  The oxide heterostructure [(YFeO$_3$)$_5$(LaFeO$_3$)$_5$]$_{40}$, which is
magnetically ordered and piezoelectric at room temperature, has been
constructed from two weak ferromagnetic AFeO$_3$ perovskites with different A
cations using RHEED-monitored pulsed laser deposition. The polarisation arises
through the removal of inversion centres present within the individual AFeO$_3$
components. This symmetry reduction is a result of combining ordering on the A
site, imposed by the periodicity of the grown structure, with appropriate
orientations of the octahedral tilting characteristic of the perovskite units
themselves, according to simple symmetry-controlled rules. The polarisation is
robust against A site interdiffusion between the two layers which produces a
sinusoidally modulated occupancy that retains the coupling of translational and
point symmetries required to produce a polar structure. Magnetization and
magneto-optical Kerr rotation measurements show that the heterostructure's
magnetic structure is similar to that of the individual components. Evidence of
the polarity was obtained from second harmonic generation and piezoelectric
force microscopy measurements. Modeling of the piezoresponse allows extraction
of $d_{33}$ (approximately 10 pC/N) of the heterostructure, which is in
agreement with DFT calculations.
