Surface Superconductivity in the `Partial' Superconductor BaFe$_{2}$As$_{2}$

The partial superconductivity (resistive transition to $\rho $=0, but no bulk anomalies) in undoped BaFe$_{2}$As$_{2}$, as well as in other MFe$_{2}$As$_{2}$ compounds, has been a puzzle. Sample dependence plays a large role in the superconductivity, and hints have been found for a sensitivity of the surface to exposure to air. Based on a fairly reliable ability to produce such superconducting samples (with a yield of $\sim $ 50{\%}), and the clue from a previous work [1] that the critical current of the superconductivity is abnormally low, we show here that the superconductivity is a 2-dimensional affect -- presumably on the surface. [1] J. S. Kim, et al., J. Phys.: Condens. Matter \textbf{21}, 342201 (2009).