Electron-mediated ferromagnetism and small spin-orbit interaction in a molecular-beam-epitaxy grown n-type $GaAs/Al_{0.3}Ga_{0.7}As$ heterostructure with Mn $\delta$-doping

We report the first evidence of electron-mediated ferromagnetism in a molecular-beam-epitaxy (MBE) grown $GaAs/Al_{0.3}Ga_{0.7}As$ heterostructure with Mn $\delta$-doping. The interaction between the magnetic dopants (Mn) and the Two-Dimensional Electron Gas (2DEG) realizes magnetic ordering when the temperature is below the Curie temperature ($T_{C} \sim 1.7K$) and the 2DEG is brought in close proximity to the Mn layer by gating. The Anomalous Hall Effect (AHE) contribution to the total Hall resistance is shown to be about three to four orders of magnitude smaller than in the case of hole-mediated ferromagnetism indicating the presence of small spin-orbit interaction.