  We investigate the effect of epitaxial strain on [001]-oriented LaAlO3 using
first-principles density functional calculations. We find a series of
structural phase transitions between states characterized by distinct patterns
of tilting of the AlO6 octahedra. By tuning the biaxial strain from compressive
to tensile, we induce an evolution in the crystal structure in which the tilt
axis changes from out-of-plane to in-plane, corresponding to space groups
I4/mcm and Imma. We also study the effect of uniaxial relaxation of the usual
biaxial epitaxial constraint and explore this as a mechanism for selectively
stabilizing different patterns of octahedral tilts.
