{'fraction_non_alphanumeric': 0.04114278968183696, 'fraction_numerical': 0.015701552446726875, 'mean_word_length': 4.704377104377104, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 3, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Magnetic and transport properties of electron-doped superconducting thin films: Pairing symmetry, pinning and spin fluctuations

In this Chapter we review our latest results on magnetic (AC susceptibility) and transport (resistivity) properties of Pr1.85Ce0.15CuO4 (PCCO) and Sm1.85Ce0.15CuO4 (SCCO) thin films grown by pulsed laser deposition technique. Three main topics of our studies will be covered. We start with a thorough discussion of the pairing symmetry mechanisms in optimally-doped SCCO thin films based on the extracted with high accuracy temperature profiles of penetration depth. In particular, we found that above and below a crossover temperature T*=0.22T_C, our films are best-fitted by a linear and quadratic dependencies, respectively, with physically reasonable values of d-wave node gap parameter and paramagnetic impurity scattering rate. Our next topic is related to the flux distribution in our films. More precisely, we present a comparative study on their pinning ability at low magnetic fields extracted from their AC susceptibilities. Depending on the level of homogeneity of our films, two different types of the irreversibility line have been found. The obtained results are described via the critical-state model taking into account the low-field grain-boundary pinning. And finally, we demonstrate our recent results on the normal state temperature behavior of resistivity R(T) for the high-quality optimally-doped SCCO thin films. In addition to the expected contributions from the electron-phonon and electron-electron scattering processes, we also observed an unusual step-like behavior of R(T) around T=87K which we attributed the to the manifestation of thermal excitations due to spin fluctuations induced by Sm3+ moments through Cu2+-Sm3+ interaction.


I. Introduction
The accurate experimental determination of the temperature behavior of the magnetic penetration depth, λ(T), has been of great interest to the scientific community since the very discovery of high-T C superconductors. Since the effective value of λ(T) is extremely sensitive to local inhomogeneities, a thorough analysis of its low-temperature profile gives probably one of the most reliable methods to determine the quality of a superconducting material (especially in the form of thin films), which is of utter importance for applications [1,2].
On the other hand, the magnetic penetration depth is strongly sensitive to the variations of the macroscopic superconducting order parameter and therefore its study can give important information about both the symmetry of the superconducting state and the pairing mechanisms. It is well established that most of the conventional low-T C superconductors have s-wave pairing symmetry. As for high-T C cuprates, the study of pairing symmetry in these materials has been (and still remains) one of the most polemical and active fields of research over the last few years [2] and the experimental determination of the temperature dependence of λ has been one of the most common methods in these studies. In particular, a power-like dependence T n of the penetration depth at low temperatures clearly points at a nodal structure of the superconducting gap (as expected for strongly correlated materials) where the exponent n depends on the type of the node in the k-space. Most phase-sensitive measurements [3,4] have revealed that hole-doped high-T C cuprates with nearly optimal doping have predominantly d x  [5]. At the same time, for electron-doped cuprates, which have composition of the form Ln 2-x Ce x CuO 4 (where Ln corresponds to Pr, Nd, or Sm), the pairing mechanisms are not yet fully understood [6][7][8][9][10]. For example, using the point contact spectroscopy technique, Biswas et al. [7] have found strong evidences in favor of d-wave pairing symmetry in under-doped (x ≈ 0.13) Pr 2-x Ce x CuO 4 (PCCO). Further studies revealed [8] that the low temperature superfluid density of Ce-based magnetic superconductors varies quadratically with temperature in the whole range of doping, in agreement with the theoretical prediction for a d-wave superconductor with impurity scattering. In addition, remeasured [9] magnetic-field dependence of the low-temperature specific heat of optimally-doped (x=0. 15

II. Magnetic penetration depth and pairing symmetry of electron-doped high-T C superconducting thin films
In this Section we study the influence of local inhomogeneities on low-temperature dependence of the magnetic penetration depth λ(T) in high-quality optimally-doped Pr 1.85 Ce 0.15 CuO 4 (PCCO) and Sm 1.85 Ce 0.15 CuO 4 (SCCO) thin films grown by the pulsed laser deposition (PLD) technique. The λ(T) profiles have been extracted from conductance-voltage data by using a highly-sensitive home-made mutual-inductance bridge.
The structural quality of our samples was verified through X-ray diffraction (XRD) and scanning electron microscopy (SEM) together with energy dispersive spectroscopy (EDS) technique. Both XRD spectra and SEM data reveal that PCCO films are of higher structural quality than SCCO films (see Figure 1).  The experimental bridge used in this work is based on the mutual-inductance method.
To measure samples in the shape of thin films, the so-called screening method has been developed [11]. It involves the use of primary and secondary coils, with diameters smaller than the dimension of the sample. When these coils are located near the surface of the film, the response (i.e., the complex voltage output V AC ) does not depend on the radius of the film or its properties near the edges. In the reflection technique [12], an excitation (primary) coil coaxially surrounds a pair of counter-wound (secondary) pick-up coils. If we take the current in the primary coil as a reference, V AC can be expressed via two orthogonal components, i.e., V AC = V L + iV R . The first one is the inductive component, V L (which is in phase with the time-derivative of the reference current) and the second one is the quadrature resistive component, V R (which is in phase with the reference current). It can be easily demonstrated that V L and V R are directly related to the average magnetic moment and the energy losses of the sample, respectively [13]. When there is no sample in the system, the net output from the secondary coils is close to zero because the pick-up coils are identical in shape but are wound in opposite directions. The sample is positioned as close as possible to the set of coils, to maximize the induced signal in the pick-up coils. An alternate current sufficient to create a magnetic field of amplitude h AC and frequency f is applied to the primary coil by an alternating voltage source, V in . The output voltage of the secondary coils V AC is measured through the usual lock-in technique [14]. To extract the profile of the penetration depth within the discussed here method, one should resolve the following equation relating the measured output voltage V AC to the λ(T) sensitive sample features [12]: where I P and ω=2πf are respectively the amplitude and the frequency of the current in the primary coil, h P (h S ) is the distance from the primary (secondary) coil to the sample, G is the total conductance of the sample, and M(x) is a geometrical factor [12]. Since the total impedance of the sample is given by [15] K L i R Z ω + = the expression for the sample's total conductance reads: Here L k and R are the kinetic inductance and the resistance of the sample, respectively. From the above equations it follows that by measuring V AC (T) we can numerically reproduce the temperature dependencies of both L k and R.
From the two-fluid model, the relation between L k and λ(T) for thin films (with thickness d<<λ) is given by [1,2,15]: This expression will be used hereafter to obtain λ(T) from the measured L K (T) dependence.
Instead of the tabulation based procedure used before [12], in the present study we have simultaneously determined G(T) from Eq.(1) and extracted both R(T) and L K (T) using Eq.(2).
Then from the temperature dependence of L K we recover the temperature dependence of λ.    By trying many different temperature dependencies (including both exponential and powerlike), we found that both our samples are best-fitted (see Fig. 5) by the so-called Goldenfeld-Hirschfeld interpolation formulae [20] ∆λ(T)/λ(0)=AT 2 /(T+T 0 ) which describes a crossover between linear and quadratic dependencies above and below some temperature T 0 . Here A=ln(2)k B /∆ 0 with 0 ∆ being the amplitude of the zero-temperature value of the d-wave gap parameter, and the crossover temperature T 0 depends on the (unitary limit) scattering rate Γ (which is proportional to the impurity concentration of the sample) as follows T 0 =ln(2)k B Γ 1/2 ∆ 0 1/2 . The fitting parameters are given in Table 1. Noticeably, the crossover temperature T 0 is lower for high-quality PCCO films (T 0 /T C =0.13). In turn, this observation

film T C (K) A T C T o /T C
). Notice that the above estimates are in good agreement with the known results for high-quality PCCO thin films [8]. On the other hand, a less homogeneous SCCO film (with T C =20.2K) exhibits a much stronger impurity scattering with the rate

III. Irreversibility line and low-field grain-boundary pinning in electron-doped superconducting thin films
The measurement of AC magnetic susceptibility still remains one of the most powerful methods to obtain important information on dissipation mechanisms in high-T C superconductors (HTS). To get useful information from such experiments, however, very careful control of sample's microstructure is required. While in high enough magnetic fields the dissipation is known to be dominated by flux motion of Abrikosov vortices [21][22][23][24], the low-field dissipation mechanisms (especially, in inhomogeneous and granular superconductors) are less obvious due to the numerous grain-boundary related effects which are better treated by the Josephson physics [25][26][27].
In this Section we present a comparative study of low-field AC magnetic susceptibility data on more homogeneous Pr  [28][29][30][31][32] and further references therein). All samples showed similar and reproducible results. The SEM experiments reveal that PCCO films are of higher structural quality (more homogeneous) than SCCO films which show a pronounced granular structure (see Figure 6). The average grain size in typical PCCO and SCCO films is estimated to be around 2µm and 0.5µm, respectively. Measurements of the real (χ') and imaginary (χ") parts of AC susceptibility were performed by using a MPMS magnetometer from the Quantum Design equipped with AC modulus [13,14,33,34]. All data are chosen from samples with the same dimensions and well placed parallel to the field in order to decrease the demagnetization correction. The symbol size used for data presentation takes into account error bars based on the temperature stability, reproducibility, and system precision. To account for a possible magnetic response from substrate, we measured several stand alone pieces of the substrate.
No tangible contribution due to magnetic impurities was found. A typical temperature behavior of the measured complex AC magnetic susceptibility in PCCO and SCCO films in a small magnetic field (of amplitude h AC =1.0Oe and frequency f AC =1.0kHz) is shown in Fig.7.
The field dependence of the imaginary part χ" of the AC susceptibility in both films for the temperatures close to T C is depicted in Fig.8.
Due to small values of the applied magnetic field, it is natural to associate the peak temperatures T p (H) in Fig.8 with intergrain losses. The extracted values of the irreversibility temperature T p (H) for both samples are shown in Fig.9 in the form of the log-log plots. As is   seen, more homogeneous PCCO films are well-fitted by the flux-creep mediated IL obeying the law 1-T p /T C ∝ H q with q=2/3 while less homogeneous SCCO films (with grain size of the order of 500 nm) follow the IL law with q=1.
To interpret the above findings, we follow Müller's approach [35] (based on the Kim-Anderson critical-state model [36]) according to which the low-field dependence of the IL

temperature T p (H) is governed by the following implicit equation (hereafter
Here, λ(T) is the London penetration depth, R is the average grain size, d is the film thickness, The observed difference in behavior of IL is attributed to difference in average grain sizes in PCCO and SCCO films which, according to SEM scans (see Figure 6) are around R=2µm and R=500 nm, respectively.
Taking into account the explicit temperature dependence of the pinning-force density within the grain-boundary pinning model [37] we propose the following scenario for the observed IL behavior.
Since near T p in more homogeneous PCCO films (see Fig.6a) , and hence , from Eq.(4) we find the usual flux-creep dominated law (see Fig.9a) On the other hand, in more granular SCCO films (see Fig.6b By calculating the coefficients A and B from the IL curve slopes on a log-log plot, we can estimate the pinning-force densities µ J (0) for both materials. Using for the film thickness d=200nm, London penetration depths [10] λ P (0)=250nm, λ S (0)=500nm, and average grain sizes R=2µm and R=0.5µm, from Eqs. (7) and (8) we obtain µ JP (0)=3x10 4 TA/m 2 and µ JS (0)= 1.2x10 5 TA/m 2 for the pinning-force densities of PCCO and SCCO films, respectively. As expected, the above pinning values are larger than those seen in bulk granular materials [25][26][27]. Thus, for small applied magnetic fields, the flux pinning is dominated by the so-called electromagnetic pinning scenario characterized by the London pentration depth rather than coherence length (the latter is responsible for the so-called core pinning scenario in high enough magnetic fields). Within this scenario, the observed higher pinning ability of SCCO films near T p can be attributed to a perfect match between the average grain size R and the correspondent London penetration depth λ S (T p ). While in the case of a more homogeneous PCCO film (with the average grain size of R=2000nm) the ratio λ P (T p )/R is much less optimal leading to a lower pinning ability of these films. And finally, it is instructive to point out that the obtained here results on low-field irreversibility lines in our granular films (governed by grain-boundary pinning of coreless Josephson vortices) principally differ from the high-field irreversibility lines observed in electron-doped single crystals (dominated by core pinning of Abrikosov vortices, including particular scenarios for melting of the vortex lattice) [24]. interaction [48].

IV. Possible manifestation
In this Section we present our latest results on the temperature behavior of resistivity for the optimally-doped Sm 1.85 Ce 0.15 CuO 4 films [42], paying special attention to their normal state properties. In addition to the expected contributions from the electron-phonon and electron-electron scattering processes, we also observed an unusual kink like behavior of ) (T ρ around T=87K very similar to the one seen in inelastic neutron scattering data [46,47]. Given that Sm has a larger ion size than Pr and assuming that the long-range AFM correlations should be even stronger in thin films (than in single crystals), we attribute the appearance of this kink in our SCCO films to the manifestation of thermal excitations due to spin fluctuations induced by + 3 Sm moments through A few SCCO thin films (d=200nm thick) grown by pulsed laser deposition on standard LaAlO 3 substrates were used in our measurements (for more details on our samples including their other physical properties, see [42]). All samples showed similar and reproducible results.
The structural quality of the samples was verified through X-ray diffraction (see Fig.1) and scanning electron microscopy together with energy dispersive spectroscopy technique. To account for a possible magnetic response from substrate, we measured several stand alone pieces of the substrate. No tangible contribution due to magnetic impurities was found. The where [50] C is the force constant of a two-dimensional harmonic oscillator, and > < 2 u is the mean square displacement of the magnetic Sm atoms from their equilibrium positions.
After trying many different temperature dependencies, we found that our SCCO films are rather well fitted (solid line in Fig.10) using the following expression for the observed resistivity: T  T  T  T   e  e  ph  e  sf  res − − + + + = ρ ρ ρ ρ ρ (10) where other two terms in the rhs of Eq.(10) are related, respectively, to electron-phonon contribution [43] AT T  [43][44][45] estimates of the plasmon frequency, the impurity scattering rate, electron-phonon coupling constant, and the Fermi energy, respectively.

V. Conclusion
In this Chapter we presented our latest results on magnetic and transport properties of electron-doped Pr 1 Sm moments.