Absence of spontaneous magnetic order of lattice spins coupled to itinerant interacting electrons in one and two dimensions

TL;DR

This paper extends the Mermin-Wagner theorem to systems of lattice spins coupled to itinerant electrons, proving the absence of spontaneous magnetic order in one and two dimensions at finite temperature, with implications for controlling magnetism in semiconductors.

Contribution

It provides a rigorous proof that no long-range magnetic order exists in low-dimensional systems with itinerant electrons, even with spin-orbit interactions, except under specific conditions.

Findings

No long-range magnetic order in 1D and 2D at finite temperature.

Magnetic order can occur with spin-orbit interactions, except when Rashba and Dresselhaus are equal.

Electrical control of magnetism in semiconductors is possible through spin-orbit tuning.

Abstract

We extend the Mermin-Wagner theorem to a system of lattice spins which are spin-coupled to itinerant and interacting charge carriers. We use the Bogoliubov inequality to rigorously prove that neither (anti-) ferromagnetic nor helical long-range order is possible in one and two dimensions at any finite temperature. Our proof applies to a wide class of models including any form of electron-electron and single-electron interactions that are independent of spin. In the presence of Rashba or Dresselhaus spin-orbit interactions (SOI) magnetic order is allowed and intimately connected to equilibrium spin currents. However, in the special case when Rashba and Dresselhaus SOIs are tuned to be equal, magnetic order is excluded again. This opens up a new possibility to control magnetism in magnetic semiconductors electrically.