Upper and lower critical magnetic fields of superconducting ${\text{NdFeAsO}}_{1-x}{\text{F}}_x$ single crystals studied by Hall-probe magnetization and specific heat

The upper and lower critical fields have been deduced from specific heat and Hall-probe magnetization measurements in nonoptimally doped Nd(O,F)FeAs single crystals $\left(T_c\sim 32–35\text{K}\right)$. The anisotropy of the penetration depth $\left({\Gamma }_{\lambda }\right)$ is temperature independent and on the order of $4.0\pm 1.5$. Similarly specific-heat data lead to an anisotropy of the coherence length ${\Gamma }_{\xi }\sim 5.5\pm 1.5$ close to $T_c$. Our results suggest the presence of rather large thermal fluctuations and the existence of a vortex liquid phase over a broad temperature range ($\sim 5\text{K}$ large at 2 T).

Figure 1

(Color online) (a) Temperature dependence of the ac transmittivity and specific heat in a non-optimally doped $\text{Nd}\left(\text{F},\text{O}\right)\text{FeAs}$ platelet (sample 1) for the indicated field values $\left(H_a\parallel c\right)$. In the inset: Remanent field $\left(B_{\text{rem}}\right)$ as a function of the applied field ${\mu }_0{H}_a$ (see text for details) for the indicated temperatures and field orientation. The solid lines are ${\left(H_a-H_p\right)}^2$ fits to the data. (b) Temperature dependence of the specific heat in a non-optimally doped $\text{Nd}\left(\text{F},\text{O}\right)\text{FeAs}$ platelet (sample 1) for $H_a\parallel c$ (closed black symbols) and $H_a\parallel ab$ (open red symbols) for the indicated field values. The inset shows sample 1 mounted on the thermocouple cross, for which the width of the legs is $\approx 50\mu \text{m}$, as well as for sample 3 (bottom left corner).

Figure 2

(a) Temperature dependence of the upper critical field [maximum of the specific-heat anomaly; see Fig. 1a] for $H_a\parallel c$ (circles) and $H_a\parallel ab$ (squares). (b) Comparison between $H_{c2}$ (deduced from $C_p$, closed symbols) and the onset of the diamagnetic response $H_{\text{irr}}$ (open symbols) for $H_a\parallel c$ suggesting the existence of a broad vortex liquid phase.

Figure 3

Temperature dependence of the lower critical field $H_{c1}$ along the $c$ direction (solid squares for sample 3 and solid lozenges for sample 1, rescaled by a factor of 1.5) and $ab$ plane for sample 3 (solid circles). The solid lines are the standard behaviors expected from the BCS theory. The corresponding temperature dependence of the anisotropy $\left({\Gamma }_{\lambda }=1.3\times {\Gamma }_{H_{c1}}\right)$ is also reported (open squares). The error bars correspond to the uncertainties on the determination of $H_p$; the whole curve might be shifted $\pm 1.5$ due to the uncertainty of the demagnetization factor. In all cases, ${\Gamma }_{\lambda }$ remains flat in $T$. The ${\Gamma }_{\xi }$ values deduced from $C_p$ (present work: open circles; Ref. 10: open lozenge) and transport (Ref. 27; open triangles) measurements are also displayed.