Antiferromagnetic $s-d$ exchange coupling in GaMnAs

Molecular beam epitaxy growth of GaMnAs is typically performed at low substrate temperatures ($\sim$250 $^{\circ}$C) and high As overpressures leading to the incorporation of excess As and Mn interstitials that quench optical signals, such as photoluminescence. In this work, optical quality samples of paramagnetic Ga$_{1-x}$Mn$_{x}$As-Al$_{0.4}$Ga$_{0.6}$As quantum wells with x $<$ 0.0005 are achieved by performing crystal growth at a substrate temperature of 400 $^o$C. Electronic and structural measurements demonstrate that this elevated temperature reduces As defects while allowing the substitutional incorporation of Mn into Ga sites. Using time-resolved optical spectroscopy, the electron spin coherence is measured allowing for the extraction of the sign and magnitude of the conduction band spin splitting due to the $s-d$ exchange interaction ($N_{0}\alpha$), whose sign is negative and magnitude varies as a function of well width. In the limit of wide quantum wells $N_{0}\alpha$ $<$ 0 indicating that antiferromagnetic $s-d$ exchange is a bulk property of GaMnAs. Polarization-resolved photoluminescence spectroscopy is used to measure the total excitonic spin splitting due to the $sp-d$ exchange interactions, $N_{0}(\alpha-\beta)$, and thus the sign and magnitude of the $p-d$ exchange constant ($N_{0}\beta$) is found.