Penetration Depth Anisotropy Research Articles

Quadrupling the depairing current density in the iron-based superconductor SmFeAsO1-xHx.

Iron-based 1111-type superconductors display high critical temperatures and relatively high critical current densities Jc. The typical approach to increasing Jc is to introduce defects to control dissipative vortex motion. However, when optimized, this approach is theoretically predicted to be limited to achieving a maximum Jc of only ∼30% of the depairing current density Jd, which depends on the coherence length and the penetration depth. Here we dramatically boost Jc in SmFeAsO1-xHx films using a thermodynamic approach aimed at increasing Jd and incorporating vortex pinning centres. Specifically, we reduce the penetration depth, coherence length and critical field anisotropy by increasing the carrier density through high electron doping using H substitution. Remarkably, the quadrupled Jd reaches 415 MA cm-2, a value comparable to cuprates. Finally, by introducing defects using proton irradiation, we obtain high Jc values in fields up to 25 T. We apply this method to other iron-based superconductors and achieve a similar enhancement of current densities.

Wavelet transform-based characterization of printing ink penetration depth and image phase dissimilarity

Abstract In this paper, continuous wavelet transform and discrete wavelet transform are used to detect transient anomalies entrained in normal information and to demonstrate their components. Multi-scale analysis of wavelet transform, Haar wavelet basis and multi-scale edge detection algorithms are utilized to determine the modal extreme points and identify the edge points for faster and more accurate extraction of edge features of the image. In order to further validate the applicability and feasibility of wavelet transform for printing images and to determine the quality inspection criteria based on ink penetration depth and image phase anisotropy, MATLAB software is utilized to perform simulation tests. The results show that the wavelet transform can remove the noise generated by uneven illumination and printing background during the printing process and can detect the edges of the printing image with an error accuracy of ±0.063mm and meet the error correction accuracy of <0.4mm as required by the printing standard. The experiments verify the feasibility of the wavelet transform, which can characterize the depth of penetration of the printing ink and the image anisotropy and provides a theoretical basis for improving the quality of printing. The experiment confirms that wavelet transform can be used to measure printing ink penetration depth and image anisotropy, giving a theoretical basis for improving printing quality.

Evidence that cuprate superconductors form an array of nanoscopic Josephson junctions

Recent measurements of charge instabilities in overdoped compounds rekindled the proposal that cuprates become superconductors by long-range order through Josephson coupling between nanoscopic charge domains. We use the theory of phase-ordering dynamics to show that incommensurate charge density waves (CDWs) are formed in the CuO planes by a series of free-energy wells separated by steep barriers. Charge oscillations in these domains give rise to a net hole-hole attraction proportional to the height of these barriers. Concomitantly, the self-consistent calculations yield localized superconducting amplitudes in the CDW domains characterizing a granular superconductor. We show that a transition by long-range phase order promoted by Josephson coupling elucidates many well-known features of cuprates like the high magnetic penetration depth anisotropy and the origin of the pseudogap, among others. Furthermore, the average Josephson energy reproduces closely the planar superfluid density temperature dependence of La-based films and the superconducting giant proximity effects of cuprates, a 20-year-old open problem.

Nodal multigap superconductivity in the anisotropic iron-based compound RbCa2Fe4As4F2

The 12442 compounds are a recently discovered family of iron-based superconductors, that share several features with the cuprates due to their strongly anisotropic structure, but are so far poorly understood. Here, we report on the gap structure and anisotropy of RbCa2(Fe1−xNix)4As4F2 single crystals, investigated by a combination of directional point-contact Andreev-reflection spectroscopy and coplanar waveguide resonator measurements. Two gaps were identified, with clear signatures of d-wave-like nodal structures which persist upon Ni doping, well described by a two-band d − d state with symmetry-imposed nodes. A large London penetration depth anisotropy was revealed, weakly dependent on temperature and fully compatible with the d − d model.

Temperature dependence of London penetration depth anisotropy in superconductors with anisotropic order parameters

We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $\gamma_\lambda(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $\Delta(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $\Delta(T)/\Delta(0)$ can be represented with good accuracy by the interpolation suggested by D. Einzel, J. Low Temp. Phys, {\bf 131}, 1 (2003), which simplifies considerably the evaluation of $\gamma_\lambda(T)$. Of particular interest is mixed order parameters of two symmetries for which $\gamma_\lambda(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $\Delta_{max}(0)/T_c$ may exceed substantially the weak coupling limit of 1.76. It, however, does not imply a strong coupling, rather it is due to significantly anisotropic angular variation of $\Delta$.

Anisotropy of field dependent penetration depth and the Sommerfeld coefficient in the pnictide superconductor

The modified phenomenological Ginzburg-Landau (MPGL) theory used to observe the anisotropy of the penetration depth as well as the Sommerfeld coefficient in the pnictide superconductor of the composition Ba0.6K0.4Fe2As2. The values of such thermodynamic parameters have been theoretically calculated and presented in this context. The qualitative, as well as quantitative results of such anisotropies indicate the successful accomplishment of this theory to the superconducting system of Ba1-xKxFe2As2composition.

Anisotropy induced vortex lattice rearrangement in CaKFe4As4

The magnetic penetration depth anisotropy $\gamma_\lambda=\lambda_{c}/\lambda_{ab}$ ($\lambda_{ab}$ and $\lambda_{c}$ are the in-plane and the out-of-plane components of the magnetic penetration depth) in a CaKFe$_4$As$_4$ single crystal sample (the critical temperature $T_{\rm c}\simeq 35$ K) was studied by means of muon-spin rotation ($\mu$SR). $\gamma_\lambda$ is almost temperature independent for $T\lesssim 20$ K ($\gamma_\lambda\simeq 1.9$) and it reaches $\simeq 3.0$ by approaching $T_{\rm c}$. The change of $\gamma_\lambda$ induces the corresponding rearrangement of the flux line lattice (FLL), which is clearly detected via enhanced distortions of the FLL $\mu$SR response. Comparison of $\gamma_\lambda$ with the anisotropy of the upper critical field ($\gamma_{H_{\rm c2}}$) studied in Phys. Rev B {\bf 94}, 064501 (2016), reveals that $\gamma_\lambda$ is systematically higher than $\gamma_{H_{\rm c2}}$ at low-temperatures and approaches $\gamma_{H_{\rm c2}}$ for $T \rightarrow T_{\rm c}$. The anisotropic properties of $\lambda$ are explained by the multi-gap nature of superconductivity in CaKFe$_4$As$_4$ and are caused by anisotropic contributions of various bands to the in-plane and the out-of-plane components of the superfluid density.

Anisotropy of Sommerfeld coefficient and penetration depth in superconducting 2H-NbS2

We proposed anisotropic properties of Sommerfeld coefficient as well as penetration depth for superconducting 2H-NbS2 by using modified phenomenological GL-theory for multi band superconducting system. Calculated results are very close with the corresponding experimental findings reported earlier. Similarly, anisotropy of penetration depths obtained successfully following the same model of GL-theory. The analysis reveals that present proposed model can successfully be used for explaining anisotropy of transitional metal dichalcogenide compounds (TMDs).

Manipulation of gap nodes by uniaxial strain in iron-based superconductors.

In the iron pnictides and chalcogenides, multiple orbitals participate in the superconducting state, enabling different gap structures to be realized in distinct materials. Here we argue that the spectral weights of these orbitals can, in principle, be controlled by a tetragonal symmetry-breaking uniaxial strain, due to the enhanced nematic susceptibility of many iron-based superconductors. By investigating multiorbital microscopic models in the presence of orbital order, we show that not only Tc can be enhanced, but pairs of accidental gap nodes can be annihilated and created in the Fermi surface by an increasing external strain. We explain our results as a mixture of nearly degenerate superconducting states promoted by strain, and show that the annihilation and creation of nodes can be detected experimentally via anisotropic penetration depth measurements. Our results provide a promising framework to externally control the superconducting properties of iron-based materials.

Probing the anisotropic vortex lattice in the Fe-based superconductor KFe2As2using small-angle neutron scattering

Using small angle neutron scattering, the anisotropy of the magnetic vortex lattice (VL), in the heavily hole-doped pnictide superconductor ${\text{KFe}}_{2}{\text{As}}_{2}$, was studied. Well-ordered VL scattering patterns were measured with fields applied in directions between $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$ and the basal plane, rotating either towards $[100]$ or $[110]$. Slightly distorted hexagonal patterns were observed when $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$. However, the scattering pattern distorted more strongly as the field was rotated away from the c axis. At low field, the arrangement of vortices is affected by the anisotropy of penetration depth in the plane perpendicular to the field. By fitting the distortion with the anisotropic London model, we obtain an estimate of $\ensuremath{\sim}$$3.4$ for the anisotropy factor $\ensuremath{\gamma}$ between the in-plane and c-axis penetration depths at the lowest temperature studied. The results further reveal VL phase transitions as a function of field direction. We discuss these transitions using the ``hairy ball'' theorem.

Intrinsic pinning and the critical current scaling of clean epitaxial Fe(Se,Te) thin films

We report on the transport properties of clean, epitaxial Fe(Se,Te) thin films prepared on Fe-buffered MgO (001) single crystalline substrates by pulsed laser deposition. Near ${T}_{\mathrm{c}}$ a steep slope of the upper critical field for $H||ab$ was observed (74.1 T/K), leading to a very short out-of-plane coherence length, ${\ensuremath{\xi}}_{\mathrm{c}}(0)$, of 0.2 nm, yielding 2${\ensuremath{\xi}}_{\mathrm{c}}(0)\ensuremath{\approx}0.4\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. This value is shorter than the interlayer distance (0.605 nm) between the Fe-Se(Te) planes, indicative of modulation of the superconducting order parameter along the $c$ axis. An inverse correlation between the power law exponent $N$ of the electric field-current density($E$-$J$) curve and the critical current density ${J}_{\mathrm{c}}$ has been observed at 4 K, when the orientation of $H$ was close to the $ab$ plane. These results prove the presence of intrinsic pinning in Fe(Se,Te). A successful scaling of the angular dependent ${J}_{\mathrm{c}}$ and the corresponding exponent $N$ can be realized by the anisotropic Ginzburg Landau approach with appropriate $\ensuremath{\Gamma}$ values $2\ensuremath{\sim}3.5$. The temperature dependence of $\ensuremath{\Gamma}$ behaves almost identically to that of the penetration depth anisotropy.

Strong Pressure Dependence of the Magnetic Penetration Depth in Single Crystals of the Heavy-Fermion SuperconductorCeCoIn5Studied by Muon Spin Rotation

In the tetragonal heavy fermion system CeCoIn(5) the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ(a)), the penetration depth anisotropy (γ = λ(c)/λ(a)) and the temperature dependence of 1/λ(i)(2) (i = a, c) were studied in single crystals. A strong decrease of λ(a) with pressure was observed, while γ and λ(i)(2)(0)/λ(i)(2)(T) are pressure independent. A linear relationship between 1/λ(a)(2)(270 mK) and T(c) was also found. The large decrease of λ(a) with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.

Vortex lattice melting andHc2in underdoped YBa2Cu3Oy

Vortices in a type-II superconductor form a lattice structure that melts when the thermal displacement of the vortices is an appreciable fraction of the distance between vortices. In an anisotropic high-Tc superconductor, such as YBa2Cu3Oy, the magnetic field value where this melting occurs can be much lower than the mean-field critical field Hc2. We examine this melting transition in YBa2Cu3Oy with oxygen content y from 6.45 to 6.92, and fit the data to a theory of vortex-lattice melting. The quality of the fits indicates that the transition to a resistive state is indeed the vortex lattice melting transition, with the shape of the melting curves being consistent with the known change in penetration depth anisotropy from underdoped to optimally doped YBa2Cu3Oy. From the fits we extract Hc2(T = 0) as a function of hole doping. The unusual doping dependence of Hc2(T =0) points to some form of electronic order competing with superconductivity around 0.12 hole doping.

Spin-Wave Excitation in Magnetic Insulators by Spin-Transfer Torque

We study the excitation of spin waves in magnetic insulators by the current-induced spin-transfer torque. We predict preferential excitation of surface spin waves induced by an easy-axis surface anisotropy with critical current inversely proportional to the penetration depth and surface anisotropy. The surface modes strongly reduce the critical current and enhance the excitation power of the current-induced magnetization dynamics.

First-Order Reorientation Transition of the Flux-Line Lattice in CaAlSi

The flux-line lattice in CaAlSi has been studied by small-angle neutron scattering. A well-defined hexagonal flux-line lattice is seen just above H(c1) in an applied field of only 54 Oe. A 30° reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be first-order and could be explained by nonlocal effects. The magnetic field dependence of the form factor is well-described by a single penetration depth of λ=1496(1) Å and a single coherence length of ξ=307(1) Å at 2 K. At 1.5 K, the penetration depth anisotropy is γ(λ)=2.7(1), with the field applied perpendicular to the c axis, and agrees with the coherence length anisotropy determined from critical field measurements.

Magnetic-field tuned anisotropy in superconducting RbxFe2−ySe2

The anisotropic superconducting properties of a Rb${}_{x}$Fe${}_{2\ensuremath{-}y}$Se${}_{2}$ single crystal with ${T}_{\mathrm{c}}\ensuremath{\simeq}32$ K were investigated by means of superconducting quantum interference device (SQUID) and torque magnetometry, probing the effective magnetic penetration depth ${\ensuremath{\lambda}}_{\mathrm{eff}}$ and the magnetic penetration depth anisotropy ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}$. Interestingly, ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}$ is found to be temperature independent in the superconducting state but strongly field dependent: ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}(0.2\phantom{\rule{0.28em}{0ex}}\mathrm{T})<4$ and ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}(1.4\phantom{\rule{0.28em}{0ex}}\mathrm{T})>8$. This unusual anisotropic behavior, together with a large zero-temperature ${\ensuremath{\lambda}}_{\mathrm{eff}}(0)\ensuremath{\simeq}1.8$ $\ensuremath{\mu}$m, is possibly related to a superconducting state heavily biased by the coexisting antiferromagnetic phase.

Th-substituted SmFeAsO: Structural details and superconductivity withTcabove 50 K

We report structural, magnetic, and transport properties of polycrystalline samples and single crystals of superconducting ${\text{Sm}}_{1\ensuremath{-}x}{\text{Th}}_{x}\text{FeAsO}$ with maximal ${T}_{c}$ above 50 K, prepared under high pressure. Bulk superconducting samples do not undergo a structural phase transition from tetragonal to orthorhombic symmetry at low temperatures. The unit-cell parameters $a$ and $c$ shrink with Th substitution and the fractional atomic coordinate of the As site ${z}_{\text{As}}$ remains almost unchanged while that of Sm/Th ${z}_{\text{Sm}/\text{Th}}$ increases. Upon warming from 5 to 295 K the increase in the FeAs layer thickness is dominant, while the changes in the other structural building blocks are minor, and they compensate each other, since the As-Sm/Th distance contracts by about the same amount as the O-Sm/Th expands. The polycrystalline and single-crystalline samples are characterized by a full diamagnetic response in low magnetic field, by a high intergrain critical current density for polycrystalline samples, and by a critical current density on the order of $8\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }\text{A}/{\text{cm}}^{2}$ for single crystals at 2 K in fields up to 7 T. The magnetic penetration depth anisotropy ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}$ increases with decreasing temperature, in a similar way to that of ${\text{SmFeAsO}}_{1\ensuremath{-}x}{\text{F}}_{y}$ single crystals. The upper critical field estimated from resistance measurements is anisotropic with slopes of $\ensuremath{\sim}5.4\text{ }\text{T}/\text{K}$ ($H\ensuremath{\parallel}ab$ plane) and $\ensuremath{\sim}2.7\text{ }\text{T}/\text{K}$ ($H\ensuremath{\parallel}c$ axis), at temperatures sufficiently far below ${T}_{c}$. The low-temperature upper critical field anisotropy ${\ensuremath{\gamma}}_{H}$ is in the range of $\ensuremath{\sim}2$, consistent with the tendency of a decreasing ${\ensuremath{\gamma}}_{H}$ with decreasing temperature, previously reported for ${\text{SmFeAsO}}_{1\ensuremath{-}x}{\text{F}}_{y}$ single crystals.

Anisotropic superconducting properties of single-crystallineFeSe0.5Te0.5

Iron-chalcogenide single crystals with the nominal composition FeSe$_{0.5}$Te$_{0.5}$ and a transition temperature of $T_{c}\simeq14.6$ K were synthesized by the Bridgman method. The structural and anisotropic superconducting properties of those crystals were investigated by means of single crystal X-ray and neutron powder diffraction, SQUID and torque magnetometry, and muon-spin rotation. Room temperature neutron powder diffraction reveals that 95% of the crystal volume is of the same tetragonal structure as PbO. The structure refinement yields a stoichiometry of Fe_1.045Se_0.406Te_0.594. Additionally, a minor hexagonal Fe_7Se_8 impurity phase was identified. The magnetic penetration depth \lambda at zero temperature was found to be 491(8) nm in the ab-plane and 1320(14) nm along the c-axis. The zero-temperature value of the superfluid density \rho_s(0) \lambda^-2(0) obeys the empirical Uemura relation observed for various unconventional superconductors, including cuprates and iron-pnictides. The temperature dependences of both \lambda_ab and \lambda_c are well described by a two-gap s+s-wave model with the zero-temperature gap values of \Delta_S(0)=0.51(3) meV and \Delta_L(0)=2.61(9) meV for the small and the large gap, respectively. The magnetic penetration depth anisotropy parameter \gamma_\lambda(T)=\lambda_c(T)/\lambda_{ab}(T) increases with decreasing temperature, in agreement with \gamma_\lambda(T) observed in the iron-pnictide superconductors.

Evidence from anisotropic penetration depth for a three-dimensional nodal superconducting gap in single-crystallineBa(Fe1−xNix)2As2

The London penetration depth, $\lambda$, is directly related to the density, $n_{s}$, of the Cooper pairs ($\lambda^{2}\propto 1/n_{s}$) and its variation with temperature provides valuable insight into the pairing mechanism. Here we study the evolution with doping of the temperature dependence of the in-plane ($\lambda_{ab}$) and out-of-plane ($\lambda_{c}$) penetration depths in single crystals of electron-doped Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$. As is the case for other pnictides, $\lambda(T) \sim T^n$ over the whole doping range and this behavior extends down to at least $T=T_c/100$, setting a very small upper limit on the gap minimum. Furthermore, in the overdoped regime: 1) the exponent $n$ becomes substantially smaller than 2, which is incompatible with the models that explain power-law behavior to be due to scattering; 2) the exponent $n$ becomes anisotropic, with $\lambda_{c}(T)$ showing a clear $T$-linear behavior over a large temperature interval. These findings suggest that in the overdoped regime the superconducting gap in iron-based pnictide superconductors develops nodal structure, which unlike in the cuprates, cannot be understood within a two-dimensional picture.

The effect of in-plane mass anisotropy on the properties of high temperaturesuperconductors in states of mixed symmetry

Experiments have suggested that the high-Tc cuprate YBCO shows marked anisotropy in penetration depth and coherence lengthmeasurements. In order to take into account the presence of this anisotropy inthe system and its corresponding effect on the various properties of the high-Tc superconducting materials, we have developed an anisotropic two-orderparameter Ginzburg–Landau (GL) theory involving a mixed symmetrystate of the order parameter components. For this we have generalized atwo-order parameter GL theory, recently developed for the isotropic high-Tc superconductors involving a mixed symmetry state of the order parameter components(Karmakar and Dey 2008 J. Phys. Condens. Matter 20 255218), in which the effect ofthe presence of in-plane anisotropy has been taken into account by an effectivemass approximation, with the anisotropy being characterized by the parameterγ = mx/my. The work goes beyond the limitations of the earlier studies in this field as it enables us tocarry out a detailed study of the various properties of the system over the entire range ofapplied magnetic field and wide range of temperature for arbitrary values of the GL parameterκy and vortex lattice symmetry. The model successfully explains not only the observed obliquevortex lattice structure in the presence of in-plane anisotropy but also the experimentallyobserved angle between the primitive axes of the vortex lattice. The generation oftwo-fold symmetry of the vortices in the presence of in-plane anisotropy, for avery low applied magnetic field can also be analyzed by our model. We havealso compared our theoretical results with various other experiments on high-Tc cuprate YBCO.