Spin-Orbit Interaction and Kondo Scattering at the PrAlO$_3$/SrTiO$_3$ Interface

We have investigated the effect of oxygen content, in the $P_{O_{2}}$ range of $6\times10^{-6}$ -- $1\times10^{-3}$ torr, on the spin-orbit (SO) interaction at PrAlO$_3$/SrTiO$_3$ interface. The most-conducting 2-D-like PrAlO$_3$ interfaces were not as conducting as comparable LaAlO$_3$ samples, indicating either a steric or mixed-valent effect. The least-conducting, most oxygenated PrAlO$_3$ interface exhibits hole conductivity, a departure from the typical electron-doped behavior. For $10^{-5}$ and $10^{-4}$ torr samples, high-temperature metallic behavior is accompanied by an upturn in resistivity at low temperatures, consistent with Kondo scattering theory; analysis gives a Kondo temperature $ \sim $17 K. The magnetoresistance (MR) for the low $P_{O_{2}}$-grown samples was modeled with a positive part due to weak anti-localization (WAL) from a strong SO interaction, and a negative part due to the Kondo effect. The variation of MR suggests a strong SO interaction for the $10^{-5}$ torr sample with $H_{SO}=$1.25 T in both field orientations. The WAL effect is smaller for higher $P_{O_{2}}$-grown samples, where the high-field MR is dominated by the Kondo effect.