Universality of the Scaling Law for Ferroic Domains

We show how the periodicity of 180^{o} domains as a function of crystal thickness scales with the thickness of the domain walls both for ferroelectric and for ferromagnetic materials. We derive an analytical expression for the universal scaling factor and use this to calculate domain wall thickness and gradient coefficients (exchange constants) in some ferroic materials. We then use these to discuss some of the wider implications for the physics of ferroelectric nano-devices and periodically poled photonic crystals.