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We report on the phase diagram of competing magnetic interactions atnanoscale in engineered ultra-thin trilayer heterostructures ofLaTiO$_{3}$/SrTiO$_{3}$/YTiO$_{3}$, in which the interfacial inversion symmetryis explicitly broken. Combined atomic layer resolved scanning transmissionelectron microscopy with electron energy loss spectroscopy and electricaltransport have confirmed the formation of a spatially separated two-dimensionalelectron liquid and high density two-dimensional localized magnetic moments atthe LaTiO$_3$/SrTiO$_3$ and SrTiO$_3$/YTiO$_3$ interfaces, respectively.Resonant soft X-ray linear dichroism spectroscopy has demonstrated the presenceof orbital polarization of the conductive LaTiO$_3$/SrTiO$_3$ and localizedSrTiO$_3$/YTiO$_3$ electrons. Our results provide a route with prospects forexploring new magnetic interfaces, designing tunable two-dimensional$d$-electron Kondo lattice, and potential spin Hall applications.

Magnetic interactions at the nanoscale in trilayer titanates LaTiO$_3$/SrTiO$_3$/YTiO$_3$