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Specific Heat vs Field in the 30 K Superconductor BaFe2(As0.7P0.3)2

We report specific heat measurements on the Fe-based superconductor BaFe2(As0.7P0.3)2, a material on which previous penetration depth, NMR, and thermal conductivity measurements have observed a high density of low-energy excitations, which have been interpreted in terms of order parameter nodes. Within the resolution of our measurements, the low temperature limiting C/T is found to be linear in field, i.e. we find no evidence for a Volovik effect associated with nodal quasiparticles in either the clean or dirty limit. We discuss possible reasons for this apparent contradiction.


I. Introduction
The investigation of a new class of superconductors, such as the recently discovered 1 'high' temperature superconductors based on iron pnictides (FePn), inevitably leads to concerted efforts to establish the symmetry of the order parameter. In the case of the FePn materials, these investigations are still returning apparently conflicting results, even in samples that are essentially identical. For example, Andreev spectroscopy 2 implies a fully gapped superconductor in the 1111 material SmFeAsO 0.85 F 0.15 , whereas at almost the same composition (SmFeAsO 0.82 F 0.18 ) infrared optical measurements 3 imply a nodal superconductor. London penetration depth measurements 4 in the 122 structure Ba(Fe 0.93 Co 0.07 ) 2 As 2 suggest nodes in the superconducting gap, while thermal conductivity measurements 5 on samples that include the same composition (Ba(Fe 1-x Co x ) 2 As 2 , 0.048 ≤ x ≤ 0.114) from the same group as ref. Recently, superconductivity at 30 K has been reported 20 in P-doped BaFe 2 As 2 , with 1/3 of the As replaced by P. This system is particularly interesting because it displays a phase diagram similar to that of other doped ferropnictides, but the process by which the system is "doped" is far from obvious, given that P and As are isoelectronic.
In addition, transport measurements 20 show indications of quantum critical behavior (consistent with dHvA measurements 21 ) near the maximum critical temperature, similar to hole-doped cuprate superconductors. Magnetic penetration depth and thermal conductivity measurements 22 , as well as NMR data 23 , indicate superconducting gaps with nodes. Here we report measurements of the specific heat divided by temperature, C/T, as a function of field in order to further investigate the gap structure with a bulk probe which is sensitive to all electronic excitations. Specific heat in field was pioneered 24

II. Experimental
Tiny platelet crystals of BaFe 2 (As 0.67 P 0.33 ) 2 were prepared as in ref. 20. A collage of 21 mg of these microcrystals was mounted on a sapphire disk using GE7031 varnish.
Approximately 75% of the crystals had the magnetic field perpendicular to the a-b plane (the plane of the crystals), with the rest randomly oriented. The sapphire disk was mounted in our time constant method calorimeter 28 , and the specific heat from 0.4 to 5 K in fields from 0 to 15 T was measured. Additionally, the specific heat of a standard (high purity Au) was measured in fields up to 14 T. Results on the standard (not shown) indicate agreement with published values to within ±3% in all fields.

III. Results and Discussion
The specific heat of BaFe 2 (As 0.7 P 0.3 ) 2 for 0 ≤ H ≤ 15 T is shown in Fig. 1. As will be discussed further below, there is a small low temperature anomaly in the specific heat data below about 1.4 K. Low temperature anomalies have been seen 29 in other FePn samples, and in some cases -for example in BaFe 2-x Co x As 2 -show rather strong magnetic field dependence. 29 In order to obtain an idea what the temperature dependence of the electronic specific heat is in 0 field, and to accentuate the small, T<1.4 K, anomaly, Fig. 2 shows a log-log plot of the data corrected for a slight residual linear term γT (γ=1.78 mJ/moleK 2 ) in the superconducting specific heat and the approximate lattice contribution to the specific heat. This plot shows clearly the low Fig. 2 (color online). Log of ∆C (= C measured -γT -C lattice ) vs logT, where γ is obtained by extrapolating C/T from the lowest temperature data to T=0 and the lattice specific heat is approximated by using a Debye temperature of 250 K for BaNi 2 As 2 30 and scaling it for BaFe 2 (As 0.7 P 0.3 ) 2 by the square root of the inverse ratio of the molar masses to arrive at ~ 257 K, or C lattice = βT 3 , with β=0.569 mJ/molK 4 . Note that the small anomaly in the specific heat appears to be finished by about 1.4 K. temperature anomaly in the zero field data. In any case, the difference ∆C, the superconducting electronic specific heat, is quite close to T 3 in temperature dependence.
Attempts to separate out a T 2 contribution, which was very difficult to achieve 31 in the high T c cuprate superconductors until superior samples were grown, were unsuccessful here.
In order to more closely consider the field dependence of the specific heat in Fig.   1, these data are shown in Fig. 3 with the zero field data subtracted. The data in   Fig. 4.) The low temperature anomaly appears to be almost field independent since the upturn in the data shown here below 1 K which increases with increasing field is due to the specific heat contribution from the splitting of the nuclear levels with field (C nuc /T ~ H 2 /T 3 ), which is calculable (3.7 mJ/moleK 2 at 0.4 K and 15 T) for the isotopes involved ( 135 Ba, 6.6% abundant, 137 Ba, 11.2 % abundant, 57 Fe, 2.14 % abundant, 75 As, 100% abundant, and 31 P, 100% abundant).
show that the low temperature anomaly in C, as well as the nuclear hyperfine splitting due to the magnetic field, appear to have little influence around 1.5 to 2 K. Thus, in order to track the behavior of γ (≡C/T as T→0) we propose three equivalent ways to treat the data. By extrapolating the data (C/T = γ + βT 2 + δT 4 ) by a three term fit from 1.5 K and above, we avoid the low temperature anomaly and can well approximate γ. Another method is to just take the value of C/T at either 1.5 K or 2 K as indicative of γ with no influence from either the anomaly or the field-induced nuclear contribution. Such a plot of γ as a function of field is shown in Fig. 4.

IV. Analysis
Here we discuss the extent to which the results presented here are consistent with those found in thermal conductivity, NMR, and penetration depth measurements on the same samples. In each of these three cases, power laws in temperature were reported at low Thus it is possible that if the masses on the respective sheets are very different, such that , the specific heat will be dominated by the hole sheets, and yield a result apparently characteristic of a fully gapped state. In such a scenario, the finite specific heat γ observed in the zero field measurements would have to be ascribed to extrinsic sources, such as two-level systems.
This simple light electron (nodal)/heavy hole (fully gapped) sheet model would be consistent with the observation of T dependence in NMR spin-lattice relaxation time measurements 23 characteristic of nodes, since the contribution from the heavy fully gapped hole sheet would be exponentially suppressed at low T. In addition, the clear nonlinear field dependence of the thermal conductivity 22 can be understood, since quasiparticle transport currents (e.g. low-temperature thermal currents) will be dominated by the lighter mass electron sheets. Longer quasiparticle lifetimes on the electron sheets may also play a role in this case. 33 Recent dHvA experiments 34 have succeeded in measuring the mass of one of the hole sheets at an overdoped concentration (BaFe 2 (As 0.4 P 0.6 ) 2 ), and find that it has approximately twice the effective mass as the electron sheets. Furthermore, an additional hole sheet expected from density functional theory has not yet been observed, possibly because its mass is too high. Clearly, further studies are necessary to substantiate this point of view.

V. Conclusions
Specific heat of BaFe 2 (As 0.67 P 0.33 ) 2 in fields to 15 T reveal that, in contrast to the penetration depth and thermal conductivity measurements, the part of the Fermi surface sampled by the specific heat reveals mixed evidence of nodal superconductivity. While the large residual γ in the superconducting state could be due to a disordered superconducting state with nodes, we observe a linear field dependence of the specific heat at low temperatures, and no evidence for the Volovik effect characteristic of nodal quasiparticles which should lead to negative curvature in C(H). We discussed a scenario in which the field dependence in our measurement might be dominated by heavy mass hole sheets of the Fermi surface corresponding to an isotropic order parameter, while electron sheets with a highly anisotropic order parameter could be difficult to observe due to a much lighter mass. Such an attempt to reconcile existing measurements on these samples requires more detailed studies probing the character of the states on the various parts of the Fermi surface in these materials.