2 1 0 2 0 3 0 4 0 - 4 0 4 0 8 0 1 2 0 1 0 2 0 3 0 0 . 0 0 . 8 x p r i m - t o t a f o r - b T r a t u r e ( K T ( K 2 0 0 4 0 0 6 0 0 8 0 0 2 0 4 0 6 0 8 0 3 4 3 6 3 8 4 0 2 2 2 4 2 6 2 8 3 1 0 2 0 3 0 1 0 2 0 a ( F 0 . 8 8 0 . 1 2 , B 0 . 6 8 0 . 3 2 r a t u r e ( K ) ( a 4 . 5 T 6 T 7 . 5 T 9 T ( b T r a t u r e ( K 0 T 3 9 T 0 ( K 3 7 . 0 3 8 . 0 1 0 T ( K ( c GLYPH<s61549> - 6 . 7 T / K FIG. 2: Superconductivity-induced specific-heat difference of Ba$_{0}$$_{.}$$_{68}$K$_{0}$$_{.}$$_{32}$Fe$_{2}$As$_{2}$ . The black solid curve is the result of a fit according to the two-gap α -model. The dashed and dash-dotted curves represent the partial contributions of the two bands. The light gray line is the electronic specific heat calculated from the four-band Eliashberg model. Inset: Temperature dependence of the thermody- namic critical field (see text). FIG. 1: (a) Temperature dependence of the specific heat C$_{p}$/T of Ba$_{0}$$_{.}$$_{68}$ K$_{0}$$_{.}$$_{32}$ Fe$_{2}$As$_{2}$ (squares) and Ba(Fe$_{0}$$_{.}$$_{88}$Mn$_{0}$$_{.}$$_{12}$)$_{2}$As$_{2}$ (cir- cles). The inset shows a plot of C$_{p}$/T vs. T 2 at low T for both samples. The lines represent the best fit to C$_{p}$ ( T ) /T = γ (0)+ βT $^{2}$. (b,c) T emperature dependence of C$_{p}$ of Ba$_{0}$$_{.}$$_{68}$K$_{0}$$_{.}$$_{32}$Fe$_{2}$As$_{2}$ near T$_{c}$ measured at different external magnetic fields applied perpendicular to the ab -plane. In order to reliably extract the electronic contribution, C$_{el}$ ( T ) , from the total measured specific heat, the contri- bution of lattice excitations, C$_{latt}$ ( T ) , has to be accurately determined. The lattice specific heat of the parent com- pound BaFe$_{2}$As$_{2}$ can not be accurately obtained because of the magnetic and structural phase transitions at ∼ 140 K. We found that substitution of 12% Fe by Mn suppresses the spin-density-wave state and does not induce superconductiv- ity. The specific heat of Ba(Fe$_{0}$$_{.}$$_{88}$Mn$_{0}$$_{.}$$_{12}$)$_{2}$As$_{2}$ (red cir- cles in Fig. 1a) was found to be independent of magnetic field. The electronic and lattice specific heat terms extracted from a fit to low-temperature data on this compound (inset in Fig. 1a) are γ (0) = γ N Mn = 14.9(2) mJ/mol K 2 and β$_{Mn}$ = 0.420(4) mJ/mol K $^{4}$, respectively. The lattice specific heat of Ba(Fe$_{0}$$_{.}$$_{88}$Mn$_{0}$$_{.}$$_{12}$)$_{2}$As$_{2}$ , C Mn $_{latt}$( T ) , was obtained by subtract- ing γ N $_{Mn}$T from its total specific heat, C Mn tot ( T ) . The esti- mated Debye temperature is 306 K, somewhat higher than the corresponding value for superconducting Ba$_{0}$$_{.}$$_{68}$K$_{0}$$_{.}$$_{32}$Fe$_{2}$As$_{2}$ (277 K). Since the difference of the lattice parameters of both compounds does not exceed 1.5%, we assume that the phonon contributions to their specific heat and to the entropy obey a law of corresponding states. The normal-state specific heat of Ba$_{0}$$_{.}$$_{68}$K$_{0}$$_{.}$$_{32}$Fe$_{2}$As$_{2}$ can then be obtained from the commonly used corresponding states approximation [13]: where γ N K is the Sommerfeld constant in the normal state of Ba$_{0}$$_{.}$$_{68}$K$_{0}$$_{.}$$_{32}$Fe$_{2}$As$_{2}$ , and A and B are close to unity. From a least-squares fit of our data to Eq. (1) within the temper- ature range 40 - 150 K (more than 300 data points) under the constraint of entropy conservation, we obtained γ N $_{K}$= 50 mJ/mol K $^{2}$, with A = 0 . 95 and B = 1 . 03 . Figure 2 shows the difference, Δ C$_{el}$ ( T ) /T , between the measured specific heat C$_{p}$ ( T ) /T of Ba$_{0}$$_{.}$$_{68}$K$_{0}$$_{.}$$_{32}$Fe$_{2}$As$_{2}$ (Fig. 1a) and its normal- state counterpart C K $_{tot}$( T ) /T estimated from Eq. (1). The Figure 1b highlights the superconductivity-induced jump anomaly of C$_{p}$ , which exhibits the largest magnitude (125 mJ/mol K $^{2}$) and smallest width ( ≤ 0 . 4 K) reported to-date [2– 4, 10, 11]. An external magnetic field applied perpendicular to the ab -plane gradually suppresses the jump and reduces the transition temperature by 1.4 K for H = 9 T. The transition temperature T$_{c}$ determined as the maximum of the derivative of C$_{p}$ ( T ) decreases linearly with magnetic field with a slope of δH$_{c}$$_{2}$ ( T ) /δT |$_{T}$$_{c}$ = - 6.7 T/K (Fig. 2c), that is consistent with the v alue reported in Ref. 10. This is a factor of two larger than the value obtained from resistivity measurements on samples from the same batch [12]. This difference may be due to flux-flo w effects. resents the residual zero-temperature electronic specific heat and the second term the lattice specific heat. The fitting pa- rameters for zero field are γ (0) = 1 . 2(2) mJ/mol K 2 and β =0.496(1) mJ/mol K $^{4}$. For magnetic field H = 9 T we used the same β and obtained γ (0) = 6 . 4(2) mJ/mol K $^{2}$. These residual specific heat values are the lowest reported for FeAs- based superconductors so far, indicating the superior quality and high purity of our samples. The ratio of the residual elec- tronic specific heat to its normal-state counterpart ( γ N $_{K}$, see below) yields an estimate of the non-superconducting phase fraction γ (0) /γ N K ≈ 1 . 2 / 50 = 2 . 4 %. C K $_{tot}$( T ) = C K $_{latt}$( T )+ γ N K · T = A · C Mn $_{latt}$( B · T )+ γ N K · T (1)