Low dimensionality, broken symmetry and easily-modulated carrier concentrations provoke novel electronic phase emergence at oxide interfaces. However, the spatial extent of such reconstructions - i.e. the interfacial depth - remains unclear. Examinin
g LaAlO$_3$/SrTiO$_3$ heterostructures at previously unexplored carrier densities $n_{2D}geq6.9times10^{14}$ cm$^{-2}$, we observe a Shubnikov-de Haas effect for small in-plane fields, characteristic of an anisotropic 3D Fermi surface with preferential $d_{xz,yz}$ orbital occupancy extending over at least 100~nm perpendicular to the interface. Quantum oscillations from the 3D Fermi surface of bulk doped SrTiO$_3$ emerge simultaneously at higher $n_{2D}$. We distinguish three areas in doped perovskite heterostructures: narrow ($<20$ nm) 2D interfaces housing superconductivity and/or other emergent phases, electronically isotropic regions far ($>120$ nm) from the interface and new intermediate zones where interfacial proximity renormalises the electronic structure relative to the bulk.
The magnetic properties of single-crystal EuTiO3 are suggestive of nanoscale disorder below its cubic-tetragonal phase transition. We demonstrate that electric field cooling acts to restore monocrystallinity, thus confirming that emergent structural
disorder is an intrinsic low-temperature property of this material. Using torque magnetometry, we deduce that tetragonal EuTiO3 enters an easy-axis antiferromagnetic phase at 5.6 K, with a first-order transition to an easy-plane ground state below 3 K. Our data is reproduced by a 3D anisotropic Heisenberg spin model.
