  The electronic structure inhomogeneities in Co, Ni, and Cr doped BaFe2As2 122
single crystals are compared using scanning tunneling microscopy/spectroscopy
(STM/S) at the nanoscale within three bulk property regions in the phase
diagram: a pure superconducting (SC) dome region (Co-122), a coexisting SC and
antiferromagnetic (AFM) region (Ni-122), and a non-SC region (Cr-122). Machine
learning is utilized to categorize the various nanometer scale inhomogeneous
electronic states, described here as in-gap, L-shape and S-shape states
immersed into the SC matrix for Ni-and Co-doped 122, and L-shape and S-shape
states into the metallic matrix for Cr-doped 122. Although the relative
percentages of in-gap, L-shape and S-shape states vary in the three samples,
the total volume fraction of the three electronic states is quite similar. This
is coincident with the number of electrons (Ni0.04 and Co0.08) and holes
(Cr0.04) doped into the 122 compound. By combining the volume fractions of the
three states, the local density of states (LDOS), magnetic field dependent
behavior and global properties in these three samples, the in-gap state is
confirmed as a magnetic impurity state from the Co or Ni dopants. In addition,
the L-shape state is identified as a spin density wave (SDW) which competes
with the SC phase, and the S-shape state is found to be another form of
magnetic order which constructively cooperates with the SC phase, rather than
competing with it. The comparison of the vortex structures indicates that the
inhomogeneous electronic states serve as pinning centers for stabilizing the
vortex lattice.
