In-plane Magnetic Penetration Depth Research Articles

In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study.

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015 K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7 K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3) nm agrees with λ_{ab}≃130 nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

Oxygen isotope effect on the superfluid density within the [formula omitted]-wave and [formula omitted]-wave pairing channels of YBa[formula omitted]Cu[formula omitted]O[formula omitted

We report on measurements of the oxygen isotope (16O/18O) effect (OIE) on the transition temperature Tc and the zero-temperature in-plane magnetic penetration depth λab(0) in the stoichiometric cuprate superconductor YBa2Cu4O8 by means of muon-spin rotation/relaxation. An analysis of the temperature evolution of λab−2 in terms of coexisting isotropic s-wave and anisotropic d-wave order parameters (s+d-wave) reveals that the OIE on the superfluid density ρs(0)∝λab−2(0) stems predominantly from the d-wave component while the contribution of the s-wave one is almost zero. The OIE on the transition temperature Tc is found to be rather small: δTc/Tc=−0.32(7)%, compared to the total OIE on the superfluid density ρs(0): δρs(0)/ρs(0)=−2.8(1.0)%. The partial OIE’s on the corresponding d-wave and s-wave components of ρs(0) are δρs,d(0)/ρs(0)=−3.0(1.2)%, and δρs,s(0)/ρs(0)=0.2(1.2)%, respectively. Our results demonstrate that polaron formation in the CuO2 planes is the origin of the observed OIE in the d-wave channel. In the much weaker s-wave channel, fermionic quasiparticles are present, which do not contribute to the OIE on ρs(0). Our results support the original idea of K. Alex Müller on the polaronic nature of the supercarriers in high-temperature cuprate superconductors.

In-plane magnetic penetration depth in FeSe1-xSx (x = 0, 0.04, 0.09) and FeTe1-xSex (x = 0.40) single crystals

ABSTRACTThe magnetization anomaly of FeSe1–xSx(x = 0, 0.04, 0.09) and FeTe1–xSex(x = 0.40) single crystals are examined through our Modified Phenomenological Ginzburg–Landau (MPGL) theory applicable to two-band superconducting systems. The theory in the London limit calculates the values of λab(0) as 445.695, 372.058 and 432.957 nm of FeSe1–xSx for x = 0, 0.04, 0.09 which are very close to the experimental values reported by Hafiez et al. [Superconducting properties of sulfur-doped iron selenide. Phys Rev B. 2015;91(16):165109–165120] and as 534 nm for FeTe1–xSex(x = 0.40) single crystal, which is close to the experimental value reported by Yadav and Paulose [Upper critical field, lower critical field and critical current density of FeTe0.60Se0.40 single crystals. New J Phys 2009;11:103046]. In addition, the variation of temperature-dependent in-plane magnetic penetration depth λab(T) with the temperature (T) has been presented, which agrees well as reported by Hafiez et al. [Superconducting properties of sulfur-doped iron selenide. Phys Rev B. 2015;91(16):165109–165120] and Yadav and Paulose [Upper critical field, lower critical field and critical current density of FeTe0.60Se0.40 single crystals. New J Phys. 2009;11:103046].

Dependence of the absolute value of the penetration depth in (Ba1−xKx)Fe2As2 on doping

We report magnetic force microscopy (MFM) measurements on the iron-based superconductor $\mathrm{Ba_{1-x}K_xFe_2As_2}$. By measuring locally the Meissner repulsion with the magnetic MFM tip, we determine the absolute value of the in-plane magnetic penetration depth ($\lambda_{ab}$) in underdoped, optimally-doped, and overdoped samples. The results suggest an abrupt increase of $\lambda_{ab}$ as doping is increased from $x_\mathrm{opt}$, which is potentially related to the presence of a quantum critical point. The response of superconducting vortices to magnetic forces exerted by the MFM tip for $x=0.19$ and $0.58$ is compatible with previously observed structural symmetries at those doping levels.

In-plane magnetic penetration depth of superconducting CaKFe4As4

The temperature dependence of the in-plane magnetic penetration depth (${\ensuremath{\lambda}}_{ab}$) in an extensively characterized sample of superconducting ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}\phantom{\rule{0.28em}{0ex}}({T}_{\mathrm{c}}\ensuremath{\simeq}35\phantom{\rule{0.28em}{0ex}}\mathrm{K})$ was investigated using muon-spin rotation ($\ensuremath{\mu}\mathrm{SR}$). A comparison of ${\ensuremath{\lambda}}_{ab}^{\ensuremath{-}2}(T)$ measured by $\ensuremath{\mu}\mathrm{SR}$ with the one inferred from angle-resolved photoemission spectroscopy (ARPES) data confirms the presence of multiple gaps at the Fermi level. An agreement between $\ensuremath{\mu}\mathrm{SR}$ and ARPES requires the presence of additional bands, which are not resolved by ARPES experiments. These bands are characterized by small superconducting gaps with an average zero-temperature value of ${\mathrm{\ensuremath{\Delta}}}_{0}=2.4(2)\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$. Our data suggest that in ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$ the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ order parameter symmetry acquires a more sophisticated form by allowing a sign change not only between electron and hole pockets, but also within pockets of similar type.

Direct measurement of the temperature dependence of the in-plane magnetic penetration depth in optimally doped BaFe2(As[formula omitted]Px)2 single crystals

Measurements of the temperature dependence of the in-plane magnetic penetration depth, Δλab(T)=λab(T)−λab(0), are presented in the isovalently substituted iron pnictide BaFe2(As1−xPx)2 near optimal doping (Tc ∼ 28K). The data were obtained directly from the shielding magnetic susceptibility of thin single crystals (∼ 20 µm thickness along the crystals c-axis) under magnetic fields parallel to the ab layers. Complications associated to flux penetration were avoided by using fields in the 10−4 T range, which ensured that the samples were well inside the Meissner region. At low temperatures (T < 0.25Tc) our data confirm the linear temperature dependence of λab(T) observed by using other procedures, and that is consistent with a nodal superconducting order parameter. By using values for λab(0) in the literature we obtained the temperature dependence up to Tc of the superfluid density, ns(T)∝1/λab2(T). It is found that samples with slightly different Tc values present a significantly different qualitative behavior of ns(T).

Direct measurement of the temperature dependence of the magnetic penetration depth in Ba(Fe1−xNix)2As2 superconductors

The temperature dependence of the in-plane magnetic penetration depth λab of Ba(Fe1−xNix)2As2 single crystals is determined directly from the shielding magnetic susceptibility, measured in the Meissner region with the field parallel to the ab layers. The doping levels studied cover the underdoped, optimally doped and overdoped regimes. At temperatures below 0.5Tc a well-defined power-law behavior λab(T) − λab(0) = ATn (with n ≈ 2.5) is observed. At lower temperatures (T < 0.3Tc) the data are still consistent with n = 2 and , as predicted by the strong pair-breaking scenario proposed by Gordon et al (2010 Phys. Rev. B 81, 180501(R)). The temperature dependence of the superfluid density presents a marked positive curvature just below Tc, which is a sign of two-gap superconductivity. The analysis of ρs(T) in terms of a two-gap model allowed estimation of parameters like the in-band and inter-band couplings, the relative weight of each band, and their dependence on the doping level. A comparison with ρs(T) data obtained by using other techniques in compounds with a similar composition is also presented.

Superconducting and normal-state properties ofAPd2As2(A = Ca, Sr, Ba) single crystals

The synthesis and crystallography, magnetic susceptibility chi, magnetization M, specific heat Cp, in-plane electrical resistivity rho and in-plane magnetic penetration depth measurements are reported for single crystals of APd2As2 (A = Ca, Sr, Ba) versus temperature T and magnetic field H. The crystals were grown using PdAs self-flux. CaPd2As2 and SrPd2As2 crystallize in a collapsed body-centered tetragonal ThCr2Si2-type structure (I4/mmm), whereas BaPd2As2 crystallizes in the primitive tetragonal CeMg2Si2-type structure (P4/mmm), in agreement with literature data. The rho(T) data exhibit metallic behavior for all three compounds. Bulk superconductivity is reported for CaPd2As2 and SrPd2As2 below Tc = 1.27 and 0.92 K, respectively, whereas only a trace of superconductivity is found in BaPd2As2. No other phase transitions were observed. The chi(T) and M(H) data reveal anisotropic diamagnetism in the normal state, with chi_c > chi_ab for CaPd2As2 and BaPd2As2, and chi_c < chi_ab for SrPd2As2. The normal and superconducting state data indicate that CaPd2As2 and SrPd2As2 are conventional type-II nodeless s-wave electron-phonon superconductors. The electronic superconducting-state heat capacity data for CaPd2As2, which has an extremely sharp heat capacity jump at Tc, are analyzed using our recent elaboration of the alpha-model of the BCS theory of superconductivity, which indicates that the s-wave gap in this compound is anisotropic in momentum space.

Magnetic penetration depth in single crystals of SrPd2Ge2superconductor

The in-plane magnetic penetration depth, $\lambda_m(T)$, was measured in single crystals of SrPd$_2$Ge$_2$ superconductor in a dilution refrigerator down to T=60 mK and in magnetic fields up to $H_{dc} = 1$ T by using a tunnel diode resonator. The London penetration depth, $\lambda$, saturates exponentially approaching $T\rightarrow 0$ indicating fully gapped superconductivity. The thermodynamic Rutgers formula was used to estimate $\lambda(0) = 426$ nm which was used to calculate the superfluid density, $\rho_s(T)=\lambda^2(0)/\lambda^2(T)$. Analysis of $\rho_s(T)$ in the full temperature range shows that it is best described by a single - gap behavior, perhaps with somewhat stronger coupling. In a magnetic field, the measured penetration depth is given by the Campbell penetration depth which was used to calculate the theoretical critical current density $j_c$. For $H \le 0.45$ T, the strongest pinning is achieved not at the lowest, but at some intermediate temperature, probably due to matching effect between temperature - dependent coherence length and relevant pinning lengthscale. Finally, we find a compelling evidence for surface superconductivity. Combining all measurements, the entire $H$-$T$ phase diagram of SrPd$_2$Ge$_2$ is constructed with an estimated $H_{c2}(0)=0.4817$ T.

Absolute value and temperature dependence of the magnetic penetration depth in Ba(Co0.074Fe0.926)2As2

The absolute value and temperature dependence of the in-plane magnetic penetration depth $\ensuremath{\lambda}$ have been measured on a single crystal of Ba(Co${}_{0.074}$Fe${}_{0.926}{)}_{2}$As${}_{2}$ using low-energy muon-spin rotation and microwave cavity perturbation. The magnetic field profiles in the Meissner state are consistent with a local London model beyond a depth of 15 nm. We determine the gap symmetry through measurements of the temperature dependence of the superfluid density which follows a two-gap $s$-wave model over the entire temperature range below ${T}_{\mathrm{c}}$. While the intermediate to high temperature data is well fit by an energy gap model in the BCS-like (weak-coupling) limit, a second smaller gap becomes apparent at low temperatures.

Muon Spin Rotation Study of the Intercalated Graphite Superconductor CaC6 at Low Temperatures

Muon spin rotation (μSR) experiments were performed on the intercalated graphite CaC6 in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field \(H_{\text{c2}}\), from which the coherence lengths ξab(0)=36.3(1.5) nm and ξc(0)=4.3(7) nm were estimated. The anisotropy parameter \(\gamma _{H}=H_{\text{c2}}^{ab}/H_{\text{c2}}^{c}\) increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behavior. From magnetic field dependent μSR experiments, the absolute value of the in-plane magnetic penetration depth λab(0)=78(3) nm was determined. The temperature dependence of the superfluid density ρs(T) is slightly better described by a two-gap than a single-gap model.

Interplay of composition, structure, magnetism, and superconductivity in SmFeAs1−xPxO1−y

Polycrystalline samples and single crystals of SmFeAs1-xPxO1-y were synthesized and grown employing different synthesis methods and annealing conditions. Depending on the phosphorus and oxygen content, the samples are either magnetic or superconducting. In the fully oxygenated compounds the main impact of phosphorus substitution is to suppress the N\'eel temperature TN of the spin density wave (SDW) state, and to strongly reduce the local magnetic field in the SDW state, as deduced from muon spin rotation measurements. On the other hand the superconducting state is observed in the oxygen deficient samples only after heat treatment under high pressure. Oxygen deficiency as a result of synthesis at high pressure brings the Sm-O layer closer to the superconducting As/P-Fe-As/P block and provides additional electron transfer. Interestingly, the structural modifications in response to this variation of the electron count are significantly different when phosphorus is partly substituting arsenic. Point contact spectra are well described with two superconducting gaps. Magnetic and resistance measurements on single crystals indicate an in-plane magnetic penetration depth of 200 nm and an anisotropy of the upper critical field slope of 4-5. PACS number(s): 74.70.Xa, 74.62.Bf, 74.25.-q, 81.20.-n

In-plane magnetic penetration depth in NbS2

We report on the temperature dependence of the in-plane magnetic penetration depth (${\ensuremath{\lambda}}_{ab}$) and first penetration field [${H}_{f}\ensuremath{\propto}1/{\ensuremath{\lambda}}_{ab}^{2}(T)$ for $H\ensuremath{\parallel}c$] in 2H-NbS${}_{2}$ single crystals. An exponential temperature dependence is clearly observed in ${\ensuremath{\lambda}}_{ab}$(T) at low temperature, marking the presence of a fully open superconducting gap. This compound is the only superconducting 2H-dichalcogenide which does not develop a charge density wave (CDW). However, as previously observed in 2H-NbSe${}_{2}$, this gap (${\ensuremath{\Delta}}_{1}=1.1\phantom{\rule{0.16em}{0ex}}{k}_{B}{T}_{c}$) is significantly smaller than the standard BCS weak-coupling value. At higher temperature, a larger gap (${\ensuremath{\Delta}}_{2}=1.8\phantom{\rule{0.16em}{0ex}}{k}_{B}{T}_{c}$) has to be introduced to describe the data which are compatible with a two-gap model. The superconducting gaps are hence very similar in NbS${}_{2}$ and NbSe${}_{2}$ and we show here that both of them open in the strongly coupled Nb tubular sheets independent of whether or not a CDW is present.

μSR investigation of the intercalated graphite superconductor CaC6

The superconducting properties of the graphite intercalation compound CaC6, available as high-quality c-axis-oriented polycrystals, were investigated through muon-spin spectroscopy measurements. An unconventional TF-μSR procedure, applicable to superconductors characterized by close-lying critical fields, was successfully adopted for measuring the muon-spin relaxation rates. Field-dependent measurements provide a value λab(0)=62(4) nm for the in-plane magnetic field penetration depth, κ=1.4(2) for the GL parameter, and hint at the presence of a slight gap anisotropy in the ab plane. The dependence of relaxation on temperature confirms the s-wave character of CaC6 superconductivity, with an average zero-temperature superconducting gap of 2.1(1) meV.

Possible secondary component of the order parameter observed in London penetration depth measurements

We discuss the effect of a secondary component of the superconducting order parameter on the superfluid density in the cuprates. If we assume a main ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap, the most stable realization of a mixed order parameter has a time-reversal breaking ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+\ifmmode \imath \else \i \fi{}{d}_{xy}$ symmetry. In this state the nodes are removed and the temperature dependence of the superfluid density changes from the linear behavior of a pure $d$ wave to a more rounded shape at low temperature. The latter is compatible with the behavior experimentally observed in the in-plane magnetic field penetration depth of optimally doped ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{2}$ and ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}y}$.

Muon spin rotation study of the magnetic penetration depth in the intercalated graphite superconductorCaC6

We report temperature- and magnetic field-dependent bulk muon spin rotation measurements in a c-axis oriented superconductor CaC6 in the mixed state. Using both a simple second moment analysis and the more precise analytical Ginzburg-Landau model, we obtained a field independent in-plane magnetic penetration depth {\lambda}ab (0) = 72(3) nm. The temperature dependencies of the normalized muon spin relaxation rate and of the normalized superfluid density result to be identical, and both are well represented by the clean limit BCS model with 2\Delta/kB Tc = 3.6(1), suggesting that CaC6 is a fully gapped BCS superconductor in the clean limit regime.

Evidence for multiple superconducting gaps in optimally dopedBaFe1.87Co0.13As2from infrared spectroscopy

We performed combined infrared reflection and ellipsometry measurements of the in-plane optical reponse of single crystals of the pnictide high temperature superconductor BaFe$_{1.87}$Co$_{0.13}$As$_{2}$ with $T_{c}$ = 24.5 K. We observed characteristic superconductivity-induced changes which provide evidence for at least three different energy gaps. We show that a BCS-model of isotropic gaps with 2$\Delta/k_{B}T_{c}$ of 3.1, 4.7, and 9.2 reproduces the experimental data rather well. We also determine the low-temperature value of the in-plane magnetic penetration depth of 270 nm.

Muon-spin-spectroscopy study of the penetration depth ofFeTe0.5Se0.5

Muon-spin-spectroscopy measurements have been used to study the superconducting state of ${\text{FeTe}}_{0.5}{\text{Se}}_{0.5}$. The temperature dependence of the in-plane magnetic penetration depth, ${\ensuremath{\lambda}}_{ab}(T)$, is found to be compatible with either a two-gap $s+s$-wave or an anisotropic $s$-wave model. The value for ${\ensuremath{\lambda}}_{ab}(T)$ at $T=0\text{ }\text{K}$ is estimated to be ${\ensuremath{\lambda}}_{ab}(0)=534(2)\text{ }\text{nm}$.

London penetration depth in single crystals of F- and Co-doped RFeAsO (R = La, Nd) superconductors

The in-plane magnetic penetration depth, λ(T), has been measured in single crystals of NdFe1−xCoxAsO, NdFeAsO1−xFx, and LaFeAsO1−xFx. In the Nd compounds we found an upturn in λ(T) below 4K and attribute it to the paramagnetic contribution from the Nd3+ ions. After the correction for this contribution, the in-plane temperature dependent London penetration depth, λL(T), in F-doped crystals was found to follow a power-law dependence, ΔλL(T)∝Tn, n≈2. Similar power-law behavior was found in direct measurements of non-magnetic LaFeAsO1−xFx with n≈2. In NdFe1−xCoxAsO, on the other hand, after the paramagnetic correction, we found n≈3. Our results indicate unconventional pairing in the pnictides, incompatible with a single isotropic gap or a gap with line nodes. The power-law behavior is observed down to T/Tc=0.02 indicating significant gap anisotropy.

Evidence for Kosterlitz-Thouless and three-dimensionalXYcritical behavior inBi2Sr2CaCu2O8+δ

We present reversible magnetization data of a high-quality ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ single crystal and explore the occurrence of three-dimensional (3D)-$xy$ critical behavior close to the bulk-transition temperature ${T}_{c}$ and of Kosterlitz-Thouless (KT) behavior. Below and above the presumed Kosterlitz-Thouless transition temperature ${T}_{\text{KT}}$ we observe the characteristic two-dimensional (2D)-$xy$ behavior: a downward shift in the crossing point phenomenon toward ${T}_{\text{KT}}$ as the field is decreased and sufficiently below ${T}_{\text{KT}}$ the characteristic 2D-$xy$ relationship between the magnetization and the in-plane magnetic penetration depth ${\ensuremath{\lambda}}_{ab}$. In contrast, the measured temperature dependence of the superfluid density does not exhibit the characteristic KT behavior around the presumed ${T}_{\text{KT}}$. The absence of this feature is traced back to the 2D- to 3D-$xy$ crossover setting in around and above ${T}_{\text{KT}}$. Invoking the Maxwell relation, the anomalous field dependence of the specific-heat peak is also traced back to the intermediate 2D-$xy$ behavior. However, close to ${T}_{c}$ we observe consistency with 3D-$xy$ critical behavior in agreement with measurements of ${\ensuremath{\lambda}}_{ab}$.