Superconducting gap evolution in overdoped BaFe$_{2}$(As$_{1-x}$P$_x$)$_2$ single crystals through nanocalorimetry

We report on specific heat measurements on clean overdoped $mathrm{BaFe_{2}(As_{1-x}P_x)_2}$ single crystals performed with a high resolution membrane-based nanocalorimeter. A nonzero residual electronic specific heat coefficient at zero temperature $gamma_mathrm{r}={C/T}|_{T to 0}$ is seen for all doping compositions, indicating a considerable fraction of the Fermi surface ungapped or having very deep minima. The remaining superconducting electronic specific heat is analyzed through a two-band s-wave $alpha$ model in order to investigate the gap structure. Close to optimal doping we detect a single zero-temperature gap of $Delta_0 sim 5.3,mathrm{meV}$, corresponding to $Delta_0 / k_mathrm{B} T_mathrm{c} sim 2.2$. Increasing the phosphorus concentration $x$, the main gap reduces till a value of $Delta_0 sim 1.9,mathrm{meV}$ for $x = 0.55$ and a second weaker gap becomes evident. From the magnetic field effect on $gamma_mathrm{r}$, all samples however show similar behavior [$gamma_mathrm{r}(H) - gamma_mathrm{r}(H=0) propto H^n$, with $n$ between 0.6 and 0.7]. This indicates that, despite a considerable redistribution of the gap weights, the total degree of gap anisotropy does not change drastically with doping.

Microscopic Parameters from High-Resolution Specific Heat Measurements on Overdoped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ Single Crystals

We investigate the electronic specific heat of overdoped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals in the superconducting state using high-resolution nanocalorimetry. From the measurements, we extract the doping dependence of the condensation energy, superconducting gap $Delta$, and related microscopic parameters. We find that the anomalous scaling of the specific heat jump $Delta C propto T_{mathrm{c}}^3$, found in many iron-based superconductors, in this system originates from a $T_mathrm{c}$-dependent ratio $Delta/k_mathrm{B}T_mathrm{c}$ in combination with a doping-dependent density of states $N(varepsilon_mathrm{F})$. A clear enhancement is seen in the effective mass $m^{*}$ as the composition approaches the value that has been associated with a quantum critical point at optimum doping. However, a simultaneous increase in the superconducting carrier concentration $n_mathrm{s}$ maintains the superfluid density, yielding an apparent penetration depth $lambda$ that decreases with increasing $T_mathrm{c}$ without sharp divergence at the quantum critical point. Uemura scaling indicates that $T_mathrm{c}$ is governed by the Fermi temperature $T_mathrm{F}$ for this multi-band system.

Thermodynamics around the First-Order Ferromagnetic Phase Transition of ${rm Fe}_2{rm P}$ Single Crystals

The specific heat and thermodynamics of ${rm Fe}_2{rm P}$ single-crystals around the first order paramagnetic (PM) to ferromagnetic (FM) phase transition at $T_{rm C} = 217 ,{rm K}$ are empirically investigated. The magnitude and direction of the magnetic field relative to the crystal axes govern the derived H-T phase diagram. Strikingly different phase contours are obtained for fields applied parallel and perpendicular to the $c$-axis of the crystal. In parallel fields, the FM state is stabilized, while in perpendicular fields, the phase transition is split into two, with an intermediate FM phase where there is no spontaneous magnetization along the $c$-axis. The zero-field transition displays a text-book example of a first order transition with different phase stability limits on heating and cooling. The results have special significance since ${rm Fe}_2{rm P}$ is the parent material to a family of compounds with outstanding magnetocaloric properties.