  First-principles calculations reveal a large cooperative coupling of
Jahn-Teller (JT) distortion to oxygen-octahedron rotations in perovskite
LaMnO$_3$. The combination of the two distortions is responsible for
stabilizing the strongly orthorhombic $A$-AFM insulating ($I$) $Pbnm$ ground
state relative to a metallic ferromagnetic (FM-$M$) phase. However, epitaxial
strain due to coherent matching to a crystalline substrate can change the
relative stability of the two states. In particular, coherent matching to a
square-lattice substrate favors the less orthorhombic FM-$M$ phase, with the
$A$-AFM phase stabilized at higher values of tensile epitaxial strain due to
its larger volume per formula unit, resulting in a coupled magnetic and
metal-insulator transition at a critical strain close to 1%. At the phase
boundary, colossal magneto-resistance is expected. Tensile epitaxial strain
enhances the JT distortion and opens the band gap in the $A$-AFM-$I$ $c$-$Pbnm$
phase, offering the opportunity for band-gap engineering. Compressive epitaxial
strain induces an orientational transition within the FM-$M$ phase from
$c$-$Pbnm$ to $ab$-$Pbnm$ with a change in the direction of the magnetic easy
axis relative to the substrate, yielding strain-controlled magnetization at the
phase boundary. The strong couplings between the JT distortion, the
oxygen-octahedron rotations and the magnetic and electronic properties, and
associated functional behavior, motivate interest in other orthorhombic $Pbnm$
perovskites with large JT distortions, which should also exhibit a rich variety
of coupled magnetic, structural and electronic phase transitions driven by
epitaxial strain.
