  Complex oxide heterostructures display some of the most chemically abrupt,
atomically precise interfaces, which is advantageous when constructing new
interface phases with emergent properties by juxtaposing incompatible ground
states. One might assume that atomically precise interfaces result from
stoichiometric growth, but here we show that the most precise control is
obtained for non-stoichiometric growth where differing surface energies can be
compensated by surfactant-like effects. For the precise growth of
Sr$_{n+1}$Ti$_n$O$_{3n+1}$ Ruddlesden-Popper (RP) phases, stoichiometric
deposition leads to the loss of the first RP rock-salt double layer, but
growing with a strontium-rich surface layer restores the bulk stoichiometry and
ordering of the subsurface RP structure. Our results dramatically expand the
materials that can be prepared in epitaxial heterostructures with precise
interface control---from just the $n=\infty$ end members (perovskites) to the
entire RP family---enabling the exploration of novel quantum phenomena at a
richer variety of oxide interfaces.
