Abstract
We study the exchange interaction and the subsequent collective behavior of magnetic impurities embedded in a disordered two-dimensional helical metal. The exchange coupling follows a statistical distribution whose moments are calculated to the lowest order in , where is the Fermi momentum of itinerant electrons and is the mean free path. We find that (i) the first moment of the distribution decays exponentially, and (ii) the variance of the interaction is long range, however, it becomes independent of the orientation of the localized magnetic moments due to the locking between spin and momentum of the electrons that mediate the interaction. As a consequence, long-range magnetic order tends to be suppressed, and a spin glass phase emerges. The formalism is applied to the surface states of a three-dimensional topological insulator. The lack of a net magnetic moment in the glassy phase and the full randomization of spin polarization at distances larger than excludes a spectral gap for surface states. Hence, nonmagnetic disorder may explain the dispersion in results for photoemission experiments in magnetically doped topological insulators.
- Received 16 April 2015
DOI:https://doi.org/10.1103/PhysRevB.92.081410
©2015 American Physical Society