  In this article we review our studies of the K0.80Fe1.76Se2 superconductor,
with an attempt to elucidate the crystal growth details and basic physical
properties over a wide range of temperatures and applied magnetic field,
including anisotropic magnetic and electrical transport properties,
thermodynamic, London penetration depth, magneto-optical imaging and Mossbauer
measurements. We find that: (i) Single crystals of similar stoichiometry can be
grown both by furnace-cooled and decanted methods; (ii) Single crystalline
K0.80Fe1.76Se2 shows moderate anisotropy in both magnetic susceptibility and
electrical resistivity and a small modulation of stoichiometry of the crystal,
which gives rise to broadened transitions; (iii) The upper critical field,
Hc2(T) is ~ 55 T at 2 K for H||c, manifesting a temperature dependent
anisotropy that peaks near 3.6 at 27 K and drops to 2.5 by 18 K; (iv) Mossbauer
measurements reveal that the iron sublattice in K0.80Fe1.76Se2 clearly exhibits
magnetic order, probably of the first order, from well below Tc to its Neel
temperature of Tn = 532 +/- 2 K. It is very important to note that, although,
at first glance there is an apparent dilemma posed by these data: high Tc
superconductivity in a near insulating, large ordered moment material, analysis
indicates that the sample may well consist of two phases with the minority
superconducting phase (that does not exhibit magnetic order) being finely
distributed, but connected with in an antiferromagnetic, poorly conducting,
matrix, essentially making a superconducting aerogel.
