Landau-Khalatnikov theory of anelastic relaxations in spin-crossover materials

Large anelastic relaxations have been found near the transition temperature in spin crossover (SCO) materials due to stress-induced changes in spin state. To investigate the mechanistic aspects of this phenomenon, we develop here a phenomenological framework, based on the Landau theory of phase transitions, incorporating coupling terms between spin state and elastic strain, which is also extended to the dynamic Landau-Khalatnikov regime. We derive an analytical solution for the mechanical response and conduct a parametric study of a cubic SCO system. Our simulations reveal bulk modulus relaxation, internal friction peaks and renormalization of elastic constants near the spin transition - qualitatively matching recent nanoindentation experiments. The work clarifies the roles of bilinear and higher-order couplings in shaping static and dynamic elastic anomalies, with relevance for mechanical actuator design.