Thermodynamics of localized magnetic moments in a Dirac conductor

Cheianov, V. and Szyniszewski, Marcin and Burovski, E. and Sherkunov, Yury and Falko, Vladimir (2012) Thermodynamics of localized magnetic moments in a Dirac conductor. Physical review B, 86 (5): 054424. -. ISSN 1098-0121

Abstract

We show that the magnetic susceptibility of a dilute ensemble of magnetic impurities in a conductor with a relativistic electronic spectrum is nonanalytic in the inverse temperature at T-1 -> 0. We derive a general theory of this effect and construct the high-temperature expansion for the disorder averaged susceptibility to any order, convergent at all temperatures down to a possible ordering transition. When applied to Ising impurities on a surface of a topological insulator, the proposed general theory agrees with Monte Carlo simulations, and it allows us to find the critical temperature of the ferromagnetic phase transition.