A generalized Stoner criterion and versatile spin ordering in two-dimensional spin-orbit coupled electron systems

TL;DR

This paper develops a generalized Stoner criterion for spin polarization in 2D spin-orbit coupled systems, predicting unconventional magnetic phases and mapping their phase diagram, with potential applications in electric-field-controlled spintronics.

Contribution

It introduces a Stoner-type criterion for spin polarization in systems with strong spin-orbit coupling and explores the resulting novel magnetic phases through phase diagram analysis.

Findings

Divergence of spin susceptibility at critical interaction strength.

Identification of out-of-plane and in-plane spin-polarized phases.

Presence of Fermi-liquid phases separated by a Lifshitz transition.

Abstract

Spin-orbit coupling is a single-particle phenomenon known to generate topological order, and electron-electron interactions cause ordered many-body phases to exist. The rich interplay of these two mechanisms is present in a broad range of materials, and has been the subject of considerable ongoing research and controversy. Here we demonstrate that interacting two-dimensional electron systems with strong spin-orbit coupling exhibit a variety of time reversal symmetry breaking phases with unconventional spin alignment. We first prove that a Stoner-type criterion can be formulated for the spin polarization response to an electric field, which predicts that the spin polarization susceptibility diverges at a certain value of the electron-electron interaction strength. The divergence indicates the possibility of unconventional ferromagnetic phases even in the absence of any applied electric or magnetic field. This leads us, in the second part of this work, to study interacting Rashba spin-orbit coupled semiconductors in equilibrium in the Hartree-Fock approximation as a generic minimal model. Using classical Monte-Carlo simulations we construct the complete phase diagram of the system as a function of density and spin-orbit coupling strength. It includes both an out-of-plane spin polarized phase and in-plane spin-polarized phases with shifted Fermi surfaces and rich spin textures, reminiscent of the Pomeranchuk instability, as well as two different Fermi-liquid phases having one and two Fermi surfaces, respectively, which are separated by a Lifshitz transition. We discuss possibilities for experimental observation and useful application of these novel phases, especially in the context of electric-field-controlled macroscopic spin polarizations.