Crystal Growth Process

The two single crystals studied were grown by Richard Greene's group at the University of Maryland, using a direct solidification technique [23]. A mixture of the compound Pr$_{2-x}$Ce$_x$CuO$_4$ and excess CuO powder was put in a Al$_{2}$O$_{3}$ crucible with a strong vertical temperature gradient. A CuO-based flux was added to lower the melting temperature. The mixture was then heated to about $1200$-$1300$ K ($T_{max}$), and allowed to cool slowly (characterized by the temperature ramp rate) until the temperature dropped below the solidification temperature ( $T \sim 1050$ K).

There are two main complications in the growth process of Pr$_{2-x}$Ce$_x$CuO$_4$ single crystals. The first problem is that for different Ce concentrations, optimal growth parameters like ($T_{max}$) and the temperature ramp rate are different. The Ce concentration in the crystal is found to have no direct correlation with the Ce concentration of the mixture, but is closely related to $T_{max}$ [24]. The optimal $T_{max}$ must be carefully chosen to avoid a substantial Ce concentration gradient along the $\hat{c}$-axis direction of the crystal. The second problem is that the as-grown crystals are not superconducting. It is generally believed that a small amount of interstitial (apical) oxygen must be removed in order to achieve superconductivity. This was done by annealing the single crystal in an argon environment at a temperature $900$-$1000$ K. However, due to the limited oxygen mobility, this reduction process often results in an oxygen gradient along the $\hat{c}$-axis direction, especially in crystals thicker than 50 $\mu$m. Increasing the annealing temperature or reduction time evaporates the Cu atoms, causing the surface of the crystal to decompose. A solution proposed by Brinkmann et. al. [24], and adopted by Greene's group, is to cover the entire crystal with polycrytalline Pr$_{2-x}$Ce$_x$CuO$_4$ pellets of the same composition during the annealing process. The pellets act as an effective Cu diffusion barrier. The introduction of a small amount of oxygen to the argon can speed up the process by increasing the annealing temperature without lowering $T_c$.

Contrary to widespread belief, there are some recent experiments suggesting that O(3) apical oxygen is not removed by the reduction process [25]. The role of oxygen in the superconductivity of electron-doped cuprates is a topic of current debate.