Thermodynamics of localized magnetic moments in a Dirac conductor

TL;DR

This paper develops a theory for the non-analytic behavior of magnetic susceptibility in Dirac conductors with impurities, predicting phase transition points and confirming results with simulations.

Contribution

It introduces a general theory for susceptibility in Dirac materials with magnetic impurities, including high-temperature expansion and phase transition analysis.

Findings

Susceptibility is non-analytic as temperature approaches zero.

The theory matches Monte Carlo simulations for topological insulator surfaces.

Critical temperature for ferromagnetic transition is determined.

Abstract

We show that the magnetic susceptibility of a dilute ensemble of magnetic impurities in a conductor with a relativistic electronic spectrum is non-analytic in the inverse tempertature at $1/T\to 0$. 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 tempertaures 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.