  Quantum materials such as antiferromagnets or superconductors are complex in
that chemical, electronic, and spin phenomena at atomic scales can manifest in
their collective properties. Although there are some clues for designing such
materials, they remain mainly unpredictable. In this work, we find that
enhancement of transition temperatures in BaFe2As2-based crystals are caused by
removing local-lattice strain and electronic-structure disorder by thermal
annealing. While annealing improves Neel-ordering temperature in BaFe2As2
crystal (TN=132 K to 136 K) by removing in-plane electronic defects and overall
reduction of a-lattice parameter, it increases superconducting-ordering
temperature in optimally cobalt-doped BaFe2As2 crystal (Tc=23 to 25 K) by
precipitating-out the cobalt dopants and giving larger overall a-lattice
parameter. Although annealing promotes local chemical and electronic uniformity
resulting in higher TN in the parent, it results in nanoscale phase separation
in the superconductor resulting in lower disparity and strong superconducting
band gaps in the dominant crystalline regions, which lead to both higher
overall Tc and critical-current-density, Jc.
