Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas

TL;DR

This paper explores how nuclear spins in a 2D electron gas can exhibit magnetic order influenced by electron-electron interactions, revealing potential for ferromagnetic ordering and increased Curie temperatures.

Contribution

It derives an effective RKKY-type Hamiltonian for nuclear spins in a 2D electron gas considering electron-electron interactions, linking low-dimensional magnetism with electron system non-analyticities.

Findings

Nuclear spins can locally order ferromagnetically.

Electron-electron interactions enhance the Curie temperature.

Magnetic ordering depends on the electron spin susceptibility behavior.

Abstract

We investigate the magnetic behavior of nuclear spins embedded in a 2D interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins which is of the RKKY type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility, and thus provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. Using various perturbative and non-perturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as function of its wave vector, we show that the nuclear spins locally order ferromagnetically, and that this ordering can become global in certain regimes of interest. We demonstrate that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.