  Quantum interference between time-reversed electron paths in two dimensions
leads to the well-known weak localization correction to resistance. If
spin-orbit coupling is present, the resistance correction is negative, termed
weak anti-localization (WAL). Here we report the observation of WAL coexisting
with exchange coupling between itinerant electrons and localized magnetic
moments. We use low-temperature magneto-transport measurements to investigate
the quasi-two-dimensional, high-electron-density interface formed between
SrTiO$_3$ (STO) and the anti-ferromagnetic Mott insulator NdTiO$_3$ (NTO). As
the magnetic field angle is gradually tilted away from the sample normal, the
data reveals the interplay between strong $k$-cubic Rashba-type spin-orbit
coupling and a substantial magnetic exchange interaction from local magnetic
regions. The resulting quantum corrections to the conduction are in excellent
agreement with existing models and allow sensitive determination of the small
magnetic moments (22 $\mu_B$ on average), their magnetic anisotropy and mutual
coupling strength. This effect is expected to arise in other 2D magnetic
materials systems.
