Scaling of the physical properties in Ba(Fe,Ni)2As2single crystals: Evidence for quantum fluctuations

Abstract

We report on local magnetization, tunnel diode oscillators, and specific-heat measurements in a series of Ba(Ni${}_{x}$Fe${}_{1\ensuremath{-}x}$)${}_{2}$As${}_{2}$ single crystals ($0.26\ensuremath{\le}x\ensuremath{\le}0.74$). We show that the London penetration depth $\ensuremath{\lambda}(T)=\ensuremath{\lambda}(0)+\ensuremath{\Delta}\ensuremath{\lambda}(T)$ scales as $\ensuremath{\lambda}(0)\ensuremath{\propto}1/{T}_{c}^{0.85\ifmmode\pm\else\textpm\fi{}0.2}$, $\ensuremath{\Delta}\ensuremath{\lambda}(T)\ensuremath{\propto}{T}^{2.3\ifmmode\pm\else\textpm\fi{}0.3}$ (for $T<{T}_{c}/3$), and $\ensuremath{\partial}\ensuremath{\Delta}\ensuremath{\lambda}/\ensuremath{\partial}{T}^{2}\ensuremath{\propto}1/{T}_{c}^{2.8\ifmmode\pm\else\textpm\fi{}0.3}$ in both underdoped and overdoped samples. Moreover, the slope of the upper critical field [${H}_{c2}^{\ensuremath{'}}=\ensuremath{-}{(d{H}_{c2}/dT)}_{|T\ensuremath{\rightarrow}{T}_{c}}$] decreases with ${T}_{c}$ in overdoped samples but increases with decreasing ${T}_{c}$ in underdoped samples. The remarkable variation of $\ensuremath{\lambda}(0)$ with ${T}_{c}$ and the nonexponential temperature dependence of $\ensuremath{\Delta}\ensuremath{\lambda}$ clearly indicates that pair-breaking effects are important in this system. We show that the observed scalings strongly suggest that those pair-breaking effects could be associated with quantum fluctuations near three-dimensional superconducting critical points.