# The Electronic Specific Heat of Ba$_{1}$$_{−}$$_{x}$K$_{x}$Fe$_{2}$As$_{2}$ from 2K to 380K. 

J.G. Storey $^{1}$, J.W. Loram$^{1}$, J.R. Cooper$^{1}$, Z. Bukowski2 and J. Karpinski 2 

$^{1}$Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, U.K. and 

$^{2}$Laboratory for Solid State Physics, ETH Zurich, Zurich, Switzerland 

(Dated: November 9, 2018) 

Using a differential technique, we have measured the specific heats of polycrystalline Ba$_{1}$$_{−}$$_{x}$K$_{x}$Fe$_{2}$As$_{2}$ samples with x = 0, 0.1 and 0.3, between 2K and 380K and in magnetic fields 0 to 13 Tesla. From this data we have determined the electronic specific heat coefficient γ ( ≡ C$_{el}$/T ) over the entire range for the three samples. The most heavily doped sample ( x = 0.3) exhibits a large superconducting anomaly Δ γ ( T$_{c}$ ) ∼ 48 mJ/mol K 2 at T$_{c}$ = 35K, and we determine the energy gap, condensation energy, superfluid density and coherence length. In the normal state for the x = 0.3 sample, γ ∼ 47 mJ/mol K 2 is constant from T$_{c}$ to 380K. In the parent compound ( x = 0) there is a large almost first order anomaly at the spin density wave (SDW) transition at T$_{o}$ = 136K. This anomaly is smaller and broader for x = 0.1. At low T , γ is strongly reduced by the SDW gap for both x = 0 and 0.1, but above T$_{o}$ , γ for all three samples are similar. 

The electronic specific heat contains a wealth of quan- titative information on the electronic spectrum over an energy region ± 100meV about the Fermi level, cru- cial to the understanding of high temperature supercon- ductivity. Measurements of the electronic specific heat played an important role in revealing key properties of the copper-oxide based ‘cuprate’ high-temperature su- perconductors (HTSCs). Some examples include the normal-state “pseudogap”[1–4], the bulk sample inho- mogeneity length scale[5], and more recently the degree to which the superconducting transition temperature is suppressed due to superconducting fluctuations[6]. In this work we extend such measurements to the recently discovered iron-arsenide based ‘pnictide’ HTSCs. Here we present results obtained from polycrystalline samples of Ba$_{1}$$_{−}$$_{x}$K$_{x}$Fe$_{2}$As$_{2}$ ( x = 0, 0.1 and 0.3) using a high- resolution differential technique[7]. 

With this technique we directly measure the difference in the specific heats of a doped sample and the undoped reference sample (BaFe$_{2}$As$_{2}$). This eliminates most of the large phonon term from the raw data and yields a curve which is dominated by the difference in electronic terms between the sample and reference. After making a small correction for any residual phonon term, this differ- ence in electronic specific heats can be determined with a resolution of ∼ 0.1 mJ/mol K 2 at temperatures from 1.8K to 380K and magnetic fields from 0 to 13T. During a measurement run the total specific heats of the sample and reference are also measured. 

The polycrystalline samples of Ba$_{1}$$_{−}$$_{x}$K$_{x}$Fe$_{2}$As$_{2}$ were prepared by a solid state reaction method similar to that reported by Chen et al [8]. First, Fe$_{2}$As, BaAs, and KAs were prepared from high purity As (99.999%), Fe (99.9%), Ba (99.9%) and K (99.95%) in evacuated quartz ampoules at 800, 650 and 500 $^{◦}$C respectively. Next, the terminal compounds BaFe$_{2}$As$_{2}$ and KFe$_{2}$As$_{2}$ were synthesized at 950 and 700 $^{◦}$C respectively, from stoi- chiometric amounts of BaAs or KAs and Fe$_{2}$As in alu- 

PACS numbers: 74.25.Bt, 74.70.-b 

mina crucibles sealed in evacuated quartz ampoules. Fi- nally, samples of Ba$_{1}$$_{−}$$_{x}$K$_{x}$Fe$_{2}$As$_{2}$ with x = 0.1 and 0.3 were prepared from appropriate amounts of single-phase BaFe$_{2}$As$_{2}$ and KFe$_{2}$As$_{2}$. The components were mixed, pressed into pellets, placed into alumina crucibles and sealed in evacuated quartz tubes. The samples were an- nealed for 50 h at 700 $^{◦}$C with one intermittent grind- ing, and were characterized by room temperature pow- der X-ray diffraction using Cu K$_{α}$ radiation. The diffrac- tion patterns were indexed on the basis of the tetragonal ThCr$_{2}$Si$_{2}$ type structure (space group I4/mmm). Lattice parameters calculated by a least-squares method agree well with those reported by Chen et al [8]. Traces of FeAs as an impurity were detected for compositions with x = 0.1 and 0.3. The samples for heat capacity measurement weighed ∼ 0.8g. 

The total specific heats of the three samples are plot- ted as γ tot ≡ C $^{tot}$/T in Fig. 1. In the x = 0 sample there is a sharp and almost first order anomaly at the magneto-structural transition at T$_{0}$ = 136K, in agree- ment with published single crystal data[9]. For the x = 0.1 sample the corresponding anomaly at T$_{0}$ = 135K is broader and considerably reduced in magnitude, in agree- ment with the data of Rotter et al .[10] who have tracked T$_{0}$ in the specific heat down to 105K in a sample with x = 0.2. The magnetic field dependence of this anomaly is extremely weak for both samples. We see no evidence for a structural transition in the x = 0.3 sample (the very weak anomaly at 67K in the differential data (Fig. 2(a)) is probably due to an FeAs impurity phase[11]). The su- perconducting transition in this sample is clearly visible in γ tot at 35K, and the field dependence is shown in the inset to Fig. 1. 

In the temperature range 2 − 8K, γ tot = γ (0)+ β (0) T 2 at zero field with γ (0) = 5.1, 9.3 and 1.8 mJ/mol K 2 and β (0) = 0.45, 0.37 and 0.57 mJ/mol K 4 for the x = 0, 0.1 and 0.3 samples respectively. On the assumption that β (0) is entirely due to phonons we obtain Debye temper- 

