  In this paper, we address a number of outstanding issues concerning the
nature and the role of magnetic inhomogenities in the iron chalcogenide system
FeTe1-xSex and their correlation with superconductivity in this system. We
report morphology of superconducting single crystals of FeTe0.65Se0.35 studied
with transmission electron microscopy, high angle annular dark field scanning
transmission electron microscopy and their magnetic and superconducting
properties characterized with magnetization, specific heat and magnetic
resonance spectroscopy. Our data demonstrate a presence of nanometre scale
hexagonal regions coexisting with tetragonal host lattice, a chemical disorder
demonstrating non homogeneous distribution of host atoms in the crystal
lattice, as well as hundreds-of-nanometres-long iron-deficient bands. From
magnetic data and ferromagnetic resonance temperature dependence, we attribute
magnetic phases in Fe-Te-Se to Fe3O4 inclusions and to hexagonal symmetry
nanometre scale regions with structure of Fe7Se8 type. Our results suggest that
nonhomogeneous distribution of host atoms might be an intrinsic feature of
superconducting Fe-Te-Se chalcogenides and we find a surprising correlation
indicating that faster grown crystal of inferior crystallographic properties is
a better superconductor.
