We reported self-organized and hierarchized domain structures on various length scales ranging from micrometer to nanometer scale in K_0.5Na_0.5NbO₃ crystals.

Enabling on-demand control of heat flow is key for the development of next-generation electronic devices, solid-state heat pumps, and thermal logic. However, precise and agile tuning of the relevant microscopic material parameters for adjusting thermal conductivities remains elusive. Here, we study several single crystals of lanthanum aluminate ($\mathrm{LaAl}{\mathrm{O}}_3$) with different domain structures and show that ferroelastic domain walls behave as boundaries that act like efficient controllers to govern thermal conductivity. At low temperature (3 K), we demonstrate a fivefold reduction in thermal conductivity induced by domain walls orthogonal to the heat flow and a twofold reduction when they are parallel to the heat flow. Atomistic calculations fully support this experimental observation. By breaking down phonon scattering mechanisms, we also analyze the temperature dependence of the thermal conductivity to derive a quantitative relation between thermal conductivity variations and domain wall organization and density.