thin films*

We establish a disorder threshold for the topological state in thin films of Sb₂Te₃ by following the disorder evolution of transport across large range of structural nonmagnetic disorder. Starting at the high disorder end, where 3D transport is found to be governed by dynamic spin correlations, we recover the low disorder state by thermal annealing. Weak antilocalization interference correction (WAL), characteristic of 2D topological transport related to the Berry phase, is recovered at a relatively low disorder level corresponding to W_th = 0.05E_g, where E_g is the bulk gap. The 3D-2D transition coincides with the disappearance of disorder-induced glassy spin correlations, directly measured using micro-Hall sensors. The sharp onset of magnetic response appears independent of disorder, consistent with the presence of FM clusters with T_C ~ 200 K that shrink in size as disorder is reduced. At W_th, transport is dominated by crystalline regions with minimal spin scattering, thereby supplying a percolative path for the carriers to travel along, with conductance of about G₀=e²/h _. We discuss the role of spin relaxation in inducing the dimensionality transition into the topological state.