence over long periods. Although simple in principle there are technical difficulties for practical implementation of this method. We present demonstrations of the utility of this approach. In particular, we show a significant extension of the effective transverse coherence time of the 13 C resonance in doubly 13 C -labeled glycerol in a resistive Bitter magnet. This was accomplished through the use of a highly conducting aluminum shield, cooled to 4 K with liquid helium.

Signals suffering from phase noise, such as spin echoes from NMR experiments in a fluctuating magnetic field, can be underestimated by traditional signal averaging. Averaging in the polar rather than in the Cartesian domain can solve this problem. However, because of background noise, there is an inherent drawback in the polar averaging technique: polar averaging under conditions of a low initial signal to noise will cause these same signals to be overestimated. We studied this problem with both numerical simulations and experiments. The quantitative results allow not only an assessment of the applicability of polar averaging for a given experiment but also possible corrections of the overestimate. © 2002 Wiley Periodicals, Inc. Concepts Magn Reson 14: 359–364, 2002

Nuclear magnetic resonance techniques are used to study anomalously high diffusion of methanol in porous silica aerogel.

In recent work, it was shown that new anisotropic p-wave states of superfluid (3)He can be stabilized within high-porosity silica aerogel under uniform positive strain. In contrast, the equilibrium phase in an unstrained aerogel is the isotropic superfluid B phase. Here we report that this phase stability depends on the sign of the strain. For a negative strain of ∼ 20% achieved by compression, the B phase can be made more stable than the anisotropic A phase, resulting in a tricritical point for A, B, and normal phases with a critical field of ∼ 100 mT. From pulsed NMR measurements, we identify these phases and the orientation of the angular momentum.

This work was supported by the National Science Foundation grants: DMR-1202991 and DMR-1103625.

Puzzling aspects of high-transition-temperature (high-Tc) superconductors include the prevalence of magnetism in the normal state and the persistence of superconductivity in high magnetic fields. Superconductivity and magnetism generally are thought to be incompatible, based on what is known about conventional superconductors. Recent results, however, indicate that antiferromagnetism can appear in the superconducting state of a high-Tc superconductor in the presence of an applied magnetic field. Magnetic fields penetrate a superconductor in the form of quantized flux lines, each of which represents a vortex of supercurrents. Superconductivity is suppressed in the core of the vortex and it has been suggested that antiferromagnetism might develop there. Here we report the results of a high-field nuclear-magnetic-resonance (NMR) imaging experiment in which we spatially resolve the electronic structure of near-optimally doped YBa2Cu3O7-delta inside and outside vortex cores. Outside the cores, we find strong antiferromagnetic fluctuations, whereas inside we detect electronic states that are rather different from those found in conventional superconductors.

We have studied the temporal instability of a high field resistive Bitter magnet through nuclear magnetic resonance (NMR). This instability leads to transverse spin decoherence in repeated and accumulated NMR experiments as is normally performed during signal averaging. We demonstrate this effect via Hahn echo and Carr--Purcell--Meiboom--Gill (CPMG) transverse relaxation experiments in a 23-T resistive magnet. Quantitative analysis was found to be consistent with separate measurements of the magnetic field frequency fluctuation spectrum, as well as with independent NMR experiments performed in a magnetic field with a controlled instability. Finally, the CPMG sequence with short pulse delays is shown to be successful in recovering the intrinsic spin--spin relaxation even in the presence of magnetic field temporal instability.

An acoustic cavity containing 3He in 98% porous silica aerogel was used to investigate the effects of impurity scattering in a Fermi liquid. The pressure and temperature dependence of the sound attenuation in the normal Fermi liquid was extracted from the cavity response. The attenuation of sound displays behavior very different from the bulk owing to strong elastic scattering of quasi-particles by the silica strands. Using a visco-elastic model of the Fermi liquid, we find a mean free path restricted to ∼340 nm. Information on the sound velocity is inferred from the pressure dependence of the oscillation period of the cavity response. The data can be accounted for by a Biot model of the 3He liquid in the porous aerogel.

We studied the anisotropic magnetic response of the internal superconducting phases of ${\mathrm{UPt}}_{3}$ and its anisotropic magnetic susceptibility with a capacitive torque meter which is very sensitive in high fields. Experiments were performed at temperatures down to 20 mK and at various angles between the c axis (hexagonal structure) and $\stackrel{\ensuremath{\rightarrow}}{B},$ ranging from 16\ifmmode^\circ\else\textdegree\fi{} to 82\ifmmode^\circ\else\textdegree\fi{}. The samples were four single crystals grown with different methods and subjected to different annealing procedures. The normal state susceptibility has a maximum around 20 K for $\stackrel{\ensuremath{\rightarrow}}{B}$ in the $a\ensuremath{-}b$ plane which we followed up to 14 T. It may arise from hybridized uranium ion states split by the hexagonal crystal field. The magnetization curves in the superconducting (SC) regime show strong irreversibilities which are highly sample dependent. They are not correlated with the internal SC phase lines but continue up to a line of fields that lies parallel to the ${B}_{c2}$ curve and even follows its kink at the tetracritical point ${(T}^{\ensuremath{\star}}{,B}^{\ensuremath{\star}}).$ In the cleanest sample this line is shifted to fields well below the $B\ensuremath{-}C$ internal phase line which then manifests itself in a pronounced kink of the magnetization curve indicating an enhanced Ginzburg-Landau parameter $\ensuremath{\kappa}.$ In another sample the $B\ensuremath{-}C$ phase line between two of the three internal SC states could be detected even in the hysteretic region. The enhanced Ginzburg-Landau parameter $\ensuremath{\kappa}$ means a larger penetration depth and/or a shorter coherence length, clear evidence for the unconventional character of the $B\ensuremath{-}C$ phase transition. With our cleanest sample we also observe an anomalous peak effect, a region of enhanced flux pinning near ${B}_{c2},$ which is probably related to the Fulde-Ferrell-Larkin-Ovchinnikov state. In yet another sample we find a crossing of the up-down magnetization curves, also near ${B}_{c2},$ but with reversed orientation of the magnetization loops. We interpret this in terms of different flux pinning in the two main crystal directions, possibly in relation to the peak effect which is, however, masked in this sample by strong irreversibilities.

We have prepared pure YBCO (YBa 2 Cu 3 O 7− δ ) and Ni-doped YBCO (YBa 2− x La x Cu 3− x Ni x O 7− δ , x =0.1) samples and performed 63,65 Cu nuclear quadrupole resonance (NQR) measurements. La substitution introduced for charge compensation, as well as Ni doping, severely distorts the electric field gradient at the copper sites inducing extra 63,65 Cu NQR peaks other than the main peaks, for both the plane and the chain sites. 63,65 Cu NQR linewidths for the plane site increased significantly whereas those for the chain site remained similar. Furthermore, both the spin–lattice and the spin–spin relaxation times for the plane copper decreased whereas those for the chain copper increased. The Ni substitutional effects on linewidths and relaxation times confirm that Ni carrying a local moment substitutes for the plane copper.

The electronic spin susceptibility of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.95}$ has been measured with high precision up to 24 T with ${}^{17}\mathrm{O}$ nuclear magnetic resonance. Its temperature dependence can be accounted for by superconducting fluctuations that result in a smooth crossover from the normal to the vortex liquid state. A magnetic-field-temperature phase diagram for this crossover has been established having strong upward curvature.

We report 63Cu(2) spin-lattice relaxation rate measurements of YBa_2Cu_3O_{6.95} in magnetic fields from 2.1 T to 27.3 T obtained from 17O(2,3) nuclear magnetic resonance spin-spin relaxation. For T < 120 K, the spin-lattice rate increases with increasing magnetic field. We identify this magnetic field dependence with the change in the low-energy spectral weight originating from d-wave pairing fluctuation corrections to the density of states.

We have measured the dc magnetization of three high-quality single crystals of ${\mathrm{UPt}}_{3}$ with a SQUID magnetometer down to $\ensuremath{\approx}5\mathrm{mK}$ in magnetic fields below 2 mT. With $\stackrel{\ensuremath{\rightarrow}}{B}$ in the $\stackrel{^}{c}$ direction we find a double superconducting transition, while for $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\parallel}\stackrel{^}{a}$ we observe only one. At lower temperatures the temperature dependence of the magnetization follows power laws indicating unconventional behavior for the penetration depth. Below 20 mK a steep diamagnetic drop occurs, coinciding with the specific heat anomaly which we found earlier at 18 mK, pointing to static antiferromagnetic order.

Neutron diffraction studies of the static structure factor S(Q) of water confined in the pore space of cement samples have been carried out for temperatures from 170 to 293 K. At high temperatures, when the water in the pores is liquid, a fraction of the water molecules are strongly bound to specific adsorption sites on the crystalline components of the cement. On cooling, the water in the pore space solidifies at 245 K into a cubic structure different from that of bulk water at similar temperatures.

High-quality single crystals of ${\mathrm{UPt}}_{3}$ have been prepared by vertical float-zone refining in ultrahigh vacuum. We find that the superconducting transition temperature can be varied systematically by annealing, revealing that the transition temperature intrinsic to ${\mathrm{UPt}}_{3}$ is $563\ifmmode\pm\else\textpm\fi{}5 \mathrm{mK}.$ The suppression of the superconducting transition from defects is consistent with a modified Abrikosov-Gor'kov formula that includes anisotropic pairing, Fermi-surface anisotropy, and anisotropic scattering by defects.

The magnetic field--temperature phase diagram for vortex dynamics in $\mathrm{Y}\mathrm{Ba}{}_{2}\mathrm{Cu}{}_{3}{\mathrm{O}}_{7}$ has been extended up to 24 T based on $^{17}O$ NMR experiments on aligned powders. Both spectrum analysis and spin-spin relaxation experiments indicate that vortices are pinned below a temperature ${T}_{p}$, which for low fields is consistent with ${T}_{m}$, the first order melting transition for clean, untwinned crystals. At high fields 10--24 T, ${T}_{p}$ is 80 K and field independent. Pinned vortices have a Lorentzian spectral density of field fluctuations with a sharp onset.

Line-shape analysis of {sup 17}O NMR spectra is used to probe vortex melting and dynamics in aligned powders of YBa{sub 2}O{sub 3}O{sub 7}. Vortex transitions are identified by comparing their dynamics with the NMR time scale. Line-shape changes indicate a well-defined melting transition at a temperature, T{sub m}. Below T{sub m} there is a coexistence regime of solid and liquid vortices with a lower bound, T{sub g}, which marks complete vortex freezing. {copyright} {ital 1997} {ital The American Physical Society}