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The effect of uniaxial strain on electronic structure and magnetism inLaMnO$_3$ is studied from a model Hamiltonian that illustrates the competitionbetween the Jahn-Teller, super exchange, and double exchange interactions. Weretain in our model the three main octahedral distortions ($Q_1, Q_2$, and$Q_3$), which couple to the Mn $(e_g)$ electrons. Our results show the groundstate to be a type A antiferromagnetic (AFM) insulating state for theunstrained case, consistent with experiments. With tensile strain (stretchingalong the c axis), the ground state changes into a ferromagnetic and eventuallyinto a type G$^\prime$ AFM structure, while with compressive strain, we findthe type A switching into a type G structure. The orbital ordering, whichdisplays the well known checkerboard $x^2-1 / y^2-1$ structure for theunstrained case, retains more or less the same character for compressivestrain, while changing into the $z^2-1$ character for tensile strains. While$Q_1$ and $Q_3$ are fixed by the strain components $\varepsilon_{xx}$ and$\varepsilon_{zz}$ in our model, the magnitude of the in-plane distortion mode(Q$_2$), which varies to minimize the total energy, slowly diminishes withtensile strain, completely disappearing as the FM state is entered. Within ourmodel, the FM state is metallic, while the three AFM states are insulating.

Magnetic and Orbital Order in LaMnO$_3$ under Uniaxial Strain: A Model Study