  In previous work in undoped MFe2As2, partial drops in the resistivity
indicative of traces of superconductivity have been observed in some samples of
M=Ba (Tc ~ 20 K, up to 25% drop in resistivity) and M=Ca (Tc ~ 10 K, up to 45 %
drop in resistivity.) A complete drop in the resistivity to 0, along with a
finite fraction of Meissner flux expulsion, has been observed in M=Sr, Tc = 22
K. Using In-flux grown single crystal samples of undoped BaFe2As2, we find a
complete drop in the resistivity to 0 in most samples beginning at Tc(onset) =
22.5 K. However, in contrast to the SrFe2As2 results, there is no measurable
Meissner effect and no suppression of the resistive superconducting transition
with annealing. The current sensitivity of the superconducting resistive
transition in our samples of BaFe2As2 is quite strong, with an increase in the
current density of a factor of 15 to ~ 1.5 A/cm2 not changing Tc(onset) but
broadening the transition significantly and causing the resistivity to remain
finite as T approaches 0. To investigate if this unusually low critical current
is indicative of filamentary conduction lacking the apparent anisotropy seen in
the critical magnetic field, Hc2, measurements of, e. g., the bulk
superconductor Co-doped BaFe2As2, Hc2 was measured in both crystalline
directions. These BaFe2As2 samples show Hc2(T) values in the ab-plane and along
the c-axis comparable to those seen in BaFe2-xCoxAs2, which has a similar Tc.
Since the lack of Tc suppression after annealing argues against strain-induced
superconductivity as proposed for the other undoped MFe2As2 materials, another
possible cause for the superconductivity in BaFe2As2 is discussed.
