Muon spin relaxation study of superconductingBi2Sr2−xLaxCuO6+δ

Abstract

We have performed transverse-field (TF) and zero-field (ZF) $\ensuremath{\mu}\mathrm{SR}$ measurements of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}\mathrm{Cu}{\mathrm{O}}_{6+\ensuremath{\delta}}$ (Bi2201) systems with $x=0.2$, 0.4, 0.6, and 1.0, using ceramic specimens with modest $c$-axis alignment and single-crystal specimens. The absence of static magnetic order has been confirmed in underdoped $(x=0.6)$ and optimally doped $(x=0.4)$ systems at $T=2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, while only a very weak signature towards static magnetism has been found at $T=2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the $x=1.0$ system, which is a lightly hole-doped nonsuperconducting insulator. In the superconducting ($x=0.6$, 0.4, and 0.2) systems, the relaxation rate $\ensuremath{\sigma}$ in TF-$\ensuremath{\mu}\mathrm{SR}$, proportional to ${n}_{s}∕{m}^{*}$ (superconducting carrier density and effective mass), followed a general trend found in other cuprate systems in a plot of ${T}_{c}$ vs ${n}_{s}∕{m}^{*}(T\ensuremath{\rightarrow}0)$. Assuming the in-plane effective mass ${m}^{*}$ for Bi2201 to be comparable to three to four times the bare electron mass ${m}_{e}$ as found in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ (LSCO) and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) systems, we obtain ${n}_{s}\ensuremath{\sim}0.15--0.2$ per Cu for the $x=0.4$ Bi2201 system. This carrier density is much smaller than the Hall number ${n}_{\mathit{\text{Hall}}}\ensuremath{\sim}10$ per Cu obtained at $Tl1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in high magnetic fields $(40--60\phantom{\rule{0.3em}{0ex}}\mathrm{T})$ along the $c$ axis applied to suppress superconductivity. The present results of the superfluid density $({n}_{s}∕{m}^{*})$ in Bi2201 are compared with those from other cuprate systems, including YBCO systems with very much reduced ${T}_{c}l20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ studied by microwave, ${H}_{c1}$, and inductance methods. Additional muon-spin-relaxation $(\ensuremath{\mu}\mathrm{SR})$ measurements have been performed on a single-crystal specimen of Bi2201 $(x=0.4)$ in a high transverse magnetic field of $5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ parallel to the $c$ axis, in order to search for the field-induced muon spin relaxation recently found in LSCO and some other high-temperature superconducting cuprate (HTSC) systems well above ${T}_{c}$. The nearly temperature-independent and very small relaxation rate observed in Bi2201 above ${T}_{c}$ rules out a hypothesis that the field-induced relaxation is directly proportional to the magnitude of the Nernst coefficient, which is a measure of the strength of dynamic superconductivity. We also describe a procedure for angular averaging of $\ensuremath{\sigma}$ in $\ensuremath{\mu}\mathrm{SR}$ measurements using ceramic specimens with modest alignment of $c$-axis orientations, together with the neutron-scattering results obtained for determining the orientation distribution of microcrystallites in the present ceramic specimens.