Explaining the origin of the orientation of the front transformation in spin-transition crystals

Abstract

Preferred orientations of the macroscopic high-spin (HS) low-spin (LS) interfaces appearing in spin transition molecular crystals during their phase transitions are explained through the study of a generalized 3D version of the electroelastic model accounting for an anisotropic change of the lattice parameters, $a, b$, and $c$ at the transition. The investigations are performed at 0 K by analyzing the energy landscape of a lattice made of two HS and LS phases, separated by a tilted interface with variable orientation, $\ensuremath{\theta}$ as a function of the anisotropy ratio, $\ensuremath{\lambda}=\frac{\mathrm{\ensuremath{\Delta}}b}{\mathrm{\ensuremath{\Delta}}a}=\frac{\mathrm{\ensuremath{\Delta}}b}{\mathrm{\ensuremath{\Delta}}c}$, where $\mathrm{\ensuremath{\Delta}}x={x}_{\mathrm{HS}}\ensuremath{-}{x}_{\mathrm{LS}}$ is the lattice misfit along $x\phantom{\rule{4pt}{0ex}}(\phantom{\rule{0.16em}{0ex}}=a,b,c)$ direction between HS and LS states. For large $\ensuremath{\lambda}<0$, the $\ensuremath{\theta}$ dependence of the relaxed total elastic energy depicts a symmetric double-well structure with two stable positions, ${\ensuremath{\theta}}_{\mathrm{min}}$, and an unstable orientation ${\ensuremath{\theta}}_{\mathrm{max}}={90}^{\ensuremath{\circ}}$. Beyond a critical value, ${\ensuremath{\lambda}}_{C}^{\ensuremath{-}}<0$, only one minimum subsists at $\ensuremath{\theta}={90}^{\ensuremath{\circ}}$, thus recalling the behavior of an order parameter of a 2nd order phase transition. On increasing $\ensuremath{\lambda}$, this minimum survives until a second threshold value ${\ensuremath{\lambda}}_{C}^{+}>0$ above which, the elastic energy recovers a double well configuration with two new preferential interface orientations, highlighting the existence of a re-entrant phenomenon. We demonstrate that the behavior of ${\ensuremath{\theta}}_{\mathrm{min}}$ versus $\ensuremath{\lambda}$ follows the same universality class as that of a second-order phase transition, for which we calculate the critical exponents $\ensuremath{\beta}$ and $\ensuremath{\nu}$ through a finite size scaling analysis. Overall, these investigations reveal that in switchable molecular solids with anisotropic unit cell deformation between the LS and HS states, there exists a stress-free interface orientation ensuring their integrity upon a large number of thermal cycles or loads during their practical utilization