Upper bound for the s-d exchange integral in n-(Ga,Mn)N:Si from magnetotransport studies

A series of recent magnetooptical studies pointed to contradicting values of the s-d exchange energy N0{\alpha} in Mn-doped GaAs and GaN as well as in Fe-doped GaN. Here, a strong sensitivity of weak-localization phenomena to symmetry breaking perturbations (such as spin-splitting and spin-disorder scattering) is exploited to evaluate the magnitude of N0{\alpha} for n-type wurtzite (Ga,Mn)N:Si films grown by metalorganic vapor phase epitaxy. Millikelvin magnetoresistance studies and their quantitative interpretation point to N0{\alpha} < 40 meV, a value at least 5 times smaller than the one found with similar measurements on, e.g., $n$-(Zn,Mn)O. It is shown that this striking difference in the values of the s-d coupling between $n$-type III-V and II-VI dilute magnetic semiconductors can be explained by a theory that takes into account the acceptor character of Mn in III-V compounds.