  Relaxor ferroelectrics are a class of materials that are widely perceived as
deriving their exotic properties from structural heterogeneities. Understanding
the microscopic origin of the superior electromechanical response requires
knowledge not only concerning the formation of polar nanodomains (PNDs) built
from individual atoms but more importantly the spatial distribution of PNDs
over longer distances. The mesoscale PND arrangement is shaped by the
interactions between these domains and, in turn, dictates the electric-field
driven PND response directly relevant to the macroscopic material properties.
Here, we show the emergence of mesoscale lattice order that we name "polar
laminates" in the canonical relaxor ferroelectric
0.68PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$-0.32PbTiO$_{3}$ (PMN-0.32PT) using X-ray
coherent nano-diffraction. These laminates are nematic with a size of ~350 nm
and arise from the staggered arrangement of ~13 nm monoclinic PNDs along the
<110> of the pseudocubic lattice. The spatial distribution of c-axis strain is
directly correlated with the tilting of the PNDs and is most prominent between
the laminates. Further operando nano-diffraction studies demonstrate
heterogeneous electric-field-driven responses. The most active regions tend to
reside inside the laminates while the spatial pinning centers are between the
laminates. This observation reveals the hierarchical assembly of lattice order
as a novel form of electron and lattice self-organization in heterogenous
materials and establishes the role of such mesoscale spatial arrangement in
connecting the nanoscale heterogeneity and macroscopic material properties.
These findings provide a guiding principle for the design and optimization of
future relaxors and may shed light on the existence of similar behavior in a
wide range of quantum and functional materials.
