Tensile Microstrain Fluctuations in the BaPbO Units in Superconducting BaPb_1−xBi_xO₃ by Scanning Dispersive Micro-XANES

Abstract

BaPb_1−xBi_xO₃ (BPBO) bismuthate, showing high T_C superconductivity for 0.05 < x < 0.35, is an archetypal system for studying the complex inhomogeneity of perovskite lattice favoring the emergence of quantum coherence, called the superstripes phase. Local lattice fluctuations, detected by EXAFS; nanoscale stripes, detected by electron microscopy; and two competing crystalline structures, detected by diffraction, are known to characterize the superconducting phase. At nanoscale [BaBiO₃] centered nanoscale units (BBO) coexist with BaPbO₃ centered (BPO) units in the BPBO perovskite; therefore, we expect a tensile microstrain in BPO units due the misfit strain between the two different lattices. Here, we report the measurement of the spatial micro-fluctuations of the local tensile microstrain ε in the BaPO units in superconducting Ba(Pb_1−xBi_x)O₃ crystals with x₁ = 0.19 an x₂ = 0.28. We show here the feasibility of applying the scanning dispersive micro-X-ray absorption near edge structure (SdμXANES) technique, using focused synchrotron radiation, to probe the microscale spatial fluctuations of the microstrain in BPO units. This unconventional real-space SdμXANES microscopy at the Pb L₃ edge has been collected in the dispersive mode. Our experimental method allows us to measure either the local Bi chemical concentration x and the local lattice microstrain of local BBO and BPO units. The 5 × 5 micron-size spots from the focused X-ray beam allowed us to obtain maps of 1600 points covering an area of 200 × 200 microns. The mapping shows a substantial difference between the spatial fluctuations of the microstrain ε and the chemical inhomogeneity x. Moreover, we show the different relations ε(x) in samples with lower (x₁ = 0.19) and higher (x₂ = 0.28) doping respect to the optimum doping (x = 0.25).

1. Introduction

The critical temperature of the superconducting transition and electronic structure at the Fermi level in quantum complex matter and high temperature superconductors is governed not only by doping, but also by the lattice strain in nickelates, iron-based superconductors, and heterostructures [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] controlling the complex landscape generated by nanoscale phase separation [24,25,26,27,28,29] near the superconductor–insulator transition [30], as it was first shown in cuprates and diborides [18,19,20,21,22,23]. In this work we apply scanning μ-X-ray absorption near edge structure (SµXANES) to unveil the spatial heterogeneity of local lattice fluctuations [31,32,33,34,35] in a selected nanocluster related to the strain at specific sites, namely, microstrain spatial fluctuations near the metal to insulator transition in BaPb_1−xBi_xO₃. [36,37,38,39].

The dimorphic crystal structure of BaPb_1−xBi_xO₃ superconducting compounds is a distorted perovskite (ABO₃) for the highest Bi concentrations and contains two Bi sites with different Bi-O bond lengths [40,41,42,43,44,45,46,47,48,49,50,51,52]. BaPb_1−xBi_xO₃ can be described as a composite heterostructure made of p-n junctions formed by a low charge carrier density (10²¹ cm⁻³) metallic BaPbO nanoscale units, and a charge density wave (CDW) of semiconducting BaBiO nanoscale units. With increasing Pb content, the insulating CDW phase disappears, giving rise to a metallic phase, where superconductivity appears at x > 0.05 and the metal insulator transition at x = 0.35. Recently, there has been increased interest in the artificial synthesis of thin film heterostructures providing the signature of 2D interface superconductivity in a landscape of nanoscale phase separation [53,54,55,56,57,58,59,60]. X-ray absorption near edge structure, called XANES spectroscopy, [61,62,63,64,65,66,67,68] provides a local and fast probe of the local lattice fluctuations probing nanoscale phase separation. It has been applied to investigate powder samples of BaPb_1−xBi_xO₃ [69,70,71] but its spatial inhomogeneities are unknown.

The BaPb_1−xBi_xO₃ structure [36,37,38,39], shown in Figure 1a, has a rich phase diagram due to the inter-relation between multiple perovskite structures as a function of temperature and doping [72,73,74,75]. In the region of 0.05 < x < 0.35, the diamagnetic signal increases and the material becomes superconducting. In this regime, its structure is polymorphic [36,37,38,39] with a fraction of its volume with orthorhombic Ibmm symmetry and the rest with tetragonal I4/mcm symmetry. The critical temperature T_C as a function of the bismuth content x for the samples under study is presented in Figure 1b. For x values over the superconducting range until about x = 0.77, only the orthorhombic Ibmm symmetry is observed. In the BaBiO₃ phase, the alternation of Bi³⁺ and Bi⁵⁺ leads to structural distortions involving both the so-called breathing distortions and the tilting of BiO₆ octahedra, which lowers the crystal symmetry from a cubic to a monoclinic space group.

High-resolution transmission electron microscopy (HRTEM) has been used to unveil the emergence of structural stripes at the nanoscale in single crystals of BaPb_1−xBi_xO₃ [39]. The stripe-like morphology found in this study has a deep significance; it might provide a natural clue to understanding the characteristic behavior observed at the superconductor–insulator transition close to optimal doping in BaPb_1−xBi_xO₃, motivating a theoretical investigation of the percolation effects near the quantum phase transition in any material with a striped morphology.

While it is known that a misfit strain generates a complex nanoscale phase separation in cuprates [19,20,21,22,23,24,25,26,27,28] and iron-based superconductors with a percolative network, the misfit strain in Ba(Pb_1−xBi_x)O₃ has not yet been reported. In this work, we have used SµXANES to investigate the spatial distribution of microstrain in three BaPb_1−xBi_xO₃ samples with x = 0, 0.19 and 0.28 (full red circles in Figure 1b) to obtain a deeper insight into the relationship between local lattice inhomogeneity and superconductivity in this system.

2. Results

2.1. Variation of the Local Structure of BaPbO₃ 0.5 nm Nano Cluster Units in BaPb_1−xBi_xO₃

In intrinsically inhomogeneous composites, in nanoscale units, the microstrain is generated by the lattice misfit strain originating from the coexistence of different units with different lattice parameters occurring during the cubic-to-tetragonal and tetragonal-to-orthorhombic transitions. This mechanism results in a multi-domain microstructure with many incoherent boundaries, and originates the local lattice microstrain ε.

It has been proposed that the mobility of the charge carriers, moving through octahedra, may be favored by the tetragonal symmetry while carriers’ localization takes place when the symmetry decreases to the orthorhombic and then to the monoclinic phase with an increasing bismuth content; still, the spatial inhomogeneity of charge and lattice remains unknown.

2.2. Scanning Micro XANES Microscopy: Microstrain Maps and Phase Separation

The SµXANES technique is a unique tool to investigate the local atomic lattice structure via multiple scattering resonances of the excited photoelectron probing the geometry of the local clusters surrounding selected atomic species. The local structure of the atomic cluster centered at the Pb-absorbing atom is shown in Figure 2a.

We have first calculated the XANES profiles at the Pb L₃ edge for the cluster with the Pb ion at the center and different microstrain values using the full multiple-scattering approach. Calculated Pb L₃ XANES are shown in Figure 2b, while the relative variation of the energy of the highest peak due to the multiple scattering resonance (MSR) as a function of the tensile or compressive microstrain is presented in Figure 2c.

The spatial distribution of the strain at different doping has been investigated by SµXANES using focused synchrotron radiation that allowed us to identify the spatial inhomogeneity at the micron scale related to incipient phase separation. Samples of superconducting BaPb_1−xBi_xO₃ single crystals with x = 0, 0.19 and 0.28 were scanned on a 200 × 200 µm² area with a 5 µm step in both directions. Data have been collected at the ESRF beamline ID24 (Grenoble, France), which is equipped with an energy dispersive X-ray spectrometer and a unique setup for real-space scanning with variable temperature [7].

In Figure 3, we show XANES spectra at the Pb L₃ edge, where the maximum absorption peak is due to the multiple scattering resonance (MSR) of the excited photoelectron, also called the Fano shape resonance in the continuum, at about 32 eV above the absorption threshold taken as zero energy. Alongside XANES spectra, we also show their first derivatives where we clearly recognize three peaks. The energy at 13027 eV has been chosen as the reference zero value for the energy scale while the energy of the multiple scattering resonance (E_MSR) has been defined as the difference between the zero of the derivatives, E₀, and the first derivative peak, P₁:

$$E_{MSR}=E_0-P_1$$

(1)

MSR energy, E_MSR, of the photoelectron confined in a nanoscale BPO cluster centered at the Pb-absorbing atom probes the variations of the average Pb–O bond length and its spatial variation. In this regard, E_MSR is a sensitive measure of the local lattice strain at Pb sites. It is fundamental to remember that slight variations of the average bond distance (R) can be attributed to the dependence of phase shifts in the framework of the multiple scattering model [39].

It is known that the energy variation of the main multiple-scattering resonance in the XANES spectra is connected with Pb–O average distance in the cluster, R, by

$$E_{MSR}\propto R^{-2}$$

(2)

where the XANES microstrain can be calculated as

$$\frac{∆R}{R}=-\frac{1}{2}\frac{{∆E}_{MSR}}{E_{MSR}}$$

(3)

where

$${∆E}_{MSR}=E_{MSR}-\overline{E_{MSR}}$$

(4)

In the undoped (x = 0) BaPbO₃ sample, the peak around its average value $\overline{E_{MSR}}$ is relatively narrow and has been taken as reference for measuring the microstrain variation.

Measurements of single crystals of BaPb_1−xBi_xO₃ with different Bi compositions around the superconducting maximum [37] (referring to the diagram 1a) show signatures of granular and inhomogeneous superconductivity possibly associated with a nanoscale structural phase separation. Due to different values of Bi valence and the variation of Pb concentration, BaPb_1−xBi_xO₃ is polymorphic where different structural phases coexist. It is interesting to analyze how these phases appear in the lattice.

From Pb L₃-edge XANES spectra, we obtained real space maps of the E_MSR for different doping of BaPb_1−xBi_xO₃; then, we have calculated the microstrain referring to Equation (3). Here, we report the micro XANES data results for x = 0.19 and x = 0.28 crystalline samples collected at low temperatures of 50 ± 10 K. The spatial fluctuations of the slight energy shift of the multiple scattering resonance energy in the superconducting Bi-doped samples are compared to the data for the reference undoped BaPbO₃ sample. The decreasing trend of the negative energy shift of the main multiple scattering resonance E_MSR is attributed to a lattice expansion [39] of the Pb-centered nanoscale puddles increasing with the negative XANES tensile strain.

Figure 4a shows the microstrain maps at different Pb contents. Between the insulating (x = 0) and metallic (x = 0.28) phases, the sample with x = 0.19 presents a large inhomogeneity with a phase separation where microstrain assumes values of insulating and metallic phases in different spatial regions. This disorder behavior is measured by the probability distribution function (PDF), shown in Figure 4b, from which information about lattice strains can be obtained. Indeed, comparing the E_MSR value of each point with the average value of the undoped sample, we obtained the local lattice strain for our differently doped compounds.

The extended X-ray absorption spectra of the BaPb_1−xBi_xO₃ at either the Pb L₃ jump and the Bi L₃ edge jump in the stoichiometric compounds at x = 0 and x = 1 allow the direct measure of the bismuth content x at each spot where the microstrain is measured (see Figure 5a).

In this way, we have obtained the maps of x content in the two samples with nominal content x = 0.19 and x = 0.28 shown Figure 5b,c, respectively.

In Figure 5d we visualize the microstrain in the BaPb_1−xBi_xO₃-doped samples vs. the Bi content x, where the x = 0.19 and x = 0.28 samples are represented with blue squares and red circles, respectively. The full circles represent the mean values of microstrain and x content in the x = 0.19 x = 0.28 samples, respectively.

The lattice tensile strain as a function of Bi content x measured by crystallography lattice parameters in BaPb_1−xBi_xO₃ going from x = 0 to x = 1 follows Vegard’s law represented by the dashed line ε = −2x [36] and the spatial average local microstrain in the Pb-centered clusters in the two BaPb_1−xBi_xO₃ samples is indicated by blue and yellow dots in Figure 5. In both samples, the average local tensile strain in Pb-centered clusters is larger than that measured in the average lattice crystal indicated by Vegard’s law.

3. Discussion

We reported local measurements of the lattice strain of BaPb_1−xBi_xO₃ for different values of doping. In complex perovskite materials, different structural phases are in competition, and their stability is tuned by the microstrain. These phases cause a local change in the atomic strain that can be observed in the MSR of XANES spectra. The BaPb_1−xBi_xO₃ superconductor shows a high-T_C superconductivity for 0.05 < x < 0.35, becoming an archetypal system with competitions of different nanoscale units with local lattice symmetry [36,37,38,39,40] which favor the emergence of macroscopic quantum coherence in complex nanoscale phase separation [36,37,38,39,40]. This compound could be described as the complex solid solution of two nanoscale clusters, resulting from metallic [BaPbO₃]_(1−x) and insulating [BaBiO₃]_(x) perovskite units, which are expected to be strained due to the misfit between their different lattices. In the underdoped superconducting phase at x = 0.19 the Pb-centered nanocluster units probed by Pb L₃ XANES spectroscopy shown in Figure 2a called BaPO unit shows large spatial tensile microstrain fluctuations in the range −0.1%<ε< −2%, while the Vegard’s law expected value is −0.38%.

In the overdoped regime at x = 0.28 the tensile microstrain fluctuations are strongly reduced and centered ε= −1% which is larger than the expected value of −0.5% predicted by the Vegard’s law as indicated in the figure. Therefore in the overdoped regime the deviation of the local microstrain ε in the probed [BPO] nanoscale cluster units from the average lattice strain measured by X-ray diffraction [36] indicates a nanoscale phase separation between first metallic units and insulating units, triggering high-temperature superconductivity, which is in agreement with high resolution electron diffraction [40].

4. Materials and Methods

Single crystals of BaPb_1−xBi_xO₃ with Bi compositions x = 0, 0.19 and 0.28 were grown by slowly cooling a solution of BaCO₃, PbO, and Bi₂O₃. The single crystals were polished in the Geballe Laboratory for Advanced Materials in Stanford to reach the optimal homogeneous hundred microns thickness for X-ray transmission experiments at the Pb L₃ edge energy in the high X-ray energy range 13 KeV.

The in-depth comprehension of local structural phases requires tools not accessible in ordinary laboratories due to the need to probe micrometric areas without moving the sample, as well as short acquisition times. Given these non-trivial premises, the micro-XANES technique makes possible the detection of nanoscopic local lattice fluctuations in in-homogeneous systems. The energy dispersive technique, necessary for studying BaPb_1−xBi_xO₃ [76], has become available thanks to the dedicated synchrotron radiation beamline ID24 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The ID24, consists of a set of mirrors in a Kirkpatrick–Baez geometry (vertical and horizontal focusing mirrors) that focus the white beam on a polychromator crystal, which splits the beam. A second vertical mirror focuses the beam on the sample. A photon flux of ~10¹⁴ ph/s goes through the sample; the transmitted photons are detected by a Ge strip CCD equipped with an acquisition electronics with a readout time of 2.8 µs and minimum integration time of ∼80 ns. The particular setup of the beamline, and the lack of moving parts provide a small and stable focal spot (5 × 5 μm² at Pb and Bi L₃-edges) suitable for the scanning micro-XAS. [7]. The reported XANES data were collected at low temperatures of 50 ± 10 K.

In order to establish the actual limitation of the measure of the local cluster microstrain by scanning micro XANES in the dispersive mode, we present in Figure 6, the typical XANES spectra collected in 12 spots of the 1681 XANES spots collected in the area of 41 × 41 spots of the pure BaPbO₃ sample shown in Figure 4. The energy of the multiple scattering resonance (E_MSR) is given by the difference between the Fermi level at the maximum of first derivative peak and the zero of the XANES spectra derivative around 32.8 eV. The energy fluctuations of the multiple scattering resonance (E_MSR) due to the noise level correspond to a noise fluctuation of the microstrain of the order of 0.12% in the undoped sample. Therefore, we can clearly measure microstrain spatial fluctuations larger than 0.12% in the doped superconducting samples.

Theoretical simulations of XANES spectra were performed in the framework of full multiple scattering theory for a finite atomic cluster centered at the absorbing Pb atom using the muffin-tin approximation [61,62,63,64] and self-consistent field using the implemented FEFF9.6 code, as described in reference [68]. The Hedin–Lundqvist exchange potential was adopted and the atomic potential was constructed in self-consistent field calculations. The full multiple scattering (MS) calculations were calculated increasing the atomic cluster radius centered at the Pb-absorbing atom. The calculated XANES spectra reproduced the experimental data for clusters with a radius larger than 5 $Å$, and remained invariant for larger clusters. This result shows that the experimental XANES spectrum probes only a BPO nanoscale cluster of 5 $Å$ radius via multiple scattering. The instrumental and core–hole-induced broadening were consistently used for all simulated spectra to be comparable with experimental spectra.

5. Conclusions

We have measured the spatial distribution of microstrain of Pb-centered clusters with two different Bi contents (x) in BaPb_1−xBi_xO₃ using scanning dispersive μ-XANES (Sdµ-XANES). Our measurements reveal a relative variation of the Pb-O bond, as determined from the energy shift of the multiple scattering resonance E_MSR. We have found that the largest inhomogeneity occurs in the under-doped regime with lower Bi dopant concentrations, with x = 0.19, close to the superconductor-to-metal transition (SMT) for the weak tensile microstrain. At variance, the sample with the higher Bi content x = 0.28, near the superconductor-to-insulator (SIT) transition shows a larger tensile strain in the Pb-centered nanoscale clusters probed by Pb L₃-XANES, called [BaPbO] nanoscale units Finally, we have shown that the amplitude of the spatial fluctuations of the tensile microstrain in the [BaPbO] nanoscale units is about −0.5% and −0.8% in the x = 0.28 and x = 0.19 samples, respectively. In these two samples, the average tensile microstrain was quite a bit larger than predicted by Vegard’s law, i.e., −0.38% and −0.56%. We assign these results to nanoscale phase separation with the first nanoscale units of metallic strained ε < 0.2 and insulating ε > 0.72% units which favors interface superconductivity triggered by the nanoscale phase separation. While the two samples investigated in this work have similar critical temperatures, the x = 0.19 sample is made of larger metallic units and a smaller insulating phase and the x = 0.28 sample is made of larger insulator units and smaller metallic units. While in the literature many authors usually assume that in these systems the lead local structure is not affected by Bi content, we have shown that the local structure near the Pb site is affected by Bi doping. Finally, this work shows the feasibility of spatial mapping intrinsic inhomogeneity by scanning micro XANES in the dispersive mode, which can be implemented by advances on focusing the X-ray beam down to the nanoscale to provide further unique additional information on the micro fluctuations of local complexity at the atomic scale in quantum materials [77,78].