Session R5: Disorder and Substitution Studies in Fe-based Superconductors

Effect of electron irradiation on (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ from London penetration depth measurements

The effects of artificial disorder induced by 2.5 MeV electron irradiation on superconducting properties of single crystals of (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (fifteen different compositions covering a wide interval of $0.20 \leq x \leq 1.0$) was systematically studied by tunnel-diode resonator measurements of the in-plane London penetration depth, $\lambda(T)$, down to ~50 mK before and after irradiation. Upon electron irradiation (with total doses up to $2\times 10^{19}$ $e^-$/cm$^2$), the increase of resistivity at \(T_{c}\), $\Delta \rho (T = T_{c })$ and the decrease of $\Delta T_{c} / T_{c0}$ was largest at heavily over-doped compositions. A non-exponential behavior in samples with $x \geq 0.8$ was found from the low-temperature variation of $\lambda(T)$ suggesting a change in the superconducting gap structure or peculiarities of (inter-, intra-) band scattering and pairing. We will discuss possible scenarios to connect a fully gapped state at the optimal doping ($x\approx 0.40$) with the apparent nodal behavior in the heavily over-doped region ($x \geq 0.8$).\\\\ The work performed in Ames Lab and Iowa State University was supported by the U.S. DOE, OS, MSED under contract DE-AC02-07CH11358. The work performed in University of Florida was supported by NSF-DMR-1005625.   

A shift of the phase diagram in BaFe$_{2}$(As$_{1-}_{x}$P$_{x})_{2\, }$by controlled disorder

The relationship between unconventional superconductivity and quantum critical point (QCP) is one of the most important issues in strongly correlated electron systems. A systematic study on the impurity scattering is performed in iron-based superconductor BaFe$_{2}$(As$_{1-}_{x}$P$_{x})_{2}$, in which clear evidence for QCP has recently been presented[1]. We introduce point defects into BaFe$_{2}$(As$_{1-}_{x}$P$_{x})_{2}$ by electron irradiation, which has less effects on lattice constant and carrier density compared to the chemical substitution of atoms[2]. Here, we report on the changes of the magnetic and superconducting transition temperatures with electron irradiation in a wide range of substitution, from which we discuss the effect of impurity scattering on superconducting dome and QCP. [1]T. Shibauchi \textit{et al}., Annu. Rev. Condens. Matter Phys. \textbf{5}, 113 (2014). [2]Y. Mizukami \textit{et al}., Nat. Commun. \textbf{5}, 5657 (2014).   

Robustness of quantum critical pairing against disorder in iron-based superconductors

Several experiments in iron pnictides and cuprates reveal a superconducting (SC) state remarkably robust against non-magnetic disorder — at least when compared to the simple extension of the Abrikosov-Gor’kov formalism to dirty unconventional superconductors. Motivated by the fact that most of these SC states appear in proximity to a magnetic instability, here we study the impact of non-magnetic disorder on the SC state promoted by quantum critical magnetic fluctuations. We go beyond the weak coupling approach by applying a variational formalism of the Eliashberg equations of the spin-fermion model, taking into account the effects of disorder on both fermionic and bosonic degrees of freedom. We find that the reduced fermionic coherent spectral weight near the magnetic quantum critical point strongly decreases the suppression rate of $T_c$ by weak disorder, as compared to the Abrikosov-Gor'kov universal value. Furthermore, because the bosons promoting the Cooper pairs emerge as collective modes of the fermions, they are also impacted by disorder, giving rise to an additional reduction of the suppression rate of $T_c$ by weak disorder. Our results qualitatively agree with experiments, shedding new light on why unconventional superconductors are robust against disorder.   

Numerical Studies of Doped Iron Pnictides

The phase diagram of electron-doped pnictides is studied varying the temperature, electronic density, and isotropic disorder strength and dilution via numerical studies of a three-orbital spin-fermion model with lattice degrees of freedom [1]. Doping introduces disorder but in theoretical studies the effect of the randomly located dopants is difficult to address. Numerically the effects of electronic doping, regulated by a chemical potential, and impurity disorder at randomly selected sites can be independently controlled. It was found that the reduction with doping of the Neel and the structural transition temperatures, and the stabilization of a nematic state, is mainly controlled by the magnetic dilution due to the disorder. Fermi surface changes due to doping affect only slightly both critical temperatures. Our findings are compatible with neutron scattering and STM results, unveiling a patchy network of locally magnetically ordered anisotropic clusters, despite the isotropic disorder. The fragile tendency to nematicity intrinsic of translational invariant electronic systems needs to be supplemented by disorder and dilution to stabilize the robust nematic phase experimentally found in electron-doped 122 pnictides. [1] S. Liang et al., Phys. Rev. B 92, 104512 (2015).   

Mechanically - induced disorder in CaFe$_2$As$_2$: a $^{57}$Fe M\"ossbauer study

$^{57}$Fe M\"ossbauer spectroscopy was used to study an extremely pressure and strain sensitive compound, CaFe$_2$As$_2$, with different degrees of strain introduced by grinding and annealing. At the base temperature, in the antiferromagnetic/orthorhombic phase, compared to a sharp sextet M\"ossbauer spectrum of single crystal CaFe$_2$As$_2$, which is taken as an un-strained sample, an obviously broadened sextet and an extra doublet were observed for ground CaFe$_2$As$_2$ powders with different degrees of strain. The M\"ossbauer results suggest that the magnetic phase transition of CaFe$_2$As$_2$ can be inhomogeneously suppressed by the grinding induced strain to such an extent that the antiferromagnetic order in parts of the grains forming the powdered sample remain absent all the way down to 4.6 K. However, strain has almost no effect on the temperature dependent hyperfine magnetic field in the grains with magnetic order. The quadrupole shift in the magnetic phase approachs zero with increasing degrees of strain, indicating that the strain reduces the average lattice asymmetry at Fe atom position.   

Effects of Tilted Columnar Defects on $J_{\mathrm{c}}$ Behavior in (Ba,K)Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$

Iron-based superconductors have very promising characteristics to be used for practical applications at high fields. We have already demonstrated a remarkable enhancement of $J_{\mathrm{c}}$ in (Ba,K)Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$ by irradiating swift particles [1,2]. In order to further enhance $J_{\mathrm{c}}$, we introduced columnar defects at an angle from the $c$-axis. We found a novel non-monotonic field dependence of $J_{\mathrm{c}}$ as well as its enhancement in such samples at relatively high temperatures. Origins of these anomalous $J_{\mathrm{c\thinspace }}$behavior and the degree of $J_{\mathrm{c}}$ enhancement with the tilted columnar defects will be discussed. [1] T. Taen \textit{et al}., Supercond. Sci. Technol. \textbf{28}, 085003 (2015). [2] F. Ohtake \textit{et al}., Physica C\textbf{518}, 47 (2015).   

Magnetic penetration depth in disordered iron-based superconductors

We study the effect of disorder on the London penetration depth in iron-based superconductors. The theory is based on a two-band model with quasi-two-dimensional Fermi surfaces, which allows for the coexistence region in the phase diagram between magnetic and superconducting states in the presence of intraband and interband scattering. Within the quasiclassical approximation we derive and solve Eilenberger's equations, which include a weak external magnetic field, and provide analytical expressions for the penetration depth in the various limiting cases. A complete numerical analysis of the doping and temperature dependence of the London penetration depth reveals the crucial effect of disorder scattering, which is especially pronounced in the coexistence phase. The experimental implications of our results are discussed.   

The study of vortex state across the phase diagram in single crystals of Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ using current voltage characteristics.

Utilizing the current voltage (I-V) characteristic measurement, we investigate the vortex state of Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ single crystals across a wide doping range: under-doped (x $=$ 0.042 and 0.056), near optimally-doped (x $=$ 0.06 and 0.072), and the over-doped (x $=$ 0.1). We compare the nature of the I-V characteristic curves obtained in our measurements with those of conventional type II superconductors. Using our data we could find a direct relationship between the critical current and flux-flow resistivity over the whole doping range studied. The implications of the comparison between the I-V curves of a conventional type II superconductor and Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ will be discussed. We will also comment on the observed relationship between the critical current and the flux-flow resistivity for the Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ crystals studied.   

The role of magnetism and disorder in superconductivity of gold-doped BaFe$_{\mathrm{2}}$As$_{\mathrm{2}}$ crystals

We present bulk magnetic and transport properties, and find structural and magnetic transitions, in order to construct the detailed T-x phase diagram for Ba(Fe$_{\mathrm{1-x}}$Au$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ single crystals [1]. The Au substitution into the FeAs-planes is only possible up to a small amount of \textasciitilde 3{\%}, probably due to the large size of gold. We find that 5$d$ is more effective in reducing magnetism in BaFe$_{\mathrm{2}}$As$_{\mathrm{2}}$ than its counter \textit{3d} Cu, and this relates to superconductivity. In this talk, we reveal more comprehensive neutron diffraction data in order to clarify some of the inferred $T_{N}$, $T_{S}$ points in our literature report [1]. New transmission electron microscopy results will be presented that sheds light on the role of chemical disorder for preventing high $T_{c}$ in these crystals. [1] L. Li et al., Phys. Rev. B 92, 094504 (2015).   

Defect-induced Superconductivity up to 49 K in (Ca1-xRx)Fe2As2

To explore the origin of the unusual non-bulk superconductivity with a Tc up to 49 K reported in the rare-earth-doped CaFe2As2 , the chemical composition, magnetization, specific heat, resistivity and low temperature annealing effect are systematically investigated on nominal (Ca1-xRx)Fe2As2 single crystals with different x's and R $=$ La, Ce, Pr and Nd. All display a doping independent Tc once superconductivity is induced, a doping dependent low field superconducting volume fraction f, and a large magnetic anisotropy $\eta $ in the superconducting state, suggesting a rather inhomogeneous superconducting state in an otherwise chemically ``homogeneous'' superconductor. The wavelength dispersive spectroscopy, specific heat and magnetization measurements show the presence of defects which form superparamagnetic clusters for R $=$ Ce, Pr and Nd, but not for La and display both inter and intra-cluster interactions, implying that defects are locally self-organized. Low temperature annealing reduces only the residual strain in the samples without varying x and suppresses f profoundly; however, the Tc was unaffected. The above observations are consistent with the interface-enhanced superconductivity recently proposed and also demonstrates the crucial role of defects in the occurrence of the unusually high Tc \textasciitilde 49 K in (Ca1-xRx)Fe2As2.   

Optical spectroscopy of superconducting Pt-doped BaFe$_{2}$As$_{2}$

Substitution of iron with platinum in BaFe$_{2}$As$_{2}$ leads to suppression of the antiferromagnetic and structural transitions, and the occurrence of bulk superconductivity with superconducting transition temperature ($T_{c})$ around 20 K. In this work, we perform optical spectroscopy study of a BaFe$_{1.9}$Pt$_{0.1}$As$_{2}$ single crystal. The \textit{ab}-plane optical conductivity has been obtained by performing cryogenic infrared reflectance spectroscopy and spectroscopic ellipsometry both above and below $T_{c}$. Below $T_{c}$, bulk superconductivity is directly observed as perfect reflectance in the far infrared data. We model the optical conductivity in the superconducting state using Mattis-Bardeen formalism and find that the data is best fit with two energy gaps. We also analyze the optical conductivity in the normal state and discuss the nature of charge transport.   

Effects of single- and multi-substituted Zn ions in doped-122 type iron-based superconductors

Recent experiments on Zn-substituted 122-type iron-based superconductors at electron- and hole- doped region provide us with a testing ground to understand the effect of Zn impurities in the system. Here, our first-principle calculations of the electronic structure reveal the Zn 4$s$-orbital is partially occupied, suggesting the effect of Zn 4$s$-orbital could not be neglected. We focus on Zn 4$s$-orbital instead of its 3$d$-orbital. Through self-consistent lattice Bogoliubov-de Gennes (BdG) calculation on a two-orbital model, our results qualitatively agree with the experimental measurements.   

From Kondo behavior to high temperature superconductivity in Sr(Ni$_{1-x}$Fe$_x$)$_2$As$_2$

SrFe$_2$As$_2$ has an antiferromagnetic groundstate at ambient pressure that can be suppressed by chemical doping or pressure to produce unconventional superconductivity. SrNi$_2$As$_2$ is a non-magnetic conventional superconductor with T$_c$ of 0.6 K. It has been shown that in Sr(Ni$_{1-x}$Fe$_x$)$_2$As$_2$ there is a dome of superconductivity between $x=0.95$ and $x=0.9$. However, little is known about this doping series for small $x$ values. We will present the study of the thermodynamic and transport properties of the doping series of Sr(Ni$_{(1-x)}$Fe$_x$)$_2$As$_2$ for $x\leq 0.6$. In the dilute Fe limit ($x \leq 0.01$) we find strong evidence for single-ion Kondo behaviour. As the concentration of Fe is increased, Fe-Fe interaction effects become significant and the Kondo scale increases. For $0.2\leq x \leq 0.6$ magnetic susceptibility measurements show the presence of a spin glass transition. The presence of Kondo behaviour in Sr(Ni$_{(1-x)}$Fe$_x$)$_2$As$_2$ indicates the formation of local moments interacting with conduction electrons. Therefore, we will address the relevance of this result to the discussion of the itineracy of the magnetism in SrFe$_2$As$_2$, as well as the observed enhancement of the effective mass seen in many pnictide compounds.   

Weak-coupling superconductivity in a strongly correlated iron pnictide

Iron-based superconductors have been found to exhibit an intimate interplay of orbital, spin, and lattice degrees of freedom, dramatically affecting their low-energy electronic properties, including superconductivity. Albeit the precise pairing mechanism remains unidentified, several candidate interactions have been suggested to mediate the superconducting pairing, both in the orbital and in the spin channel. Here, we employ optical spectroscopy (OS), angle-resolved photoemission spectroscopy, ab initio band-structure, and Eliashberg calculations to show that nearly optimally doped NaFe$_{0.978}$Co$_{0.022}$As exhibits some of the strongest orbitally selective electronic correlations in the family of iron pnictides. Unexpectedly, we find that the mass enhancement of itinerant charge carriers in the strongly correlated band is dramatically reduced near the $\Gamma$ point and attribute this effect to orbital mixing induced by pronounced spin-orbit coupling. Embracing the true band structure allows us to describe all low-energy electronic properties obtained in our experiments with remarkable consistency and demonstrate that superconductivity in this material is rather weak and mediated by spin fluctuations.   

In situ characterization of pulsed-laser-deposition grown Co doped BaFe$_{\mathrm{2}}$As$_{\mathrm{2}}$ on SrTiO$_{\mathrm{3}}$ (001)

We report epitaxial growth of Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ (BFCA) thin films on SrTiO$_{\mathrm{3}}$ (001) substrates using pulsed laser deposition (PLD) technique under ultrahigh vacuum. The growth was performed using a pellet with the optimal Co concentration x$=$0.08. The temperature dependent conductivity of BFCA films was compared with those in the pellet form. The crystallinity was monitored with reflection high-energy electron diffraction during the growth and low energy electron diffraction (LEED) patterns. Optimal growth condition was obtained at the substrate temperature of 700$\pm $20${^\circ}$. The grown sample was immediately transferred to measure the topography and spectroscopy using a scanning tunneling microscope. LEED/STM result reveals modulation of $\sqrt 2 \times \sqrt 2 $ surface reconstruction on the top plane and STM result shows the same structure. The average sizes of terraces were $\approx $10mn with a homogeneous electronic structure. The geometric and electronic structure of BFCA films will be reported.