Skyrmion Crystal from RKKY Interaction Mediated by 2D Electron Gas

TL;DR

This paper demonstrates that RKKY interactions mediated by a 2D electron gas can stabilize a skyrmion crystal, with magnetic ordering wave vectors determined by the Fermi wave number, affecting the Hall conductivity.

Contribution

It introduces a mechanism for skyrmion crystal formation via RKKY interactions influenced by a 2DEG, linking magnetic order to electronic properties.

Findings

Skyrmion crystal stabilized by RKKY interaction in 2DEG.

Magnetic wave vectors proportional to Fermi wave number.

Topological Hall conductivity approaches quantized value.

Abstract

We consider a C$_6$ invariant lattice of magnetic moments coupled via a Kondo exchange $J$ with a 2D electron gas (2DEG). The effective Ruderman-Kittel-Kasuya-Yosida interaction between the moments stabilizes a magnetic skyrmion crystal in the presence of magnetic field and easy-axis anisotropy. An attractive aspect of this mechanism is that the magnitude of the magnetic ordering wave vectors, ${\mathbf Q}_{\nu}$ ($\nu=1,2,3$), is dictated by the Fermi wave number $k_F$: $|{\mathbf Q}_{\nu} |=2k_F$. Consequently, the topological contribution to the Hall conductivity of the 2DEG becomes of the order of the quantized value, $e^2/h$, when $J$ is comparable to the Fermi energy $\epsilon_F$.