Skyrmion crystal from RKKY interaction mediated by 2DEG

Skyrmion crystals have been found in centro-symmetric itinerant magnets, where the long-range Ruderman-Kittel-Kasuya-Yoshida (RKKY) effective coupling is believed to be the dominant interaction between the local moments. In this work we show that the RKKY interaction mediated by a dilute (k_F«1) 2D electron gas (2DEG) on a C₆ invariant lattice stabilizes a magnetic skyrmion crystal in the presence of magnetic field and easy-axis anisotropy. A remarkable aspect of this mechanism is that the ordering wave vectors of the resulting skyrmion crystal are dictated by the Fermi wave vector: |Q_ν|=2k_F (ν=1,2,3). Consequently, the topological contribution to the Hall conductivity of the 2DEG becomes very large within the weak-coupling regime: the quantized value e²/h is reached when J becomes comparable to the Fermi energy E_F.