Specific heat versus field in the 30 K superconductor ${\text{BaFe}}_2{\left({\text{As}}_{0.7}{\text{P}}_{0.3}\right)}_2$

We report specific-heat measurements on well characterized single crystals of the Fe-based superconductor ${\text{BaFe}}_2{\left({\text{As}}_{0.7}{\text{P}}_{0.3}\right)}_2$, from the same batch 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, which may be an intrinsic feature of the multiple Fermi-surface sheets present in the iron pnictide superconductors.

Figure 1

Field-cooled and zero-field-cooled magnetization data on a 150 mg collage of single crystals of ${\text{BaFe}}_2{\left({\text{As}}_{0.7}{\text{P}}_{0.3}\right)}_2$. Note the rather sharp superconducting transition, indicating good sample homogeneity. A further indication of the quality of these crystals is their (Ref. 4) residual resistivity ratio $\left[\rho \left(300\text{K}\right)/\rho \left(T\to 0\right)\right]$ of about 10.

Figure 2

(Color online) Specific heat divided by temperature vs the square of the temperature of ${\text{BaFe}}_2{\left({\text{As}}_{0.7}{\text{P}}_{0.3}\right)}_2$ as a function of field in 3 T steps. Data at another five fields are not shown for clarity. The absolute accuracy of these data, $\pm 5\mathrm{\%}$, is shown by representative error bars in the figure; the precision (intercomparability) of the data is approximately $\pm 2\mathrm{\%}$.

Figure 3

(Color online) Log of $\Delta C\left(=C_{\text{measured}}-\gamma T-C_{\text{lattice}}\right)$ vs $\text{log}T$, where $\gamma$ 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 ${\text{BaNi}}_2{\text{As}}_2$ (Ref. 17) and scaling it for ${\text{BaFe}}_2{\left({\text{As}}_{0.7}{\text{P}}_{0.3}\right)}_2$ by the square root of the inverse ratio of the molar masses to arrive at $\sim 257\text{K}$, or $C_{\text{lattice}}=\beta T^3$, with $\beta =0.569\text{mJ}/\text{mole}{\text{K}}^4$. Note that the small anomaly in the specific heat appears to vanish by about 1.4 K, i.e., does not affect the estimate for $\gamma$ discussed below using data from 1.5 K and above.

Figure 4

(Color online) Specific heat divided by temperature vs temperature, with the zero-field result subtracted. Note the increase in $C/T$ at low temperatures with increasing field (the field dependence of which is the goal of the measurements of this work and discussed below in Fig. 5). The low-temperature anomaly (Fig. 3) 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 $\left(C_{\text{nuc}}/T\sim H^2/T^3\right)$, which is calculable ($3.7\text{mJ}/\text{mole}{\text{K}}^2$ at 0.4 K and 15 T) for the isotopes involved (${}^{135}\text{B}\text{a}$, 6.6% abundant, ${}^{137}\text{B}\text{a}$, 11.2% abundant, ${}^{57}\text{F}\text{e}$, 2.14% abundant, ${}^{75}\text{A}\text{s}$, 100% abundant, and ${}^{31}\text{P}$, 100% abundant). Representative $\pm 5\mathrm{\%}$ absolute error bars are shown on the 15 T data.

Figure 5

(Color online) Three methods of determining the behavior of $\gamma$ $\left(C/T\right)$ in ${\text{BaFe}}_2{\left({\text{As}}_{0.7}{\text{P}}_{0.3}\right)}_2$ as a function of field up to 15 T, with $C/T$ at 2 K, 1.5 K, and extrapolated to $T=0$ plotted vs field. All methods result in $\gamma \sim H$. Extrapolating the specific heat $\gamma$ determined at $T\to 0$ (upside down triangles) to the upper critical field $H_{c2}$ of about 52 T (from Ref. 7) gives a value of $16\text{mJ}/\text{mole}{\text{K}}^2$ for the normal state $\gamma$, which is comparable to the value of $18\text{mJ}/\text{mole}{\text{K}}^2$ determined (Ref. 19) recently for $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$.