Strongly dissimilar vortex-liquid regimes in single-crystalline NdFeAs(O,F) and $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$: A comparative study

The extent of the vortex-liquid state in underdoped single crystals of the oxypnictide superconductors NdFeAs(O,F) and $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ is investigated using specific heat $\left(C_p\right)$ and Hall-probe magnetization experiments. In both materials, the vortex liquid lies entirely in the regime where the three-dimensional lowest Landau-level (3D-LLL) approximation is valid and both systems present a very small shift in the specific heat anomaly with increasing field. The irreversibility line, defined as the onset of diamagnetic response, is very rapidly shifted toward lower temperatures in NdFeAs(O,F) but remains close to the $C_p$ anomaly in $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$. These measurements strongly suggest that a vortex-liquid phase occupies a large portion of the mixed-state phase diagram of NdFeAs(O,F) but not in $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$. This difference can be attributed to different Ginzburg numbers $Gi$, the latter being about 100 times larger in NdFeAs(O,F) than in $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$. The angular dependence of the upper critical field, derived from 3D-LLL scaling of the irreversibility lines, presents deviations from the standard 3D effective-mass model in both materials with an anisotropy being about three times smaller in $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ $\left(\gamma \sim 2.5\right)$ than in Nd(F,O)FeAs $\left(\gamma \sim 7.5\right)$.

Figure 1

(a) Polarized light image of the NdFeAs(O,F) sample used for the $C_p$ and transmittivity measurements and five differential magneto-optical images showing the onset of diamagnetic screening of a external field of 1 Oe by this sample. The first signs of screening are observed in the upper right-hand corner at $T=36.5\text{K}$, diamagnetic screening is complete for $T\le 33.0\text{K}$. This corresponds to a transition width $\Delta T_c=3.5\text{K}$. The ring-shaped outer area with higher $T_c$ leads to flux concentration in the inner region and the paramagnetic peak in Fig. 2. (b) Direct magneto-optical images of flux penetration at $T=9.3\text{K}$, for $H_a=206\text{Oe}$ at 500 Oe, and the trapped flux at 26 Oe, after the application of 500 Oe. The sample consists of two crystals joined by a grain boundary. At temperatures below 32 K, the flux distributions in both crystallites are in conformity with what is expected for the Bean critical state (Refs. 18, 19).

Figure 2

(a) Temperature dependence of the ac transmittivity and specific heat for the indicated field values $\left(H_a\parallel c\right)$ in a NdFeAs(O,F) crystallite emphasizing the large difference between the position of the irreversibility line (onset of diamagnetic response at 213 Hz: vertical lines) and the specific-heat jump. (b) Similar data for $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$, showing that the specific heat and the susceptibility data both present only a minor downward shift with applied field. The paramagnetic bump observed in both systems [although larger in $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ than in NdFeAs(O,F)] reflects the presence of $T_c$ inhomogeneities in the platelets [see Fig. 1 for magneto-optical images of the NdFeAs(O,F) sample]. However the reduced shift is observed on all probe positions, open symbols corresponding to the center of the sample, and closed symbols to the sample edge (with a slightly higher $T_c$ value). Inset: temperature dependence of the specific heat of a $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ crystal for $H_a\parallel c=3\text{T}$ (closed symbols) and $H_a\parallel ab=7\text{T}$ (open symbols).

Figure 3

(a) Position in the $\left(B,T\right)$ plane of the maximum of the $C_p$ anomaly. (b) Position in the $\left(B,T\right)$ plane of the irreversibility line $T_{\text{irr}}\left(B\right)$, measured as the onset of diamagnetic response, at the center of the sample. In both panels, the circles indicate $H_a\parallel c$ while squares correspond to $H_a\parallel ab$. Closed symbols are data for NdFeAs(O,F) and open symbols correspond to $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$. The crosses in Fig. 3b correspond to the following intermediate field directions: $\theta =35°$ (left) and $65°$ (right) for $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ and $\theta =30°$, $50°$, $70°$, and $80°$ (from left to right) in Nd(F,O)FeAs. Solid lines in Fig. 3b are loci of constant $Q$, Eqs. (1, 2), where we have used the linear slope of the solid lines in Fig. 3a to approximate $\partial B_{c2}/\partial$.

Figure 4

Angular dependence of the upper critical field. This was extracted from fits of the IRL to Eq. (2) with a freely scaled upper critical field, for both single-crystalline NdFeAs(O,F) (●) and $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$. The data for the latter compound were taken near the sample edge (◻) and near the sample center (○). The crosses correspond to the values deduced from specific-heat measurements in Ref. 10. Thick solid lines correspond to the 3D effective-mass model for the indicated anisotropy factors $\gamma$.