Physical properties of FeSe$_{0.5}$Te$_{0.5}$ single crystals grown under different conditions
We report on structural, magnetic, conductivity, and thermodynamic studies of FeSe$_{0.5}$Te$_{0.5}$ single crystals grown by self-flux and Bridgman methods. The samples were prepared from starting materials of different purity at various temperatures and cooling rates. The lowest values of the susceptibility in the normal state, the highest transition temperature $T_c$ of 14.5 K, and the largest heat-capacity anomaly at $T_c$ were obtained for pure (oxygen-free) samples. The critical current density $j_c$ of $8 \times 10^4$ A/cm$^2$ (at 2 K) achieved in pure samples is attributed to intrinsic inhomogeneity due to disorder at the cation and anion sites. The impure samples show increased $j_c$ up to $2.3 \times 10^5$ A/cm$^2$ due to additional pinning centers of Fe$_3$O$_4$. The upper critical field $H_{c2}$ of $\sim 500$ kOe is estimated from the resistivity study in magnetic fields parallel to the \emph{c}-axis. The anisotropy of the upper critical field $\gamma_{H_{c2}} = H_{_{c2}}^{ab}/H_{_{c2}}^{c}$ reaches a value $\sim 6$ at $T\longrightarrow T_c$. Extremely low values of the residual Sommerfeld coefficient for pure samples indicate a high volume fraction of the superconducting phase (up to 97%). The electronic contribution to the specific heat in the superconducting state is well described within a single-band BCS model with a temperature dependent gap $\Delta_0 = 27(1)$ K. A broad cusp-like anomaly in the electronic specific heat of samples with suppressed bulk superconductivity is ascribed to a splitting of the ground state of the interstitial Fe$^{2+}$ ions. This contribution is fully suppressed in the ordered state in samples with bulk superconductivity.