Measurements of nematic susceptibility with phase sensitive nuclear magnetic resonance in pulsed strain fields.

We present nuclear magnetic resonance data in BaFe2As2 in the presence of pulsed strain fields that are interleaved in time with the radio frequency excitation pulses. In this approach, the preceding nuclear magnetization acquires a phase shift that is proportional to the strain and pulse time. The sensitivity of this approach is limited by the homogeneous decoherence time, T2, rather than the inhomogeneous linewidth. We measure the nematic susceptibility as a function of temperature and demonstrate a three orders of magnitude improvement in sensitivity. This approach will enable studies of the strain response in a broad range of materials that previously were inaccessible due to inhomogeneous broadening.

Possible unconventional order parameter in single crystals of SrPt3P superconductor.

Anisotropic properties of single crystals of SrPt3P were studied using London penetration depth and electrical resistivity measurements. The upper critical field,Hc2(T), was determined from four-probe electrical resistivity measurements for three orthogonal directions of a magnetic field with respect to the crystal. The London penetration depth,λ(T), was determined from the magnetic susceptibility of the Meissner-London state measured using a tunnel-diode resonator technique. WhereasHc2(T)and the normal-stateρ(T)are practically identical for all three magnetic field orientations, the London penetration depth shows significant unidirectional anisotropy. The low-temperatureλ(T)is exponentially attenuated when a small excitation radiofrequency magnetic field,Hrf, is applied along thec''-direction, in which case screening currents flow in thea''b''-plane, while for the other two orientations,Hrf∥a''andHrf∥b'', the London penetration depth shows a much stronger,λ(T)∼T2, variation. Such unusual and contrasting behavior of the two anisotropies,γHT=Hc2,ab/Hc2,c=ξab/ξcandγλT=λc/λab, imposes significant constraints on the possible order parameter. Although our measurements are insufficient to derive conclusively the superconducting gap anisotropy, the order parameter with two point nodes and a modulation in the perpendicular direction is qualitatively consistent with the experimental observations.

Low-temperature high-frequency dynamic magnetic susceptibility of classical spin-ice Dy2Ti2O7.

Radio-frequency (14.6 MHz) AC magnetic susceptibility,χAC', of Dy2Ti2O7was measured using self-oscillating tunnel-diode resonator. Measurements were made with the excitation AC field parallel to the superimposed DC magnetic field up to 5 T in a wide temperature range from 50 mK to 100 K. At 14.6 MHz, a known broad peak ofχAC'(T)from kHz-range audio-frequency measurements around 15 K for both [111] and [110] directions shifts to 45 K, continuing the Arrhenius activated behavior with the same activation energy barrier ofEa≈ 230 K. Magnetic field dependence ofχAC'along [111] reproduces previously reported low-temperature two-in-two-out to three-in-one-out spin configuration transition at about 1 T, and an intermediate phase between 1 and 1.5 T. The boundaries of the intermediate phase show reasonable overlap with the literature data and connect at a critical endpoint of the first order transition line, suggesting that these features are frequency independent. An unusual upturn of the magnetic susceptibility atT→ 0 was observed in magnetic fields between 1.5 T and 2 T for both magnetic field directions, before fully polarized configuration sets in above 2 T.

Mechanical detwinning device for anisotropic resistivity measurements in samples requiring dismounting for particle irradiation.

Uniaxial stress is used to detwin the samples of orthorhombic iron based superconductors to study their intrinsic electronic anisotropy. Here, we describe the development of a new detwinning setup enabling variable-load stress-detwinning with easy sample mounting/dismounting without the need to re-solder the contacts. It enables the systematic study of the anisotropy evolution as a function of an external parameter when the sample is modified between the measurements. In our case, the external parameter is the dose of 2.5 MeV electron irradiation at low temperature. We illustrate the approach by studying resistivity anisotropy in single crystals of Ba1-xKxFe2As2 at x = 0.25, where the much discussed unusual re-entrance of the tetragonal C4 phase, C4 → C2 → C4, is observed on cooling. With the described technique, we found a significant anisotropy increase in the C2 phase after electron irradiation with a dose of 2.35 C/cm2.

Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields.

Precision radio-frequency measurements of the magnetic susceptibility using the tunnel diode resonator (TDR) technique are used to study the delicate effects in magnetic and superconducting materials. High resolution (in ppb range) measurements are particularly important for studies of the London and Campbell penetration depths in a superconductor and for the investigation of magnetic transitions in (anti)ferromagnets. Due to the small rf magnetic-excitation in a mOe range, the TDR is especially useful at low-temperatures in a mK range, if Joule heating generated in the TDR circuitry is efficiently removed and the circuit is stabilized with sub-mK precision. Unfortunately, the circuit has significant magnetic field dependence, and therefore, most of the precision TDR measurements at low-temperatures were conducted in zero magnetic field. In this work, we describe the design of a setup for precision TDR measurements in a dilution refrigerator down to ∼40 mK with a 14 T superconducting magnet. The key features of our design are the separated electronics components and the placement of the most field sensitive parts in the field-compensated zone far from the center of solenoid as well as the heat-sinking at a higher temperature stage. The performance of the working setup is demonstrated using several superconductors.

Disorder-Driven Transition from s_{±} to s_{++} Superconducting Order Parameter in Proton Irradiated Ba(Fe_{1-x}Rh_{x})_{2}As_{2} Single Crystals.

Microwave measurements of the London penetration depth and critical temperature T_{c} were used to show evidence of a disordered-driven transition from s_{±} to s_{++} order parameter symmetry in optimally doped Ba(Fe_{1-x}Rh_{x})_{2}As_{2} single crystals, where disorder was induced by means of 3.5 MeV proton irradiation. Signatures of such a transition, as theoretically predicted [V. D. Efremov et al., Phys. Rev. B 84, 180512(R) (2011)PRBMDO1098-012110.1103/PhysRevB.84.180512], are found as a drop in the low-temperature values of the London penetration depth and a virtually disorder-independent superconducting T_{c}. We show how these experimental observations can be described by multiband Eliashberg calculations in which the effect of disorder is accounted for in a suitable way. To this aim, an effective two-band approach is adopted, allowing us to treat disorder in a range between the Born approximation and the unitary limit.

Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2.

The interplay between superconductivity and charge-density wave (CDW) in 2H-NbSe2 is not fully understood despite decades of study. Artificially introduced disorder can tip the delicate balance between two competing long-range orders, and reveal the underlying interactions that give rise to them. Here we introduce disorder by electron irradiation and measure in-plane resistivity, Hall resistivity, X-ray scattering, and London penetration depth. With increasing disorder, the superconducting transition temperature, Tc, varies non-monotonically, whereas the CDW transition temperature, TCDW, monotonically decreases and becomes unresolvable above a critical irradiation dose where Tc drops sharply. Our results imply that the CDW order initially competes with superconductivity, but eventually assists it. We argue that at the transition where the long-range CDW order disappears, the cooperation with superconductivity is dramatically suppressed. X-ray scattering and Hall resistivity measurements reveal that the short-range CDW survives above the transition. Superconductivity persists to much higher dose levels, consistent with fully gapped superconductivity and moderate interband pairing.

Multi-band effects in in-plane resistivity anisotropy of strain-detwinned disordered Ba(Fe1-xRux)2As2.

In-plane resistivity anisotropy was measured in strain-detwinned as-grown and partially annealed samples of isovalently-substituted [Formula: see text] ([Formula: see text]) and the results were contrasted with previous reports on anneal samples with low residual resistivity. In samples with high residual resistivity, detwinned with application of strain, the difference of the two components of in-plane resistivity in the orthorhombic phase, [Formula: see text], was found to obey Matthiessen rule irrespective of sample composition, which is in stark contrast with observations on annealed samples. Our findings are consistent with two-band transport model in which contribution from high mobility carriers of small pockets of the Fermi surface has negligible anisotropy of residual resistivity and is eliminated by disorder. Our finding suggests that magnetic/nematic order has dramatically different effect on different parts of the Fermi surface. It predominantly affects inelastic scattering for small pocket high mobility carriers and elastic impurity scattering for larger sheets of the Fermi surface.

Universal doping evolution of the superconducting gap anisotropy in single crystals of electron-doped Ba(Fe1-x Rh x )2As2 from London penetration depth measurements.

Doping evolution of the superconducting gap anisotropy was studied in single crystals of 4d-electron doped Ba(Fe1-x Rh x )2As2 using tunnel diode resonator measurements of the temperature variation of the London penetration depth [Formula: see text]. Single crystals with doping levels representative of an underdoped regime x = 0.039 ([Formula: see text] K), close to optimal doping x = 0.057 ([Formula: see text] K) and overdoped x = 0.079 ([Formula: see text] K) and x = 0.131([Formula: see text] K) were studied. Superconducting energy gap anisotropy was characterized by the exponent, n, by fitting the data to the power-law, [Formula: see text]. The exponent n varies non-monotonically with x, increasing to a maximum n = 2.5 for x = 0.079 and rapidly decreasing towards overdoped compositions to 1.6 for x = 0.131. This behavior is qualitatively similar to the doping evolution of the superconducting gap anisotropy in other iron pnictides, including hole-doped (Ba,K)Fe2As2 and 3d-electron-doped Ba(Fe,Co)2As2 superconductors, finding a full gap near optimal doping and strong anisotropy toward the ends of the superconducting dome in the T-x phase diagram. The normalized superfluid density in an optimally Rh-doped sample is almost identical to the temperature-dependence in the optimally doped Ba(Fe,Co)2As2 samples. Our study supports the universal superconducting gap variation with doping and [Formula: see text] pairing at least in iron based superconductors of the BaFe2As2 family.

Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2.

The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe2As2 acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.

Modular portable unit for thermal conductivity measurements in multiple cryogenic/magnetic field environments.

A modular design for a miniature thermal conductivity cell suitable for a dilution refrigerator and other sample-in-vacuum cryogenic environments with different magnet options is described. The sample is mounted once and the contacts remain in place when the unit is repositioned or transported between different magnets and cryostats. This mobility enables comprehensive measurements with access to specific options, such as vector magnet in one lab and ultra-high field in another. This design enables significant expansion of the temperature range by using not only dilution refrigerators but also 3He, 4He cryostats and even ubiquitous Quantum Design Physical Property Measurement System.

Origin of the Resistivity Anisotropy in the Nematic Phase of FeSe.

The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the tetragonal-to-orthorhombic transition at T_{s}≈90 K. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strain-free samples. The anisotropy peaks slightly below T_{s} and decreases to nearly zero on cooling down to the superconducting transition. This behavior is consistent with a scenario in which the in-plane resistivity anisotropy is dominated by inelastic scattering by anisotropic spin fluctuations.

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}.

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.

Nodal to nodeless superconducting energy-gap structure change concomitant with fermi-surface reconstruction in the heavy-fermion compound CeCoIn(5).

The London penetration depth λ(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd, and Yb down to T_{min}≈50 mK (T_{c}/T_{min}∼50) using a tunnel-diode resonator. In the cleanest samples Δλ(T) is best described by the power law Δλ(T)∝T^{n}, with n∼1, consistent with the existence of line nodes in the superconducting gap. Substitutions of Ce with La, Nd, and Yb lead to similar monotonic suppressions of T_{c}; however, the effects on Δλ(T) differ. While La and Nd substitution leads to an increase in the exponent n and saturation at n∼2, as expected for a dirty nodal superconductor, Yb substitution leads to n>3, suggesting a change from nodal to nodeless superconductivity. This superconducting gap structure change happens in the same doping range where changes of the Fermi-surface topology were reported, implying that the nodal structure and Fermi-surface topology are closely linked.

Superconductivity and physical properties of CaPd2Ge2 single crystals.

We present the superconducting and normal state properties of CaPd(2)Ge(2) single crystals investigated by magnetic susceptibility χ, isothermal magnetization M, heat capacity Cp, in-plane electrical resistivity ρ and London penetration depth λ versus temperature T and magnetic field H measurements. Bulk superconductivity is inferred from the ρ(T) and Cp(T) data. The ρ(T) data exhibit metallic behavior and a superconducting transition with T(c onset) = 1.98 K and zero resistivity at T(c 0) = 1.67 K. The χ(T) reveals the onset of superconductivity at 2.0 K. For T > 2.0 K, the χ(T) and M(H) are weakly anisotropic paramagnetic with χ(ab) > χ(c). The Cp(T) data confirm the bulk superconductivity below T(c) = 1.69(3) K. The superconducting state electronic heat capacity is analyzed within the framework of a single-band α-model of BCS superconductivity and various normal and superconducting state parameters are estimated. Within the α-model, the Cp(T) data and the ab plane λ(T) data consistently indicate a moderately anisotropic s-wave gap with Δ(0)/k(B)T(c) ≈ 1.6, somewhat smaller than the BCS value of 1.764. The relationship of the heat capacity jump at Tc and the penetration depth measurement to the anisotropy in the s-wave gap is discussed.

Intrinsic nanostructure in Zr2-xFe4Si16-y(x = 0.81, y = 6.06).

We present a study of the crystal structure and physical properties of single crystals of a new Fe-based ternary compound, Zr2-xFe4Si16-y(x = 0.81, y = 6.06). Zr1.19Fe4Si9.94 is a layered compound, where stoichiometric ß-FeSi2-derived slabs are separated by Zr-Si planes with substantial numbers of vacancies. High resolution transmission electron microscopy (HRTEM) experiments show that these Zr-Si layers consist of 3.5 nm domains where the Zr and Si vacancies are ordered within a supercell sixteen times the volume of the stoichiometric cell. Within these domains, the occupancies of the Zr and Si sites obey symmetry rules that permit only certain compositions, none of which by themselves reproduce the average composition found in x-ray diffraction experiments. Magnetic susceptibility and magnetization measurements reveal a small but appreciable number of magnetic moments that remain freely fluctuating to 1.8 K, while neutron diffraction confirms the absence of bulk magnetic order with a moment of 0.2µB or larger down to 1.5 K. Electrical resistivity measurements find that Zr1.19Fe4Si9.94 is metallic, and the modest value of the Sommerfeld coefficient of the specific heat γ = C/T suggests that quasi-particle masses are not particularly strongly enhanced. The onset of superconductivity at Tc ≃ 6 K results in a partial resistive transition and a small Meissner signal, although a bulk-like transition is found in the specific heat. Sharp peaks in the ac susceptibility signal the interplay of the normal skin depth and the London penetration depth, typical of a system in which nano-sized superconducting grains are separated by a non-superconducting host. Ultra low field differential magnetic susceptibility measurements reveal the presence of a surprisingly large number of trace magnetic and superconducting phases, suggesting that the Zr-Fe-Si ternary system could be a potentially rich source of new bulk superconductors.

Sign-reversal of the in-plane resistivity anisotropy in hole-doped iron pnictides.

Unconventional superconductivity usually originates from several strongly coupled degrees of freedom, such as magnetic, charge and elastic. A highly anisotropic electronic phase, not driven by lattice degrees of freedom, has been proposed in some of these superconductors, from cuprates to iron-based compounds. In the iron pnictide BaFe2As2, this nematic phase arises in the paramagnetic phase and is present for wide doping and temperature ranges. Here we probe the in-plane electronic anisotropy of electron- and hole-doped BaFe2As2 compounds. Unlike other materials, the resistivity anisotropy behaves very differently for electron- and hole-type dopants and even changes sign on the hole-doped side. This behaviour is explained by Fermi surface reconstruction in the magnetic phase and spin-fluctuation scattering in the paramagnetic phase. This unique transport anisotropy unveils the primary role played by magnetic scattering, demonstrating the close connection between magnetism, nematicity and unconventional superconductivity.

Interlayer coherence and superconducting condensate in the c-axis response of optimally doped Ba(Fe(1-x)Co(x))2As2 high-T(c) superconductor using infrared spectroscopy.

We report on the infrared studies of the interlayer charge dynamics of a prototypical pnictide superconductor Ba(Fe(0.926)Co(0.074))(2)As(2). We succeeded in probing the intrinsic interlayer response by performing infrared experiments on the crystals with a cleaved ac surface. Our experiments identify the coexistence of the suppression of the electronic spectral weight and the development of a coherent Drude-like response in the normal state. The formation of the interlayer condensate is clearly observed in the superconducting state and appears to be linked to coherent contribution to the normal-state conductivity.

Infrared measurement of the pseudogap of P-doped and Co-doped high-temperature BaFe2As2 superconductors.

We report on infrared studies of charge dynamics in a prototypical pnictide system: the BaFe2As2 family. Our experiments have identified hallmarks of the pseudogap state in the BaFe2As2 system that mirror the spectroscopic manifestations of the pseudogap in the cuprates. The magnitude of the infrared pseudogap is in accord with that of the spin-density-wave gap of the parent compound. By monitoring the superconducting gap of both P- and Co-doped compounds, we find that the infrared pseudogap is unrelated to superconductivity. The appearance of the pseudogap is found to correlate with the evolution of the antiferromagnetic fluctuations associated with the spin-density-wave instability. The strong-coupling analysis of infrared data further reveals the interdependence between the magnetism and the pseudogap in the iron pnictides.

Universal heat conduction in the iron arsenide superconductor KFe2As2: evidence of a d-wave state.

The thermal conductivity κ of the iron arsenide superconductor KFe2As2 was measured down to 50 mK for a heat current parallel and perpendicular to the tetragonal c axis. A residual linear term at T→0, κ(0)/T is observed for both current directions, confirming the presence of nodes in the superconducting gap. Our value of κ(0)/T in the plane is equal to that reported by Dong et al. [Phys. Rev. Lett. 104, 087005 (2010)] for a sample whose residual resistivity ρ(0) was 10 times larger. This independence of κ(0)/T on impurity scattering is the signature of universal heat transport, a property of superconducting states with symmetry-imposed line nodes. This argues against an s-wave state with accidental nodes. It favors instead a d-wave state, an assignment consistent with five additional properties: the magnitude of the critical scattering rate Γ(c) for suppressing T(c) to zero; the magnitude of κ(0)/T, and its dependence on current direction and on magnetic field; the temperature dependence of κ(T).