Charge compensation and optimal stoichiometry in superconducting (Ca${}_{x}$La${}_{1\ensuremath{-}x}$)(Ba${}_{1.75\ensuremath{-}x}$La${}_{0.25+x}$)Cu${}_{3}$O${}_{y}$

Charge compensation and optimal stoichiometry in superconducting (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$

Dale R. Harshman and Anthony T. Fiory

Phys. Rev. B 86, 144533 – Published 31 October 2012

Abstract

The superconductive and magnetic properties of charge-compensated (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$ (normally denoted as CLBLCO) are considered through quantitative examination of data for electrical resistivity, magnetic susceptibility, transition width, muon-spin rotation, x-ray absorption, and crystal structure. A derivative of LaBa $_{2}$ Cu $_{3}$ O $_{y}$ , cation doping of this unique tetragonal cuprate is constrained by compensating La substitution for Ba with Ca substitution for La, where for 0 ≤ $x$ ≤ 0.5 local maxima in $T_{C}$ occur for $y$ near 7.15. It is shown that optimum superconductivity occurs for 0.4 ≤ $x$ ≤ 0.5, that the superconductivity and magnetism observed are nonsymbiotic phenomena, and that charge-compensated doping leaves the carrier density in the cuprate planes nearly invariant with $x$ , implying that only a small fraction of superconducting condensate resides therein. Applying a model of electronic interactions between physically separated charges in adjacent layers, the mean in-plane spacing between interacting charges, $ℓ = 7.1206$ Å, and the distance between interacting layers, ζ = 2.1297 Å, are determined for $x$ = 0.45. The theoretical optimal $T_{C 0} \propto ℓ^{- 1} ζ^{- 1}$ of 82.3 K is in excellent agreement with experiment (≈80.5 K), bringing the number of compounds for which $T_{C}$ $_{0}$ is accurately predicted to 37 from six different superconductor families (overall accuracy of $\pm$ 1.35 K).

Received 5 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.144533

Authors & Affiliations

Dale R. Harshman^1,2,* and Anthony T. Fiory³

¹Physikon Research Corporation, Lynden, Washington 98264, USA
²Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
³Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA

^*drh@physikon.net

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Vol. 86, Iss. 14 — 1 October 2012

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Figure 1
Transition temperatures $T_{C}$ for (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$ , maximized by oxygen content $y$ , extracted from electrical resistivity (filled circles after Ref. 1, open circles after Ref. 4) and magnetic susceptibility (filled triangles after Ref. 1, open triangles after Ref. 2) as a function of $x$ . Star symbol denotes theoretical $T_{C}$ $_{0}$ averaged over $x$ = 0.4 $-$ 0.5. Inset represents $d T_{C}$ / $d P$ vs $T_{C}$ after Ref. 2; curve denotes trend.Reuse & Permissions
Figure 2
Resistivity measurements ρ( $T_{C}$ $^{+}$ ) and ρ(0), left scale, and the percentage transition widths $Δ T_{C}$ / $T_{C}$ , right scale, plotted as functions of $x$ for (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$ , with $y$ set to maximize $T_{C}$ (after Ref. 1). Inset shows $ℏ τ^{- 1} (0) / k_{B} T_{C}$ plotted against doping $x$ ; horizontal dashed line denotes unity.Reuse & Permissions
Figure 3
Transition temperature measured by $μ^{+}$ SR plotted against the $μ^{+}$ SR Gaussian relaxation parameter divided by the muon gyromagnetic ratio, $σ_{μ}$ / $γ_{μ}$ , for polycrystalline samples of (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$ with depleted oxygen at $x$ = 0.4 (filled circles), excess oxygen at $x$ = 0.4 (filled triangles), and optimum oxygen at $x$ = 0.1 and $x$ = 0.4 (filled squares, distinguished by arrows) after Ref. 6. Similarly obtained $μ^{+}$ SR data for ceramic samples of YBa $_{2}$ Cu $_{3}$ O $_{7 - δ}$ for various δ are presented for comparison; A (open diamonds) after Ref. 23 and B (open circles) after Ref. 24. Dashed line is reproduced from Ref. 26.Reuse & Permissions
Figure 4
Experimental $T_{C}$ $_{0}$ vs ${(ℓ ζ)}^{- 1}$ , where $ℓ$ is intralayer mean spacing of interacting charges and ζ is interlayer interaction distance, for (Ca $_{0.45}$ La $_{0.55}$ )(Ba $_{1.30}$ La $_{0.70}$ )Cu $_{3}$ O $_{y}$ ( $x$ = 0.45, star symbol), compared to other cuprates (open circles), Fe-based pnictides and chalcogenides (open triangles), a ruthenate (filled circle), and an organic (filled triangle). The solid line through the data points represents Eq. (1). Inset: transition temperatures $T_{C}$ $^{χ}$ of (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$ (filled symbols) and pair-breaking theory [Eq. (4), open symbols] as a function of doping $x$ .Reuse & Permissions
Figure 5
Variation of oxygen parameters $y$ with transition temperatures for LaBa $_{2}$ Cu $_{3}$ O $_{y}$ and YBa $_{2}$ Cu $_{3}$ O $_{y}$ (filled symbols, $T_{C}$ $_{0}$ at optimum $y$ ) and for (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$ from resistive onset $T_{C}$ at $x$ = 0.1, 0.2, 0.3, and 0.4 after Ref. 4, open circles, and experimental optimum $T_{C}$ $_{0}$ at $x$ = 0.45 (see Sec. 3b), filled circle. Dashed line denotes linear fit to the optimum compounds.Reuse & Permissions

Physical Review B

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Charge compensation and optimal stoichiometry in superconducting (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$

Dale R. Harshman and Anthony T. Fiory

Phys. Rev. B 86, 144533 – Published 31 October 2012

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Physical Review B

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Charge compensation and optimal stoichiometry in superconducting (CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy

Dale R. Harshman and Anthony T. Fiory

Phys. Rev. B 86, 144533 – Published 31 October 2012

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Charge compensation and optimal stoichiometry in superconducting (Ca $_{x}$ La $_{1 - x}$ )(Ba $_{1.75 - x}$ La $_{0.25 + x}$ )Cu $_{3}$ O $_{y}$