Decoupling the effects of geometry and nature of strain in LaMnO$_3$: Interplay of dynamic correlations and uniaxial strain driving magnetic phase transitions

Abstract: Recent years have seen tremendous progress in experimental techniques to create uniaxial strain. Motivated by these advances we investigate the effect of uniaxial strain on LaMnO$_3$ employing ab-initio dynamical mean-field theory, and put it in contrast to biaxial strain that occurs in epitaxial systems. Projecting on the low-energy subspace of Mn $3d$ states, and solving multi-impurity problems, our approach emphasizes on local dynamic correlations at Mn sites. At ambient pressures, LaMnO$_3$ crystallizes in an orthorhombic unit cell, with in-plane lattice constants $a<b$, and shows an A-type antiferromagnetic ground state. If we apply uniaxial compressive strain such that the in-plane lattice becomes square with lattice constant $a$, we find a ferromagnetic insulating state. This is in sharp contrast to DFT results using various functionals like PBE, PBE+$U$, and hybrid functionals like HSE, which all predict a half-metallic ferromagnetic behaviour. Interestingly, applying uniaxial tensile strain, such that the in-plane lattice becomes square with the longer lattice constant $b$, an antiferromagnetic insulating state is observed. We trace back these results to the reduction in Jahn-Teller distortion in the case of compressive strain, favoring a ferromagnetic state. This reduction is absent in the tensile case, and the antiferromagnetic state therefore survives. Our study shows that it is the flavour of the strain (compressive or tensile) which is decisive for the magnitude of Jahn-Teller distortions and, hence, the magnetic state.