  Chiral spin textures are researched widely in condensed matter systems and
show potential for spintronics and storage applications. Along with extensive
condensed-matter studies of chiral spin textures, photonic counterparts of
these textures have been observed in various optical systems with broken
inversion symmetry. Unfortunately, the resemblances are only phenomenological.
This work proposes a theoretical framework based on the variational theorem to
show that the formation of photonic chiral spin textures in an optical
interface is derived from the system's symmetry and relativity. Analysis of the
optical system's rotational symmetry indicates that conservation of the total
angular momentum is preserved from the local variations of spin vectors.
Specifically, although the integral spin momentum does not carry net energy,
the local spin momentum distribution, which determines the local subluminal
energy transport and minimization variation of the square of total angular
momentum, results in the chiral twisting of the spin vectors. The findings here
deepen the understanding of the symmetries, conservative laws and energy
transportation in optical system, construct the comparability in the formation
mechanisms and geometries of photonic and condensed-matter chiral spin
textures, and suggest applications to optical manipulation and chiral
photonics.
