Microscopic Insight into the Isosymmetric Jahn-Teller Bond Axis Reorientation in Na$_3$MnF$_6$

Using first-principles density functional theory calculations, we investigate the hydrostatic pressure-induced spontaneous reorientation of the Jahn-Teller bond axis in the fluoride cryolite Na$_3$MnF$_6$. We find a first-order isosymmetric transition occurs between crystallographically equivalent monoclinic structures at approximately 2.15 GPa, consistent with earlier experimental studies. Analogous calculations for Na$_3$ScF$_6$ show no evidence of a transition up to 6.82 GPa. Mode crystallography analysis of the pressure-dependent structures in the vicinity of the transition reveals a clear evolution of the Jahn-Teller bond distortions in cooperation with an asymmetrical stretching of the equatorial fluorine atoms in the MnF$_6$ octahedral units. We identify a change in orbital occupancy of the e$_g$ manifold in the d$^4$ Jahn-Teller active Mn(III) to be responsible for the transition, which stabilizes one monoclinic P2$_1$/n variant over the other. From our results, we conjecture that the same transition may be accessible in epitaxially grown thin films of Na$_3$MnF$_6$ with a modest biaxial tensile strain.