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

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.

18 pages, 2 figures, final version

References in corpus (9)

• Single-shot read-out of an individual electron spin in a quantum dot
• Driven coherent oscillations of a single electron spin in a quantum dot
• Theory of ferromagnetic (III,Mn)V semiconductors
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Recipes for spin-based quantum computing
• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
• Coulomb scattering cross-section in a 2D electron gas and production of entangled electrons
• Temperature dependence of spin susceptibility in two-dimensional Fermi liquid systems

Cited by in corpus (15)

• Nuclear Spins in Nanostructures
• Nuclear Magnetism and Electronic Order in 13C Nanotubes
• RKKY interaction in carbon nanotubes and graphene nanoribbons
• Spin interactions, relaxation and decoherence in quantum dots
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling
• On-and-off chip cooling of a Coulomb blockade thermometer down to 2.8 mK
• Cooling low-dimensional electron systems into the microkelvin regime
• Momentum dependence of the spin susceptibility in two dimensions: nonanalytic corrections in the Cooper channel
• Spin ordering in magnetic quantum dots: From core-halo to Wigner molecules
• Carrier-density-controlled anisotropic spin susceptibility of two-dimensional hole systems
• Voltage induced conversion of helical to uniform nuclear spin polarization in a quantum wire
• Anisotropic RKKY interactions mediated by $j=3/2$ quasiparticles in half-Heusler topological semimetal
• RKKY interaction at helical edges of topological superconductors
• Coupled-wire descriptions of unconventional quantum states in twisted nanostructures