  To understand and harness the physical mechanisms of ferroelectric Hafnium
Zirconium Oxide (HZO)-based devices, there is a need for clear understanding of
domain interactions, their dynamics, negative capacitance effects, and other
multi-domain characteristics. These crucial attributes depend on the coupling
between neighboring domains quantified by the gradient energy coefficient (g).
Furthermore, HZO has unique orientation-dependent lateral multidomain
configurations. To develop an in-depth understanding of multi-domain effects,
there is a need for thorough analysis of g. In this work, the energetics of
multidomain configurations and domain growth mechanism corresponding to lateral
domain walls of HZO are analyzed and gradient energy coefficients are
quantified using first-principles Density Functional Theory calculations. These
results indicate that one lateral direction exhibits the following
characteristics: i) DW is ultra-sharp and domain growth occurs
unit-cell-by-unit-cell, ii) the value of g is negative and in the order of
$10^{-12} Vm^{3}C^{-1}$, and iii) g reduces (increases) with compressive
(tensile) strain. In contrast, in the other lateral direction, the following
attributes are observed: i) DW is gradual and domain growth occurs in quanta of
half-unit-cell, ii) g is positive and in the order of $10^{-10} Vm^{3}C^{-1}$,
and iii) g increases (reduces) with compressive (tensile) strain.

Materials Science;Applied Physics;Computational Physics