  Translational/rotational symmetry breaking and recovery in condensed matter
systems are closely related to exotic physical properties such as
superconductivity (SC), magnetism, spin density waves (SDW) and charge density
waves (CDW). The interplay between different order parameters is intricate and
often subject to intense debate, as in the case of CDW order and
superconductivity. In La1:875Ba0:125CuO4 (LBCO), the locations of CDW domains
are found to be pinned on the nanometer size scale. Coherent X-ray diffraction
techniques open routes to directly visualize the domain structures associated
with these symmetry changes. We have pushed Bragg Coherent Diffractive Imaging
(BCDI) into the cryogenic regime where most phase transitions in quantum
materials reside. Utilizing BCDI, we image the structural evolution of LBCO
microcrystal samples during the high-temperature-tetragonal (HTT) to
low-temperature-orthorhombic (LTO) phase transition. Our results show the
formation of LTO domains close to the transition temperature and how the domain
size varies with temperature. The LTO domain size is shown to decrease with
temperature and to be inversely proportional to the magnitude of the
orthorhombic distortion. The number of domains follows the secondary order
parameter (or orthorhombic strain) measurement with a critical exponent that is
consistent with the 3D universality class.
