Landau theory for non-symmetry-breaking electronic instability coupled to symmetry-breaking order parameter applied to Prussian blue analog

Different types of ordering phenomena may occur during phase transitions, described within the universal framework of the Landau theory through the evolution of one, or several, symmetry-breaking order parameters \ensuremath{\eta}. In addition, many systems undergo phase transitions related to an electronic instability, in the absence of symmetry breaking and eventually described through the evolution of a totally symmetric order parameter $q$ linearly coupled to volume change. Analyzing the coupling of a non-symmetry-breaking electronic instability, responsible for volume strain, to symmetry-breaking phenomena is of importance for many systems in nature and here we show that the symmetry-allowed $q{\ensuremath{\eta}}^{2}$ coupling plays a central role. We use as a case study the rubidium manganese hexacyanoferrate Prussian blue analog, exhibiting phase transitions with hysteresis that may exceed 100 K, and based on intermetallic charge transfer (CT). During the phase transition, the intermetallic CT described through the evolution of $q$ is coupled to cubic-tetragonal ferroelastic symmetry breaking described through the evolution of \ensuremath{\eta}. In this system, the symmetry-breaking and non-symmetry-breaking deformations have similar amplitudes but the large volume strain is mainly due to CT. We analyze both the ferroelastic and the CT features of the phase transition within the frame of the Landau theory, taking into account the $q{\ensuremath{\eta}}^{2}$ coupling, stabilizing concomitant CT, and Jahn-Teller distortion. The results show that the phase transition and its wide thermal hysteresis originate from the coupling between both processes and that the elastic coupling of each order parameter with the volume strain is responsible for the $q{\ensuremath{\eta}}^{2}$ coupling. The phase diagrams obtained with this model are in good qualitative agreement with various experimental findings and apply to diverse families of materials undergoing Mott transition, spin-crossover, neutral-ionic transition, etc., for which isostructural electronic instability driving volume strain can couple to symmetry-breaking or not, create phase transition lines, and drive cooperative phenomena.