Fig. 8: Equation of state fit for bulk Ca2RuO4, the resulting energy, and energy as a function of epitaxial strain.
From: Quantifying the role of the lattice in metal–insulator phase transitions
a Electronic disproportionation as a function of structural disproportionation ΔN(Q) from5 (heavy black points) and polynomial fit (solid line) used for the equation of state. b Correlated electron free energy, and total free energy as a function of the electronic disproportionation order parameter characterizing the orbital polarization: Fel(ΔN) and Ftotal(ΔN) for bulk Ca2RuO4. c Total energy plotted against orbital disproportionation ΔN for materials grown on four substrates indicated in the legend (NSAT is Nd0.4Sr0.6Al0.7Ta0.3O3) which provide different strains relative to the metallic phase of Ca2RuO4. For compressive strain (NdAlO3), the material is always metallic and the orbital polarization has the opposite sign from the insulating state. d Total free energy versus electronic disproportionation ΔN : Ftotal(ΔN) computed for bulk Ca2RuO4 different values of the linear coupling term F3. e Phase diagram of epitaxially constrained Ca2RuO4 in plane of tensile strain (defined as difference of mean in-plane Ru–O bond length from value in the high temperature structure) in Å and electron-lattice coupling parameter F3. Red dashed line: value of F3 at which metal insulator transition occurs in bulk system. Arrows (red on line) indicate strain imposed by epitaxial growth.
