The spin-orbital superexchange model is derived for the cubic (perovskite) symmetry of ${\mathrm{LaMnO}}_3$, whereas real crystal structure is strongly deformed. We identify and explain three a priori important physical effects arising from tetragonal deformation: (i) the splitting of $e_g$ orbitals $\propto E_z$, (ii) the directional renormalization of $d\text{−}p$ hybridization $t_{pd}$, and (iii) the directional renormalization of charge excitation energies. Using the example of ${\mathrm{LaMnO}}_3$ crystal we evaluate their magnitude. It is found that the major effects of deformation are an enhanced amplitude of $x^2\text{−}{y}^2$ orbitals induced in the orbital order by $E_z\simeq 300$ meV and anisotropic $t_{pd}\simeq 2.0$ (2.35) eV along the $ab$ ($c$) cubic axis, in very good agreement with Harrison's law. We show that the improved tetragonal model analyzed within mean field approximation provides a surprisingly consistent picture of the ground state. Excellent agreement with the experimental data is obtained simultaneously for: (i) $e_g$ orbital mixing angle, (ii) spin exchange constants, and (iii) the temperatures of spin and orbital phase transition.

• Received 12 September 2017
• Revised 3 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.104417