Universal temperature dependence of the London penetration depth in κ - ( ET ) 2 X superconductors
High-precision radio-frequency magnetic susceptibility measurements were performed on single crystals of fully deuterated $κ-(ET)_2Cu[N(CN)_2]\,Br$, hereafter designated as $κ-(ET)_2Cu[N(CN)_2]\,Br$. This material phase separates into superconducting and antiferromagnetic regions, the degree of which depends strongly upon the cooling rate. Here, we show that the screening fraction $η_{sc}$ varies logarithmically with the cooling rate over nearly five decades. The average size of superconducting regions is estimated to vary from 5 to $40μm$, depending upon cooling rate, consistent with previous infrared microscopy measurements. In the region $T≲T_c/3$, the effective magnetic penetration depth exhibits power-law behavior $λ(T)-λ(0)~T^n$ 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 $κ-(ET)_2Cu[N(CN)_2]\,Br$ and $κ-(ET)_2Cu(NCS)_2$ [A. Carrington et al., Phys. Rev. Lett 83, 4172 (1999)]. The transition temperature fell linearly with $1-η_{sc}$. Measurements were also made on $κ-(ET)_2Cu[N(CN)_2]\,Cl$ of normal isotopic abundance in which a very small amount of superconducting phase $η_{sc}≈10^{-4}$ developed, presumably through the strain-induced sample mounting. This material showed a power-law exponent of $n=1.64$, independent of the cooling rate.