In-plane Magnetic Penetration Depth Research Articles

Magnetic penetration depth of single-crystallineSmFeAsO1−xFy

We report measurements of the in-plane magnetic penetration depth $\ensuremath{\lambda}$ in single crystals of ${\text{SmFeAsO}}_{1\ensuremath{-}x}{\text{F}}_{y}$ $(x\ensuremath{\simeq}y\ensuremath{\simeq}0.2)$ with ${T}_{c}\ensuremath{\simeq}44\text{ }\text{K}$. We find that at low temperature $\ensuremath{\lambda}$ has an exponential temperature dependence which suggests that the Fermi surface is fully gapped. The magnitude of the minimum energy gap, ${\ensuremath{\Delta}}_{1}=1.1\ifmmode\pm\else\textpm\fi{}0.1{k}_{B}{T}_{c}$ at $T=0$, is significantly smaller than the BCS weak-coupling value suggesting that the gap is either strongly anisotropic or varies significantly between the different Fermi-surface sheets. Our data are well fitted by a two-gap model with the larger gap $({\ensuremath{\Delta}}_{2}=1.7\ifmmode\pm\else\textpm\fi{}0.2{k}_{B}{T}_{c})$ associated with $\ensuremath{\sim}80%$ of the total superfluid density.

Evidence of nodeless superconductivity inFeSe0.85from a muon-spin-rotation study of the in-plane magnetic penetration depth

The in-plane magnetic penetration depth ${\ensuremath{\lambda}}_{ab}$ of the iron selenide superconductor with the nominal composition ${\text{FeSe}}_{0.85}$ was studied by means of muon-spin rotation. The measurements of ${\ensuremath{\lambda}}_{ab}^{\ensuremath{-}2}(T)$ are inconsistent with a simple isotropic $s$-wave type of the order parameter but are rather in favor of two-gap $(s+s)$ and anisotropic $s$-wave order parameter symmetries, thus implying that the superconducting energy gap in ${\text{FeSe}}_{0.85}$ contains no nodes.

Evidence for a Competition between the Superconducting State and the Pseudogap State of(BiPb)2(SrLa)2CuO6+δfrom Muon Spin Rotation Experiments

The in-plane magnetic penetration depth lambda ab in optimally doped (BiPb)2(SrLa)2CuO6+delta (OP Bi2201) was studied by means of muon-spin rotation. The measurements of lambda ab(-2)(T) are inconsistent with a simple model of a d-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett. 98, 267004 (2007)], which suggest that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. The remaining parts of the Fermi surface, which are strongly affected by the pseudogap state, do not contribute significantly to the superconducting condensate.

Nodeless superconductivity in the infinite-layer electron-doped cuprate superconductorSr0.9La0.1CuO2

We report on measurements of the in-plane magnetic penetration depth ${\ensuremath{\lambda}}_{ab}$ in the infinite-layer electron-doped high-temperature cuprate superconductor ${\text{Sr}}_{0.9}{\text{La}}_{0.1}{\text{CuO}}_{2}$ by means of muon-spin rotation. The observed temperature and magnetic field dependences of ${\ensuremath{\lambda}}_{ab}$ are consistent with the presence of a substantial $s$-wave component in the superconducting order parameter, in good agreement with the results of tunneling, specific heat, and small-angle neutron scattering experiments.

Synthesis and bulk properties of oxychloride superconductor Ca2-xNaxCuO2Cl2

A series of polycrystalline samples and submillimeter size single crystals of a cuprate oxychloride Ca2-xNaxCuO2Cl2 (Na-CCOC) with values of Na content ranging from underdoped to optimally doped regions were synthesized at pressure of 30-55 kbar and temperature of 1250-1700 °C. A systematic variation of the transition temperature Tc with a maximum value of 29 K for x≈0.20 has been found as a function of Na content. In order to check the role of the apical oxygen for high-temperature superconductivity, we performed muon-spin rotation and magnetization studies of the in-plane magnetic penetration depth λabfor Ca2-xNaxCuO2Cl2 samples with x≈0.11, 0.12, 0.15, 0.18, and 0.19. The absolute value of the in-plane magnetic penetration depth at T=0 was found to increase with decreasing doping from λab(0)=316(19) nm for the x≈0.19 sample to λab(0)=430(26) nm for the x≈0.11 one. Based on a comparison of the present Na-CCOC data with the data of La2-xSrxCuO4 cuprate superconductors, it is concluded that replacing of apical oxygen by chlorine decreases the coupling between the superconducting CuO2 planes, leading to an enhancement of the two-dimensional properties of Na-CCOC. The torque studies implies that the anisotropy coefficient λ=84(1) of Ca1.82Na0.18CuO2Cl2 single crystals is much more enhanced compared to the structurally related La1.82Sr0.18CuO4 where for same doping λ is much lower, i.e. γ ≈ 11.

Superconducting graphite intercalation compounds with calcium

In the graphite–lithium–calcium system, four well-defined intercalation compounds were synthesised. Two of them, CaC 6 and Li 3Ca 2C 6, exhibit superconducting properties at 11.5 K and 11.15 K, respectively, the highest critical temperatures among those of graphite intercalation compounds. The samples are synthesised using a liquid–solid method allowing the preparation of pure bulk samples, auspicious for crystallographic and magnetic measurements. The crystal structure of CaC 6 was entirely specified; this compound crystallises in the R-3 m space group. The two-dimensional unit cell of Li 3Ca 2C 6 is hexagonal and commensurate with that of graphite and the intercalated sheets, very rich in metal, are seven-layered. The magnetic properties of these phases were studied with an applied field parallel and perpendicular to the graphene sheets. In both cases the magnetic phase diagram indicates that these compounds are type II superconducting materials slightly anisotropic in spite of their lamellar structure. In the case of CaC 6, in-plane magnetic penetration depth measurements show a clear exponential behaviour at low temperatures, consistent with an s-wave symmetry of the gap function, well fitted by the standard BCS theory in the dirty limit.

Hole-doping dependence of the magnetic penetration depth and vortex core size inYBa2Cu3Oy: Evidence for stripe correlations near18hole doping

We report on muon spin rotation measurements of the internal magnetic field distribution $n(B)$ in the vortex solid phase of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ (YBCO) single crystals, from which we have simultaneously determined the hole-doping dependences of the in-plane Ginzburg-Landau (GL) length scales in the underdoped regime. We find that ${T}_{c}$ has a sublinear dependence on $1∕{\ensuremath{\lambda}}_{ab}^{2}$, where ${\ensuremath{\lambda}}_{ab}$ is the in-plane magnetic penetration depth in the extrapolated limits $T\ensuremath{\rightarrow}0$ and $H\ensuremath{\rightarrow}0$. The power coefficient of the sublinear dependence is close to that determined in severely underdoped YBCO thin films, indicating that the same relationship between ${T}_{c}$ and the superfluid density is maintained throughout the underdoped regime. The GL coherence length ${\ensuremath{\xi}}_{ab}$ (vortex core size) is found to increase with decreasing hole-doping concentration and to exhibit a field dependence that is explained by proximity-induced superconductivity on the CuO chains. Both ${\ensuremath{\lambda}}_{ab}$ and ${\ensuremath{\xi}}_{ab}$ are enhanced near $\frac{1}{8}$ hole doping, supporting the belief by some that stripe correlations are a universal property of high-${T}_{c}$ cuprates.

Impurity Effect on Superconducting Properties in Molecular Substituted Organic Superconductor κ-(ET)2Cu(NCS)2

We report an impurity effect in the organic superconductor κ-(ET) 2 Cu(NCS) 2 by substitution of the ET molecule with an analogue, bis(methylenedithio)tetrathiafulvalene (MT). The superconducting transition temperature decreases with increasing substitution. The in-plane magnetic penetration depth is enhanced with substitution, which is quantitatively attributed to the decrease in the in-plane mean free path. The enhancement of the penetration depth can also explain the reduction of the effective pinning in terms of the condensation energy.

In-plane magnetic penetration depthλabinCa2−xNaxCuO2Cl2: Role of the apical sites

A study of the in-plane magnetic penetration depth \lambda_ab in a series of the cuprate superconductors Ca_2-xNa_xCuO_2Cl_2 (Na-CCOC) with Na content x=0.11, 0.12, 0.15, 0.18, and 0.19 is reported. The zero temperature values of \lambda_ab(0) were obtained by means of the muon-spin rotation technique, as well as from measurements of the intrinsic susceptibility \chi^int(0) by using the procedure developed by Kanigel et al. [Phys.Rev.B 71, 224511 (2005)]. \lambda_ab at T=0K was found to increase with decreasing doping from \lambda_ab(0)=316(19)nm for the x=0.19 sample to \lambda_ab(0)=430(26)nm for the x=0.11 one. From a comparison of the present Na-CCOC data with those of Bi2201 and La214 cuprate superconductors it is concluded that substitution of the apical oxygen by chlorine decreases the coupling between the superconducting CuO_2 planes, leading to an enhancement of the two-dimensional properties of Na-CCOC.

Superfluid density of bulk CaC6

The recent discovery of superconductivity at 11.5K in the graphite intercalation compound (GIC) CaC6 has opened new perspectives in the physics of graphite. One of the main open questions for superconducting GICs is related to the nature of the pairing mechanism, since the possibility of an unconventional, excitonic or plasmonic, origin of superconductivity has also been invoked as an alternative to a simple electron–phonon interaction. To better understand the origin of pairing mechanism in these compounds, a first step is to determine the symmetry of the superconducting gap function and the nature of the elementary excitations. To this aim, we have performed the first high-resolution measurement of the in-plane magnetic penetration depth, λab(T), in a c-axis oriented polycrystalline CaC6 bulk sample using a high-resolution mutual inductance technique. A clear exponential behavior of λab(T) has been observed at low temperatures, strongly suggesting isotropic s-wave pairing. Data fit using the standard BCS theory yields λab(0)=(720±80)Å and Δ(0)=(1.79±0.08)meV. The ratio 2Δ(0)/kBTC=(3.6±0.2) gives therefore indication for a conventional weakly coupled superconductor. By using these results as fixed parameters, a BCS calculation on the superfluid density in the overall temperature range shows that the sample under test lies in the local dirty limit.

Magnetic-field dependence of the oxygen isotope effect on the magnetic penetration depth of hole-doped cuprate superconductors

The magnetic field dependence of the oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic field penetration depth \lambda_{ab} was studied in the hole-doped high-temperature cuprate superconductors YBa_2Cu_4O_8, Y_0.8Pr_0.2Ba_2Cu_3O_7-\delta, and Y_0.7Pr_0.3Ba_2Cu_3O_7-\delta. It was found that \lambda_ab for the ^{16}O substituted samples increases stronger with increasing magnetic field than for the ^{18}O ones. The OIE on \lambda_ab decreases by more than a factor of two with increasing magnetic field from \mu_0H=0.2 T to \mu_0H=0.6 T. This effect can be explained by the isotope dependence of the in-plane charge carrier mass m^\ast_{ab}.

Experimental Evidence for Two Gaps in the High-TemperatureLa1.83Sr0.17CuO4Superconductor

The in-plane magnetic field penetration depth (lambda(ab)) in single-crystal La1.83Sr0.17CuO4 was investigated by muon-spin rotation (muSR). The temperature dependence of lambda(ab)(-2) has an inflection point around 10-15 K, suggesting the presence of two superconducting gaps: a large gap (Delta(1)(d)) with d-wave and a small gap (Delta(2)(s)) with s-wave symmetry. The zero-temperature values of the gaps at mu(0)H=0.02 T were found to be Delta(1)(d)(0)=8.2(1) meV and Delta(2)(s)(0)=1.57(8) meV.

Correlation between oxygen isotope effects on transition temperature and magnetic penetration depth in high-temperature superconductors close to optimal doping

The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic penetration depth \lambda_{ab}(0) in optimally-doped YBa_2Cu_3O_{7-\delta} and La_{1.85}Sr_{0.15}CuO_4, and in slightly underdoped YBa_2Cu_4O_8 and Y_{0.8}Pr_{0.2}Ba_2Cu_3O_{7-\delta} was studied by means of muon-spin rotation. A substantial OIE on \lambda_{ab}(0) with an OIE exponent \beta_O=-d\ln\lambda_{ab}(0)/d\ln M_O\approx - 0.2 (M_O is the mass of the oxygen isotope), and a small OIE on the transition temperature T_c with an OIE exponent \alpha_O=-d\ln T_{c}/d \ln M_O\simeq0.02 to 0.1 were observed. The observation of a substantial isotope effect on \lambda_{ab}(0), even in cuprates where the OIE on T_c is small, indicates that lattice effects play an important role in cuprate HTS.

Low-energy physical properties of high-Tcsuperconducting Cu oxides: A comparison between the resonating valence bond and experiments

In a recent review by Anderson and coworkers\cite{Vanilla}, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high temperature superconducting (SC) Cu-oxides. Here we extend previous calculations \cite{anderson87,FC Zhang,Randeria} to study more systematically low energy physical properties of the plain vanilla d-wave RVB state, and to compare results with the available experiments. We use a renormalized mean field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t-J$ model in a square lattice with parameters suitable for the hole doped Cu-oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\pi, 0)$, the superconducting energy gap, the quasiparticle spectra and the Drude weight. The traits of nodes (including $k_{F}$, the Fermi velocity $v_{F}$ and the velocity along Fermi surface $v_{2}$), as well as the SC order parameter are also studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.

Experimental Evidence ofs-Wave Superconductivity in BulkCaC6

The temperature dependence of the in-plane magnetic penetration depth, lambda(ab)(T), has been measured in a c-axis oriented polycrystalline CaC(6) bulk sample using a high-resolution mutual inductance technique. A clear exponential behavior of lambda(ab)(T) has been observed at low temperatures, strongly suggesting isotropic s-wave pairing. Data fit using the standard BCS theory yields lambda(ab)(0) = (720 +/- 80) A and delta(0) = (1.79 +/- 0.08) meV. The ratio 2delta(0)/k(B)T(c) = (3.6 +/- 0.2) gives indication for a weakly coupled superconductor.

Magnetic penetration depth measurements of the heavy-fermion superconductor [formula omitted

Previous studies of the magnetic penetration depth in the heavy-fermion superconductor PrOs 4 Sb 12 reported contradictory results about its pairing state. While muon spin rotation measurements report a fully gapped quasiparticle spectrum, inductive measurements at radio frequencies suggest the existence of point nodes in the energy gap. Here, we report on new measurements of the in-plane magnetic penetration depth of PrOs 4 Sb 12 . The measurements were performed using a tunnel diode oscillator that exhibits excellent frequency stability and low-power dissipation. We report the first ever measurements of the penetration depth of this material at temperatures as low as 20 mK. At about 450 mK, we observe the onset of a superconducting-transition-like drop in the magnetic penetration depth.

Effect of magnetic order on the superfluid response of single-crystalErNi2B2C: A penetration depth study

We report measurements of the in-plane magnetic penetration depth $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}(T)$ in single crystals of ${\mathrm{ErNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ down to $\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using a tunnel-diode based, self-inductive technique at $21\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. We observe four features: (1) a slight dip in $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}(T)$ at the N\'eel temperature ${T}_{N}=6.0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, (2) a peak at ${T}_{WFM}=2.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where a weak ferromagnetic component sets in, (3) another maximum at $0.45\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and (4) a final broad drop down to $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Converting to superfluid density ${\ensuremath{\rho}}_{s}$, we see that the antiferromagnetic order at $6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ only slightly depresses superconductivity. We seek to explain some of the above features in the context of antiferromagnetic superconductors, where competition between the antiferromagnetic molecular field and spin fluctuation scattering determines increased or decreased pair breaking. Superfluid density data show only a slight decrease in pair density in the vicinity of the $2.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ feature, thus supporting other evidence against a pure ferromagnetic state in this temperature range.

High-resolution measurements of the magnetic penetrationdepth on Yba2Cu4O8 single crystals

Abstract In order to unveil the intrinsic electrodynamic response of the CuO2 layers of cuprate superconductors and to differentiate this response from that of the charge reservoir layers, we measured the in-plane (ab) magnetic penetration depth on Yba2Cu4O8 (Y124) single crystals by using a high-resolution mutual inductance technique. Among the various high-Tc families of cuprate superconductors, Y124 is a stoichiometric compound characterized by a double CuO chain per unit cell acting as charge reservoir and by the absence of any disorder or structural inhomogeneities arising from chemical substitutions and/or oxygen vacancies. This feature makes Y124 an ideal system for our study. The experimental data show, in the low temperature region down to 4.2 K, a marked linear dependence of the variation Δλab≡λab(T)−λab (4.2 K) with a small downturn at 9 K. This behavior confirms the existence of zero-energy thermally activated excitations, that are also observed in the Yba2Cu3O7−δ (Y123) counterpart possessing only one CuO chain per unit cell. Whilst such linear behavior is consistent with the d-wave symmetry picture previously established for cuprates, the measured thermal activation rate, ∝∂λab/∂T, is however, more than a factor 4 larger in comparison with Y123. This result is consistent with a proximity model of superconducting planes and metallic chains and suggests that the reservoir layers strongly affect the low temperature behavior of the magnetic penetration depth in cuprates.

Comment on “Nodeless pairing state in single-crystalYBa2Cu3O7”

In a recent article, Harshman et al. [Phys. Rev. B 69, 174505 (2004)] claim that our $\ensuremath{\mu}\mathrm{SR}$ measurements [Phys. Rev. Lett. 83, 4156 (1999)] of the effective in-plane magnetic penetration depth ${\ensuremath{\lambda}}_{ab}(T,H)$ in high-quality single crystals of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.95}$ are dominated by flux pinning effects, and hence are inconsistent with $d$-wave superconductivity. The purpose of this Comment is to point out that the phenomenological $s$-wave pinning model applied by Harshman et al. to ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ is invaild. The model does not account for the finite size of the vortex cores or the field-induced vortex-lattice transformation, and hence yields inaccurate information on the magnetic penetration depth. We also comment on the criticism of zero-field microwave measurements that show excellent agreement with our $\ensuremath{\mu}\mathrm{SR}$ results for the limiting low-temperature behavior of ${\ensuremath{\lambda}}_{ab}(T)$.

Temperature dependence of superfluid density in YBa2Cu3O7−δ and Y0.7Ca0.3Ba2Cu3O7−δ thin films: A doping dependence study of the linear slope

By using a microstrip ring resonator to measure the temperature dependence of the in-plane magnetic penetration depth λ(T) in YBa2Cu3O7−δ (YBCO) and Y0.7Ca0.3Ba2Cu3O7−δ (Ca-YBCO) epitaxially grown thin films, the linear temperature dependence of the superfluid density ρs/m∗≡1/λ2(T) was observed from the under- to the overdoped regime at the temperatures below TTc≈0.3. For the underdoped regime of YBCO and Ca-YBCO thin films, the magnitude of the slope d(1/λ2(T))/dT is insensitive to doping, and it can be treated in the framework of projected d-density-wave model. Combining these slope values with the thermal conductivity measurements, the Fermi-liquid correction factor α2 from the Fermi-liquid model, suggested by Wen and Lee, was revealed here with various doping levels.