Pseudogap in BaPb_xBi_1‒xO₃ (x = 0.7, 0.75 and 1.0)

The powder samples of all compositions were prepared via the solid state route from BaCO₃, Bi₂O₃ and Pb₃O₄. The raw materials were first preheated at 450 $^\circ \mathrm{C}$ for 2 h to remove any traces of moisture absorbed by the raw materials. For the preparation of BPBO70 and BPO samples, proper stoichiometric ratios of the raw materials were ground thoroughly in an agate mortar for 6–10 h. This finely ground powder was then calcined in a box furnace at 900 $^\circ \mathrm{C}$ for 48 h. The heating rate was maintained at 5 $^\circ \mathrm{C}$ min⁻¹ and the samples were allowed to cool down to room temperature naturally inside the box furnace. The calcined powders were then sintered in the box furnace at 900 $^\circ \mathrm{C}$ for around 48–96 h, with intermediate grinding every 24 h. In the case of BPBO75 sample, a similar procedure was adopted, the details of which are published elsewhere [22]. After each grinding, the powders were then pressed into pellets of 10 mm diameter under a hydrostatic pressure of 5 tons. It was found that covering the pellets with a thin layer of powder of the sample ensured a good stoichiometric compound, and prevented the escape of Bi or Pb from the surface of the pellet. It is to be noted that despite not sintering the sample in oxygen atmosphere, we were able to obtain a superconducting transition in the BPBO75 compound. The final sintering was at 950 $^\circ \mathrm{C}$ for 24 h. The BPBO70 sample was allowed to cool down to room temperature normally, where as, the BPO sample was cooled to room temperature over a period of 24 h. We observe a difference in both physical and structural properties due to the differences in the sample preparation routes.

The temperature dependent XRD (T-XRD) measurements were performed using Rigaku's Smart Lab x-ray diffractometer powered by a 9 kW rotating anode x-ray generator. The T-XRD patterns were collected using Cu K$_\alpha$ radiations and were collected in the 2θ range of 19^∘–87^∘ at a scanning speed of 1^∘ per minute with a step size of 0.02^∘. The Magnetic Properties Measurement System from Quantum Design, Inc. was used in the measurement of temperature dependent DC magnetisation measurements. The measurement was performed at an applied magnetic field of 0.5 T, in the temperature range of 300 K to 2 K. Electrical resistivity measurements were performed on the sample using Physical Properties Measurement System setup from Quantum Design, Inc.

The photoemission spectra were collected on Scienta R4000 hemispherical analyser using a monochromatic Al K$_\alpha$ (1486.6 eV) x-ray, He$_\text{II}$ (40.8 eV) and He$_\text{I}$ (21. eV) sources. The binding energy scale was calibrated by measuring the Fermi level of Ag pellet, cleaned in-situ by scraping, using monochromatic Al K$_\alpha$ and He$_\text{I}$. In-situ cleaning of the surface of a polycrystalline is commonly done using (a) scraping, (b) ion-sputtering and (c) fracturing. However, the work by Nagoshi et al [17, 23–25] show that scraping and ion-sputtering can lead to significant modifications of the surface states and that the best way of surface cleaning is by fracturing the sample in ultra-high vacuum. Keeping this in mind, a clean sample surface was obtained by fracturing the mounted samples in UHV. All the spectra were collected within 60 min from the time of fracturing and it was repeated for the next set of measurements to ensure a clean surface. The base pressure during the measurement was $2 \times 10^{-11}$ mbar.

The top row of figure 1 shows the field emission scanning electron (FE-SEM) micrographs of the BPBO70, BPBO75 and BPO pellets, respectively. The average grain sizes of the three compounds are listed in table 1. The BPBO70 and BPBO75 compounds which are expected to show similar physical and chemical properties, show a deviation in the grain size—the BPBO75 compound which was ground for a longer time has a much smaller grain size. Conversely, the BPBO70 sample has a much larger grain size. The BPO compound which was cooled slower than the others, shows the largest grain size.

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Table 1. Grain sizes of the compound under study, calculated from the SEM micrographs.

Compound	$\quad x = 0.7\quad$	$\quad x = 0.75\quad$	$\quad x = 1.0\quad$
Grain size (µm)	29.34	8.04	39.56

At RT, the parent compound BaBiO₃ stabilises in the monoclinic structure in the I2/m space group. In this structure there is both breathing and tilting mode distortions. This breathing mode distortion is driven by the bond disproportionation of the Bi–O bond:

$$\begin{equation} 2\text{Bi}^{3+}\underline{L} \to \text{Bi}^{3+}\underline{L}^2+ \text{Bi}^{3+}. \end{equation} \tag{ 1 }$$

As we begin to introduce Pb into the compound, at Bi site, there is random occupation of Pb⁴⁺ ions in the Bi–O₆ octahedra. Since the size of the Pb⁴⁺ is smaller than the Bi³⁺ ions, the average size of the Bi³⁺–O₆ octahedra are expected to reduce. This will reduce the size difference between the Bi³⁺–O₆ and the Bi$^{3+}\underline{L}^2$–O₆ octahedra, thus reducing the breathing mode distortion. Furthermore, upon Pb doping of the Bi-sites in BBO, the average ionic radii of the B-site cations reduces, resulting in the improvement of the Goldschmidt tolerance factor (equation (2)),

$$\begin{equation} \tau = \frac{r_A+R_O}{\sqrt{2}\left(r_B+r_O\right)} \end{equation} \tag{ 2 }$$

leading to the stabilisation of the compounds in the higher symmetry orthorhombic and/or tetragonal phases, above x = 0.2. As a result of this structural transformation, the number of peaks in the Pb-doped compound reduces. This is especially visible in the higher 2θ ranges, as seen from the insets (b1) and (b2) of figure 1(b).

In figures 1(a)–(c), we show the typical Rietveld fitting of the XRD patterns of BPBO collected at 10 K. The BPBO70 compound was refined using orthorhombic structure with space group Ibmm. We were able to index all the peaks with a single Ibmm phase, indicating that the compound is single phase. On the other hand, a two phase refinement was carried out for the BPBO75 compound using I4/mcm and Ibmm phases, whose crystal structure properties have been reported in our previous work [22]. The BPO compound stabilises in Ibmm space group of the orthorhombic crystal structure. The room temperature crystal structure and the lattice parameters of BPBO75 and BPO are in good agreement with the values reported in literature [6, 21]. Panels (d)–(f) of figure 1 show the (004) and (220) peaks in the three compounds.

It is worth noting that various studies [2, 6, 7] have reported that the BPBO70 compound is diphasic. Chemically, the two compounds BPBO70 and BPBO75, are very similar, and are hence expected to show similar structure. However, in the present study, we observe that the BPBO70 compound does not show phase separation (detectable by conventional XRD), where as the BPBO75 is diphasic. The difference in the two compounds arises due to the change in the sample preparation conditions.

In the orthorhombic crystal structure, unlike the monoclinic phase, there is only one crystallographic position for the B-site atom (Bi/Pb), which effectively quenches the breathing mode distortions. This is also very clearly visible in the Raman spectra of BPBO, where the 569 cm⁻¹ peak which is associated with the breathing mode of BaBiO₃, is strongly suppressed above a Pb concentration of 20% [29].

BaBiO₃ exhibits an anisotropy in the Bi-O bonds along the apical and the basal planes. The Bi–O₁ (apical) bonds are slightly smaller than the Bi–O₂ (basal) bonds in the larger octahedra and the trend reverses in the smaller octahedra. As the Pb concentration increases, we see the anisotropy increase as well, with the orthorhombic phase of BPBO75 having the largest anisotropy between the apical and the basal bond lengths ($\Delta \approx 0.02$). This anisotropy nearly vanishes in case of BPO, which has nearly identical apical and basal bonds lengths ($\Delta \approx 0.003$). This reduction in the Bi–O bond length anisotropy is visible in the reduced orthorhombicity of the end compound (as discussed on the forth-coming section).

The top panel of figure 2 shows the magnetic moment of the BaPb_0.7Bi_0.3O₃ (BPBO70) and BaPb_0.75Bi_0.25O₃ (BPBO75) as a function of temperature which is consistent with the previous reports [6]. Both the compounds are diamagnetic across the whole temperature range; these samples show sharp drop at ∼10 K and ∼11 K, respectively, indicative of the superconducting transition. In the right panel of figure 2, we have shown the resistivity versus temperature data for the BPBO70 compound. It is evident from the graph that it shows semiconductor-like behaviour. The BPBO75 compound, on the other hand, shows a sharp transition at ∼11 K, indicating a superconducting transition, the details of which are reported elsewhere [22].

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BPBO70 is reported [6] to be di-phasic with the coexistence of both orthorhombic (Ibmm) and tetragonal (I4/mcm) phases at all temperatures below 150 $^\circ \mathrm{C}$. The Rietveld refinements of our XRD data revealed that the compound has crystallised in a single phase—orthorhombic Ibmm space group. This however is not very uncommon, as there have been reports of finding monophasic BPBO70 [30–34]. However, unlike the previous reports, we observe a semiconductor-like behaviour of the dc resistivity, even though, a superconducting-like transition was observed in the dc susceptibility measurements at around 10 K. Revisiting the SEM micrographs shown in figure 1 gives us a clue regarding the absence of superconducting transition in the resistivity data. It is quite easily visible that the sample density of BPBO70 compound is lower compared to the BPBO75 sample. A similar observation has been made by Marx et al [6]. Also, it is worth noting that the size of the grains is much larger in case of BPBO70, as compared to BPBO75.

Usually, it is expected that with an increase in grain size, the number of grain boundaries would reduce leading to increased inter-grain connectivity. It is interesting to note that in the compounds under study, that shows superconductivity (BPBO75) has a lower grain size as compared to the non-superconducting phase, BPBO70. For practical applications of superconductors, it is required not only to have high transition temperature (T_C ) but also high critical current density J_C , i.e. the ability to carry large currents without resistance. With regard to the tuning of J_C , the microstructure details of the sample play an important role. These results also emphasise the need for investigation of the concentrations of oxygen and Bi/Pb ions at the grain boundaries.

To understand the structural link with the transport properties, we have carried out temperature dependent XRD on all three compounds. Various lattice parameters, bond lengths and angles were obtained from the Rietveld refinement of the collected XRD patterns. The behaviour of the lattice parameters are illustrated as a function of temperature in figure 3.

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The variations of the various lattice parameters can be divided into four regions for the BPBO70, BPBO75 compounds, based on the change in the slope. This change in slope is very evident in the variation of the lattice parameters, a, b and c, normalised with respect to their value at room temperature. In the temperature range 300 K–220 K, all three lattice parameters a, b and c of BPBO75, are found to reduce monotonically. As the temperature drops, for T < 220 K the lattice parameters a and b show a broad minimum and maximum around 125 K respectively; for T < 50 K, there occurs a cross-over in their behaviour. The c parameter is found to decrease until 25 K. Below 25 K, all three lattice parameters become constant. A similar trend is observed in case of BPBO70 compound as well, however, the variations are much smaller. The similarity between behaviour of the lattice parameters of the two compounds indicates that the variations of the lattice parameters of the orthorhombic phase of BPBO75 appear enhanced due to the presence of the tetragonal phase. In case of the end compound, the lattice parameter a shows a muted response to variations in temperature—a slight reduction is observed until 200 K, beyond which it increases monotonically until 10 K. On the other hand, b and c show a steady decrease until 25 K, beyond which we observe a slight increase.

Figures 4(a)–(c) shows the variation of the strain as a function of temperature in the three planes that bound the unit cell—ab, ac and bc planes. In case of BPBO75 compound, the orthorhombic strain becomes a maximum as the temperature nears the T_C in the ab plane, as noted previously [22]. On the other hand, in the ac and bc planes, the strain reduces with temperature, attaining a minimum near T_C . In case of the non-superconducting BPBO70 compound, the strain in the ab plane is nearly constant, and the strain in the bc and ac planes reduces monotonically with decreasing temperature and attains a minimum when approaching the expected superconducting transition temperature. In case of BPO compound, the orthorhombic strain steadily increases in the ab plane with decreasing temperature, attaining a maximum around 25 K, and reducing slightly below 25 K. The strain in the ac plane, on the other hand, reduces until ∼10 K; the strain in the bc plane remains almost unchanged with temperature. When we compare the BPBO70 and BPBO75 compounds, where the former is non-superconducting and the latter is superconducting, the orthorhombic strain is found to increase in the compound that is observed to be superconducting, suggesting the important role played by the lattice strain towards superconductivity. Despite the orthorhombic phase not exhibiting superconductivity, we observe a significant increase in the lattice strain as the temperature approaches the T_C . In addition, the particle size appears to play an important role in the stabilisation of structural phase separation in the case of BPBO75. This underscores the importance of sample preparation techniques as a tool to tune superconductivity in this compound.

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4.3.1. XPS and band structure calculations.

To understand the evolution of the electronic structure of the BPBO with increasing Pb content, we have performed electronic structure calculations. Figure 5 shows the total DOS and partial DOS for the three compositions. Both BPBO70, and BPBO75 lie in the region of metal-semiconductor transition. As a result of this, it is reasonable to expect both metallic and semiconducting regions in the sample. Thus, to account for this, we have performed TB mBJ calculations for these two compounds. Further more, the BPBO75 compound is diphasic, and to account for it, the calculations were performed on both the phases, and have been added in 70:30 ratio (tetragonal:orthorhombic), as was observed experimentally [22]. When the TB-mBJ calculations for BPBO70 and BPBO75 are compared, we observe an additional feature B₀ in the latter. This feature arises because of the increased orthorhombicity. The structural parameters of the orthorhombic phase of BPBO70 are closer to tetragonal crystal structure—the difference between a and b lattice parameters is very small, ($a - b = 0.0045$ Å). The structural parameters of the orthorhombic phase of BPBO75, on the other hand, have a distinct difference between the a and b lattice parameters, i.e. $a - b = 0.029$ Å. This structural distinction between the orthorhombic phases of the two compounds, namely BPBO70 and BPBO75, are reflected in their electronic structure as well.

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The end compound, on the other hand, has been reported [6, 9, 10, 18, 21] to be metallic. However, our LDA calculations show a finite gap at the Fermi level. The origin of the metallicity in this compound is an open question. One of the mechanisms suggested to be at work by Ikushima and Hayakawa [9] and Shannon and Bierstedt [10] is by means of oxygen vacancies. To ascertain whether oxygen deficiency plays any role in this compound, we performed electronic structure calculations using LDA, and an oxygen vacancy of 8.3% was introduced. We observe that introducing oxygen vacancy results in a finite DOS at Fermi level, as seen in panel C1 of figure 5, thus indicating to some extent that oxygen vacancies play a role in the metallic behaviour of this compound. The presence of oxygen vacancies can be confirmed using core level studies.

To understand the behaviour of the valence band spectra, XPS measurements were carried out on the compounds under study at 300 K; figure 6(a) shows the XPS valence band spectra of these compounds. The comparison of XPS and He$_\textrm{II}$ valence band spectra collected at 300 K is shown in figures 6(b)–(d). The inset in panel (a) of the figure shows finite DOS at E_F for all three compounds. In all the compounds, we observe six features in the spectra labelled as A, B₁, B₂, B₃, C and D (see figures 6(b)–(d)). To ascertain the presence of feature B₀ in BPBO75, the intensity ratio corresponding to the features around −2 eV to −1.35 eV in BPBO70 and BPBO75 was calculated. Our results show that in the case of BPBO70, it is around 1.9 and BPBO75, it is around 4.3. This confirms the presence of the feature B₀ in BPBO75. In table 2, various contributions that make up the features are listed.

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Table 2. Contributions to various features A, B₀, B₁, B₂, B₃ and C. The intensity of feature D is mainly due to surface oxygen states.

	Contribution
Feature	BPBO70	BPBO75	BPO
A	Bi 6s, Pb 6s	Bi 6s, Pb 6s	Pb 6s, O 2p;
	O 2p	O 2p	Pb 6p, 6d (weak)
B0	—	Bi/Pb 6d, 5f, O 2p;	—
		Bi/Pb 6p (weak)
B1	Bi/Pb 6p, 6d	Bi/Pb 6p, 6d, 5f	Pb 6d, 5f, O 2p;
	5f, O 2p	O 2p	Pb 6s, 6p (weak)
B2	Bi/Pb 6p, 6d, 5f	Bi/Pb 6p, 6d, 5f	Pb 6p, 6d, 5f
	O 2p; Bi 6s (weak)	O 2p; Bi 6s (weak)	O 2p; Pb 6s (weak)
B3	Bi/Pb 6p, 6d, O 2p;	Bi/Pb 6s, 6p, 6d	Pb 6s, 6p, 6d
	Bi/Pb 6s, 5f (weak)	5f (weak), O 2p	5f, O 2p
C	Bi/Pb 6p, O 2p;	Bi/Pb 6p, O 2p;	Pb 6p, O 2p;
	Bi/Pb 6d, 5f (weak)	Bi/Pb 6d, 5f (weak)	Pb 6d, 5f (weak)

Feature D represents the surface cleanliness; its intensity in XPS spectrum is lower compared to the He$_{II}$ spectrum due to the higher sensitivity of the He$_{II}$ radiation to the surface oxygen. We can clearly observe from the table, that despite the similarity in the electronic structure, the origin of the intensities in different regions is different, thus indicating the dependence on the crystal structure of the compound.

Figures 7(a)–(e) shows the XPS spectrum of various core levels of BPBO (BPBO70 (black), BPBO75 (red) and BPO (blue)) at RT.

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In the case of O 1s spectra, the most intense feature A corresponds to the contribution arising from the oxygen ions in the bulk. The feature $A^*$ around 529.5 eV is attributed to oxygen vacancies [35] and the feature $A^{**}$ is attributed to contribution of surface oxygen and is observed around 531 eV. The contribution of feature $A^*$ is significant in the case of the end compound as compared to the rest of the compounds suggesting a significant role played by oxygen vacancies. This behaviour is in line with our electronic structure calculations where introduction of oxygen vacancies gives rise to metallic behaviour in the end compound.

The Bi and Pb 4$f_{7/2}$ peaks exhibit twin features labelled as B and $B^*$. These features are attributed to poorly screened and well screened final states, respectively. The well screened feature arises when the Bi/Pb 4$f_{7/2}$ hole is screened by the transfer of electrons from the ligand and the poorly screened feature arises when no such transfer occurs. The intensity ratio of feature $B^*$ to B is the least in BPBO70, and is nearly thrice as large in case of the other two compounds. It is important to note that the separation between the features B to $B^*$ in binding energy and its relative intensity depends on the charge transfer energy and the hybridisation between the O 2p and Bi/Pb site 4$f_{7/2}$ hybridisation. The high intensity of the feature B as compared to $B^*$ in BPBO70 compound suggests weak hybridisation between the above two sites as compared to the rest of the compounds.

The width and the asymmetry of the Ba core levels of the end compound is maximum as compared to the rest of the compounds. The behaviour of the asymmetry suggests that the density of states at the Fermi level in the case of the end compound is expected to be more as compared to the rest of the compounds, as observed in the XPS valence band spectra, inset of figure 6(a). This aspect is also observed in behaviour of room temperature valence band spectra close to the Fermi level using high resolution UPS.

Apart from the behaviours of the relative intensities of the features, the shift in the binding energy of the core levels as a function of composition carries vital information about the properties of the systems. The shift in the binding energy can be written as $\Delta\epsilon = \Delta\mu + \Delta\,V_M + \Delta\,Q + \Delta\,E_R$; where µ, V_M , $\Delta\,Q$ and E_R correspond to the chemical potential shift, Madelung potential, chemical shift and extra atomic relaxation energy of the core hole state, respectively.

For the case of BPBO70, BPBO75 and the end compounds, the average Ba–O bond distance obtained from the Rietveld analysis is around 3.07 Å, 3.04 Å and 3.03 Å, respectively. From this behaviour, it is expected that the Ba core levels of the end compound to be shifted towards higher binding energy as compared to the rest of the compounds. But we observe opposite behaviour. Hence, the role of the terms other than $\Delta\,V_M$ in the above equation are expected to be at play. However, it is important to note that Ba–O bonds being ionic in nature, the contributions due to $\Delta\,Q$ and $\Delta\,E_R$ are insignificant. Hence, the shift of the Ba core levels towards lower binding energy suggests the role played by the shift in the chemical potential towards the valence band as the concentration of Pb increases from 75% in BPBO75 to 100% in the end compound.

4.3.2. UPS valence band studies near E_F .