Universal temperature dependence of the London penetration depth in κ−(ET)2X superconductors

Abstract

High-precision radio-frequency magnetic susceptibility measurements were performed on single crystals of fully deuterated $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_{2}]\mathrm{Br}$, hereafter designated as $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{D}8\phantom{\rule{0.16em}{0ex}}\mathrm{ET})}_{2}\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_{2}]\mathrm{Br}$. This material phase separates into superconducting and antiferromagnetic regions, the degree of which depends strongly upon the cooling rate. We show that the screening fraction ${\ensuremath{\eta}}_{\text{sc}}$ varies logarithmically with the cooling rate over nearly five decades. The average size of superconducting regions is estimated to vary from 5 to $40\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$, depending upon cooling rate, consistent with previous infrared microscopy measurements. In the region $T\ensuremath{\lesssim}{T}_{c}/3$, the effective magnetic penetration depth exhibits power-law behavior $\ensuremath{\lambda}(T)\ensuremath{-}\ensuremath{\lambda}(0)\ensuremath{\sim}{T}^{n}$ with $n=1.6$, independent of the cooling rate. Changes in cooling rate and the consequent phase separation evidently do not introduce the kind of disorder that would alter the exponent $n$ in a $d$-wave superconductor. The exponent remains close to $n=$ 1.5, reported in single crystals of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_{2}]\mathrm{Br}$ and $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$ [A. Carrington et al., Phys. Rev. Lett 83, 4172 (1999)]. The transition temperature fell linearly with $1\ensuremath{-}{\ensuremath{\eta}}_{\text{sc}}$. Measurements were also made on $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_{2}]\mathrm{Cl}$ of normal isotopic abundance in which a very small amount of superconducting phase ${\ensuremath{\eta}}_{\text{sc}}\ensuremath{\approx}{10}^{\ensuremath{-}4}$ developed, presumably through the strain-induced sample mounting. This material showed a power-law exponent of $n=1.64$, independent of the cooling rate.