Search

Landau predicted that transverse sound propagates in a Fermi liquid with sufficiently strong Fermi liquid interactions, unlike a classical fluid which cannot support shear oscillations. Previous attempts to observe this unique collective mode yielded inconclusive results due to contributions from single particle excitations. Here, we have microfabricated acoustic cavities with a micron-scale path length that is suitable for direct detection of this sound mode. The interference fringes of these acoustic Fabry-Perot cavities can be used to determine both the real and imaginary parts of the acoustic impedance. We report a null-result in this search as no clear interference fringe has been observed in the Fermi liquid, indicating the attenuation of TZS is likely above 2000 cm^-1. We provide theoretical justification for why the sound mode may yet exist but not being directly detectable due to high attenuation.

Anisotropic aerogel possesses structure which exhibits a strong influence over the composition and orientation of the order parameter of imbibed superfluid $^3$He. Computational studies have identified stretched aerogel with plane-like structures and compressed aerogel with nematic-like structures. Studies of the B phase of superfluid $^3$He in stretched aerogel display an enhanced nuclear magnetic susceptibility likely caused by Andreev bound states near plane-like impurity sites. We report further details on the influence of these planar structures on both magnetic and orbital orientation transitions. The orbital orientation transitions appear in both the B and A phases of stretched and compressed aerogels. These transitions result from a crossover of the superfluid coherence length with long and short length scale structure with the coherence length and are consequently magnetic field independent. Additionally, the apparent temperature-independence of the susceptibility of the B phase equal to that of the A phase in stretched aerogel, is in marked contrast with the field dependence of the superfluid A to B phase transition, indicating that it is a near-isentropic transition.

Nuclear magnetic resonance measurements of the magnetic susceptibility of superfluid $^3$He imbibed in anisotropic aerogel reveal anomalous behavior at low temperatures. Although the frequency shift clearly identifies a low-temperature phase as the $B$ phase, the magnetic susceptibility does not display the expected decrease associated with the formation of the opposite-spin Cooper pairs. This susceptibility anomaly appears to be the predicted high-field behavior corresponding to the Ising-like magnetic character of surface Andreev bound states within the planar aerogel structures., Comment: Published version

We perform cluster aggregation simulations to model the structure of anisotropic aerogel. By biasing the diffusion process, we are able to obtain two distinct types of globally anisotropic aerogel structures which we call "nematic", with long strands along the anisotropy axis, and "planar", with long strands in planes perpendicular to the anisotropy axis. We calculate the auto-correlation function, the structure factor, and the angular dependence of the free-path distribution for these samples. The calculated structure factor from simulated aerogels can be compared with data from small-angle X-ray scattering (SAXS) of lab-grown aerogel allowing us to classify the spatial structure of the lab-grown samples. We find that the simulated "nematic" aerogel has a structure factor consistent with lab-grown, axially-compressed silica aerogel while the simulated "planar" aerogel has a structure factor consistent with lab-grown "stretched" silica aerogel. Unexpectedly, compressing previously isotropic silica aerogel leads to the formation of long strands along the compression axis while stretching silica aerogel leads to formation of planes perpendicular to the stretching axis. We discuss the implication of this determination on experiments of superfluid $^3$He in anisotropic aerogel, in particular the orbital analog of the spin-flop transition., Comment: 25 pages, 9 figures

Axions and axion-like particles may couple to nuclear spins like a weak oscillating effective magnetic field, the "axion wind." Existing proposals for detecting the axion wind sourced by dark matter exploit analogies to nuclear magnetic resonance (NMR) and aim to detect the small transverse field generated when the axion wind resonantly tips the precessing spins in a polarized sample of material. We describe a new proposal using the homogeneous precession domain (HPD) of superfluid helium-3 as the detection medium, where the effect of the axion wind is a small shift in the precession frequency of a large-amplitude NMR signal. We argue that this setup can provide broadband detection of multiple axion masses simultaneously, and has competitive sensitivity to other axion wind experiments such as CASPEr-Wind at masses below $10^{-7}$ eV by exploiting precision frequency metrology in the readout stage., Comment: v2: typos fixed and references added. v1: 5+1 pages, 3 figures

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt3 for the applied magnetic field along the crystalline c-axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal place that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt +/-15 degree vortex lattice rotation was previously reported by Huxley et al., Nature 406, 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al., Nature Physics 16, 531-535 (2020), can be attributed directly to the symmetry breaking field., Comment: To appear in Frontiers of Electronic Materials, Research topic on "New Heavy Fermion Superconductors"

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.

When studied by small-angle neutron scattering the vortex lattice (VL) in UPt3 undergoes a gradual disordering as a function of time due to 235U fission. This temporarily heats regions of the sample above the critical temperature, where, upon re-cooling, the vortices remain in a quenched vortex glass state. The disordering rate is proportional to the magnetic field, suggesting that it is governed by collective VL properties such as the elastic moduli. An ordered VL can be re-formed by applying a small field oscillation, showing that the fission does not cause significant radiation damage to the UPt3 crystals, even after long exposure., Comment: Multiple revisions

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., Comment: 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., Comment: Main Text: 6 pages, 3 figures SM: 19 pages, 23 figures Some clarifications are made relative to previous version

Neutron scattering measurements have demonstrated that the heavily Cu-doped NaFe$_{1-x}$Cu$_{x}$As compound behaves like a Mott insulator exhibiting both real space Fe-Cu stripes, as well as antiferromagnetism below a N\'eel temperature for $x\lesssim 0.5$. We have investigated evolution of structural and magnetic ordering using $^{23}$Na and $^{75}$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 $^{75}$As spectra, we show that a staggered magnetization at the Fe sites is induced by non-magnetic Cu dopants., Comment: 8 pages, 11 figures

The critical field for superfluid $^3$He in axially compressed, anisotropic silica aerogel is shown to be the result of an anisotropic distribution of magnetic impurities affecting the superfluid $A$ phase. The critical field results from the fact that the $A$ phase is suppressed relative to the $B$ phase which is immune to the effects of magnetic impurities. In the absence of magnetic quasiparticle scattering in anisotropic aerogel, we find that the relative symmetry of $A$ and $B$ phase order parameters is the same as in isotropic aerogel, just as it is in pure superfluid $^3$He. These results are of potential importance for understanding unconventional superconductivity.

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., Comment: 20 pages, 10 figures

The topological superconductor UPt3, has three distinct vortex phases, a strong indication of its unconventional character. Using small-angle neutron scattering we have probed the vortex lattice in the UPt3 B phase with the magnetic field along the crystal c-axis. We find a difference in the vortex lattice configuration depending on the sign of the magnetic field relative to the field direction established upon entering the B phase at low temperature in a field sweep, showing that the vortices in this material posses an internal degree of freedom. This observation is facilitated by the discovery of a field driven non-monotonic vortex lattice rotation, driven by competing effects of the superconducting gap distortion and the vortex-core structure. From our bulk measurements we infer that the superconducting order parameter in the UPt3 B phase breaks time reversal symmetry and exhibits chiral symmetry with respect to the c-axis., Comment: 7 pages plus 3 pages of supplementary material

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)., Comment: 9 pages, 5 figures

Superfluid 3He has a rich spectrum of collective modes with both massive and massless excitations. The masses of these modes can be precisely measured using acoustic spectroscopy and fit to theoretical models. Prior comparisons of the experimental results with theory did not include strong-coupling effects beyond the weak-coupling-plus BCS model, so-called non-trivial strong-coupling corrections. In this work we utilize recent strong-coupling calculations to determine the Higgs masses and find consistency between experiments that relate them to a sub-dominant $f$-wave pairing strength., Comment: 5 pages, 2 figures

The direction of the orbital angular momentum of the $B$-phase of superfluid $^3$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 $^3$He is amazingly simple. In the Ginzburg-Landau regime, i.e. close to $T_c$, 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 $^3$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 $^3$He-A is a useful reference, and this simple pressure dependence greatly facilitates identification.

Superfluids and superconductors have a common conceptual basis in systems ranging from the lightest to the heaviest.

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

Experiment and theory indicate that UPt3 is a topological superconductor in an odd-parity state, based in part from 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||c, finding consistency with the Knight shift but inconsistent with theory for this field orientation. We infer that neither spin susceptibility nor Knight shift are a reliable indication of odd-parity.

Measurements of the $^{17}$O nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in HgBa$_{2}$CuO$_{4+\delta}$ were performed over a range of magnetic fields from 6.4 to 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. Non-vortex 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 $73^{\circ}$ at low magnetic fields to a triangular lattice with $60^{\circ}$ stabilized at high field. The temperature for onset of vortex dynamics has been identified with vortex lattice melting. This is independent of the magnetic field at sufficiently high magnetic field similar to that reported for YBa$_2$Cu$_3$O$_7$ and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and is correlated with mass anisotropy of the material. This behavior is accounted for theoretically only in the limit of very high anisotropy.

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 present nuclear magnetic resonance evidence that very slow ($\leq 1$ MHz) spin fluctuations persist into the overdoped regime of Ba(Fe$_{1-x}$Rh$_{x}$)$_2$As$_2$ superconductors. Measurements of the $^{75}$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 $(\pi/a,0)$ from $(0,\pi/a)$ 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., Comment: 7 pages, 7 figures

It has been shown that the relative stabilities of various superfluid states of 3He 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 3He 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.

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., Comment: 19 pages, 7 figures

In recent work it was shown that new anisotropic p-wave states of superfluid 3He can be stabilized within high porosity silica aerogel under uniform positive strain [1]. In contrast, the equilibrium phase in an unstrained aerogel, is the isotropic superfluid B-phase [2]. Here we report that this phase stability depends on the sign of the strain. For 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., Comment: 4 pages and 3 figures

This work presents 75As NMR spin echo decay rate (1/T2) measurements in Ba(Fe1-xRhx)2As2 superconductors, for 0.041 < x < 0.094. It is shown that 1/T2 increases upon cooling, in the normal phase, suggesting the onset of an unconventional very low-frequency activated dynamic. The correlation times of the fluctuations and their energy barriers are derived. The motion is favored at large Rh content, while it is hindered by the application of a magnetic field perpendicular to the FeAs layers. The same dynamic is observed in the spin-lattice relaxation rate, in a quantitatively consistent manner. These results are discussed in the light of nematic fluctuations involving domain wall motion. The analogies with the behaviour observed in the cuprates are also outlined.

We present data for energy dissipation factor (Q^{-1}) over a broad temperature range at various pressures of a torsion pendulum setup used to study 3He confined in a 98% open silica aerogel. Values for Q^{-1} above T_c are temperature independent and have a weak pressure dependence. Below T_c, a deliberate axial compression of the aerogel by 10% widens the range of metastability for a superfluid Equal Spin Pairing (ESP) state; we observe this ESP phase on cooling and the B phase on warming over an extended temperature region. While the dissipation for the B phase tends to zero as T goes to 0, Q^{-1} exhibits a peak value greater than that at T_c at intermediate temperatures. Values for Q^{-1} in the ESP phase are consistently higher than in the B phase and are proportional to \rho_s/\rho until the ESP to B phase transition is attained. We apply a viscoelastic collision-drag model, which couples the motion of the helium and the aerogel through a frictional relaxation time \tau_f. Our dissipation data is not sensitive to the damping due to the presumed small but non-zero value of \tau_f. The result is that an additional mechanism to dissipate energy not captured in the collision-drag model and related to the emergence of the superfluid order must exist. The extra dissipation below T_c is possibly associated with mutual friction between the superfluid phases and the clamped normal fluid. The pressure dependence of the measured dissipation in both superfluid phases is likely related to the pressure dependence of the gap structure of the "dirty" superfluid. The large dissipation in the ESP state is consistent with the phase being the A or the Polar with the order parameter nodes oriented in the plane of the cell and perpendicular to the aerogel anisotropy axis., Comment: 12 pages, 7 figures

It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder [1, 2]. This principle is of central importance in a wide variety of condensed systems including superconducting vortices [3, 4], Ising spin models [5] and their dynamics [6], and liquid crystals in porous media [7, 8], where some degree of disorder is ubiquitous, although its experimental observation has been elusive. Based on these ideas it was predicted [9] that 3He in high porosity aerogel would become a superfluid glass. We report here our nuclear magnetic resonance measurements on 3He in aerogel demonstrating destruction of long range orientational order of the intrinsic superfluid orbital angular momentum, confirming the existence of a superfluid glass. In contrast, 3He-A generated by warming from superfluid 3He-B has perfect long-range orientational order providing a mechanism for switching off this effect., Comment: 5 pages, 5 figures and supplementary information

We have performed $^{75}$As and $^{23}$Na nuclear magnetic resonance (NMR) measurements on a single crystal of NaFe$_{0.9835}$Co$_{0.0165}$As and found microscopic coexistence of superconductivity with a two-component spin density wave (SDW). Using $^{23}$Na NMR we measured the spatial distribution of local magnetic fields. The SDW was found to be incommensurate with a major component having magnetic moment ($\sim0.2\,\mu_B$/Fe) and a smaller component with magnetic moment ($\sim0.02\,\mu_B$/Fe). Spin lattice relaxation experiments reveal that this coexistence occurs at a microscopic level., Comment: 5 figures

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]., Comment: 3 pages, 3 figures

The simple structure of HgBa$_2$CuO$_{4+\delta}$ (Hg1201) is ideal among cuprates for study of the pseudogap phase as a broken symmetry state. We have performed $^{17}$O nuclear magnetic resonance (NMR) on an underdoped Hg1201 crystal with transition temperature of 74 K to look for circulating orbital currents proposed theoretically and inferred from neutron scattering. The narrow spectra preclude static local fields in the pseudogap phase at the apical site, suggesting that the moments observed with neutrons are fluctuating. The NMR frequency shifts are consistent with a dipolar field from the Cu$^{+2}$ site., Comment: 6 pages, 5 figures

Spanning a broad range of physical systems, complex symmetry breaking is widely recognized as a hallmark of competing interactions. This is exemplified in superfluid $^3$He which has multiple thermodynamic phases with spin and orbital quantum numbers $S=1$ and $L=1$, that emerge on cooling from a nearly ferromagnetic Fermi liquid. The heavy fermion compound UPt$_3$ exhibits similar behavior clearly manifest in its multiple superconducting phases. However, consensus as to its order parameter symmetry has remained elusive. Our small angle neutron scattering measurements indicate a linear temperature dependence of the London penetration depth characteristic of nodal structure of the order parameter. Our theoretical analysis is consistent with assignment of its symmetry $L=3$ odd parity state for which one of the three thermodynamic phases in non-zero magnetic field is chiral., Comment: 7 pages, 7 figures

We have performed $^{75}$As nuclear magnetic resonance (NMR) Knight shift measurements on single crystals of NaFe$_{0.975}$Co$_{0.025}$As to show that its superconductivity is a spin-paired, singlet state consistent with predictions of the weak-coupling BCS theory. We use a spectator nucleus, $^{23}$Na, uncoupled from the superconducting condensate, to determine the diamagnetic magnetization and to correct for its effect on the $^{75}$As NMR spectra. The resulting temperature dependence of the spin susceptibility follows the Yosida function as predicted by BCS for an isotropic, single-valued energy gap. Additionally, we have analyzed the $^{23}$Na spectra that become significantly broadened by vortices to obtain the superconducting penetration depth as a function of temperature with $\lambda_{ab}(0) = 5,327 \pm$ 78$\,\AA$., Comment: 4pages, 5 figures

The heavy fermion superconductor UPt$_3$ is thought to have odd-parity, a state for which the temperature dependence of the spin susceptibility is an important signature. In order to address conflicting reports from two different experiments, the NMR Knight shift and measurements of the anisotropy of the upper critical field, we have measured the bulk susceptibility in a high quality single crystal using polarized-neutron diffraction. A temperature independent susceptibility was observed for $H||a$ through the transitions between the normal state and the superconducting A-, B- and C-phases, consistent with odd-parity, spin-triplet superconductivity., Comment: 5 pages, 4 figures. Submitted to Physical Review Letters

We present results of transverse acoustics studies in superfluid ^{3}He-B at fields up to 0.11 T. Using acoustic cavity interferometry, we observe the Acoustic Faraday Effect for a transverse sound wave propagating along the magnetic field, and we measure Faraday rotations of the polarization as large as 1710^{\circ}. We use these results to determine the Zeeman splitting of the Imaginary Squashing mode, an order parameter collective mode with total angular momentum J=2. We show that the pairing interaction in the f-wave channel is attractive at a pressure of P=6 bar. We also report nonlinear field dependence of the Faraday rotation at frequencies substantially above the mode frequency not accounted for in the theory of the transverse acoustic dispersion relation formulated for frequencies near the mode. Consequently, we have identified the region of validity of the theory allowing us to make corrections to the analysis of Faraday rotation experiments performed in earlier work., Comment: 7 pages, 5 figures

We have studied the acoustic Faraday effect in superfluid 3He up to significantly larger magnetic fields than in previous experiments achieving rotations of the polarization of transverse sound as large as 1710^{\circ}. We report nonlinear field effects, and use the linear results to determine the Zeeman splitting of the imaginary squashing mode (ISQ) frequency in 3He-B., Comment: 7 pages, 5 figures, to appear in JLTP

A rich variety of Fermi systems condense by forming bound pairs, including high temperature [1] and heavy fermion [2] superconductors, Sr2RuO4 [3], cold atomic gases [4], and superfluid 3He [5]. Some of these form exotic quantum states having non-zero orbital angular momentum. We have discovered, in the case of 3He, that anisotropic disorder, engineered from highly porous silica aerogel, stabilizes a chiral superfluid state that otherwise would not exist. Additionally, we find that the chiral axis of this state can be uniquely oriented with the application of a magnetic field perpendicular to the aerogel anisotropy axis. At suffciently low temperature we observe a sharp transition from a uniformly oriented chiral state to a disordered structure consistent with locally ordered domains, contrary to expectations for a superfluid glass phase [6]., Comment: 6 pages, 4 figure, and Supplementary Information

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 YBa$_2$Cu$_3$O$_{7-x}$, Bi$_2$SrCa$_2$Cu$_2$O$_{8+\delta}$, and Tl$_2$Ba$_2$CuO$_{6+\delta}$. 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 Bi$_2$SrCa$_2$Cu$_2$O$_{8+\delta}$. 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., Comment: 13 pages, 13 figures, to appear in Frontiers of Physics

Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we measure the pressure dependent superfluid fraction of 3He entrained in 10% axially compressed, 98% porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at Tc, is in contrast to its absence in uncompressed aerogel. The phase diagram is modified from that of pure 3He, with the disappearance of the polycritical point (PCP) and the appearance of a region of A phase extending below the PCP of bulk 3He, even in zero applied magnetic field. The expected alignment of the A phase texture by compression is not observed., Comment: 4 pages, 4 figures. Submitted for review to PRL

The spatially averaged density of states, , of an unconventional d-wave superconductor is magnetic field dependent, proportional to $H^{1/2}$, owing to the Doppler shift of quasiparticle excitations in a background of vortex supercurrents[1,2]. This phenomenon, called the Volovik effect, has been predicted to exist for a sign changing $s\pm$ state [3], although it is absent in a single band s-wave superconductor. Consequently, we expect there to be Doppler contributions to the NMR spin-lattice relaxation rate, $1/T_1 \propto $, for an $s\pm$ state which will depend on magnetic field. We have measured the $^{75}$As $1/T_1$ in a high-quality, single crystal of Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ over a wide range of field up to 28 T. Our spatially resolved measurements show that indeed there are Doppler contributions to $1/T_1$ which increase closer to the vortex core, with a spatial average proportional to $H^2$, inconsistent with recent theory [4], Comment: 5 pages, 5 figures

Superfluid 3He confined to high porosity silica aerogel is the paradigm system for understanding impurity effects in unconventional superconductors. However, a crucial first step has been elusive; exact identification of the microscopic states of the superfluid in the presence of quenched disorder. Using a new class of highly uniform aerogel materials, we report pulsed nuclear magnetic resonance experiments that demonstrate definitively that the two observed superfluid states in aerogel are impure versions of the isotropic and axial p-wave states. The theoretically predicted destruction of long-range orbital order (Larkin-Imry Ma effect) in the impure axial state is not observed., Comment: 4 pages, 5 figures, to appear in Phys. Rev. Lett

The superconducting state of an optimally doped single crystal of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$ was investigated by $^{75}$As NMR in high magnetic fields from 6.4 T to 28 T. It was found that the Knight shift is least affected by vortex supercurrents in high magnetic fields, $H>11$ T, revealing slow, possibly higher order than linear, increase with temperature at $T \lesssim 0.5 \, T_c$, with $T_c \approx 23 \, K$. This is consistent with the extended s-wave state with $A_{1g}$ symmetry but the precise details of the gap structure are harder to resolve. Measurements of the NMR spin-spin relaxation time, $T_2$, indicate a strong indirect exchange interaction at all temperatures. Below the superconducting transition temperature vortex dynamics lead to an anomalous dip in $T_2$ at the vortex freezing transition from which we obtain the vortex phase diagram up to $H = 28$ T., Comment: 13 pages, 9 figures

Competition with magnetism is at the heart of high temperature superconductivity, most intensely felt near a vortex core. To investigate vortex magnetism we have developed a spatially resolved probe using nuclear magnetic resonance. Our spin-lattice-relaxation spectroscopy is spatially resolved both within a conduction plane as well as from one plane to another. With this approach we have found a spin-density wave associated with the vortex core in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, which is expected from scanning tunneling microscope observations of "checkerboard" patterns in the local density of electronic states.[1] We determine both the spin-modulation amplitude and decay length from the vortex core in fields up to H=30 T., Comment: 7 pages, 5 figures

We present results of the $Q^{-1}$ and period shift, $\Delta P$, for $^3$He confined in a 98% nominal open aerogel on a torsion pendulum. The aerogel is compressed uniaxially by 10% along a direction aligned to the torsion pendulum axis and was grown within a 400 $\mu$m tall pancake (after compression) similar to an Andronikashvili geometry. The result is a high $Q$ pendulum able to resolve $Q^{-1}$ and mass coupling of the impurity-limited $^3$He over the whole temperature range. After measuring the empty cell background, we filled the cell above the critical point and observe a temperature dependent period shift, $\Delta P$, between 100 mK and 3 mK that is 2.9$%$ of the period shift (after filling) at 100 mK. The $Q^{-1}$ due to the $^3$He decreases by an order of magnitude between 100 mK and 3 mK at a pressure of $0.14\pm0.03$ bar. We compare the observable quantities to the corresponding calculated $Q^{-1}$ and period shift for bulk $^3$He., Comment: 8 pages, 3 figures

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