Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder

Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in a spinful Qi-Wu-Zhang model of a two-dimensional Chern insulator coupled to disordered classical spins of unit length. The topological phase diagram is computed numerically using two complementary approaches: twisted boundary conditions and the topological Hamiltonian technique. Our results show that strong disorder can act as a fundamental topological mechanism rather than merely a perturbation. For strong exchange coupling, tuning the mass parameter reveals a transition between phases with different Chern numbers $C$. Remarkably, this transition is driven by zeros, rather than poles, of the disorder-averaged Green's function crossing the chemical potential, and has no analogue in any clean system. We further identify a strong-coupling phase with $C = 0$ that is nonetheless topologically nontrivial, characterized by a distinct Chern number $C^{(\mathrm{S})} \neq 0$ over the manifold of classical spin configurations. This phase is also disorder-driven, as $C^{(\mathrm{S})} = 0$ in the clean limit.