Isomorphism between the electro-elastic modeling of the spin transition and Ising-like model with competing interactions: Elastic generation of self-organized spin states

Abstract

Elastic modeling of spin-crossover materials has boomed remarkably these last years. Among these models, the electro-elastic model combining spin and lattice degrees of freedom showed good abilities of fair description of the thermodynamics and spin-crossover solids. In the present work, we explore a new treatment of this model based on a homogeneous description of the lattice spacing with well separate relaxation timescales for the lattice and spin state degrees of freedom. This description is analogous to the Born–Oppenheimer approximation and allows analytic treatment of the elastic part of the model, thus simplifying considerably the model resolution. As a result, we have been able to demonstrate the equivalence between the genuine electro-elastic model and an Ising-like Hamiltonian with competing long-range ferro-like and short-range (nearest neighbors and next-nearest neighbors along diagonals) antiferro-like interactions, whose relationship with the high-spin to low-spin misfit elastic energy has been established. This model generates intrinsic elastic frustration in the lattice, which leads to a rich variety of hysteretic first-order transitions made of one- two-, three-, or four-step behaviors. Complex self-organizations of the spin states are evidenced in the plateau regions in the form of checkerboard-like, stripes-like patterns, constituted of alternate high-spin and low-spin ferro-like stripes or alternate ferro high-spin (or low-spin) and antiferro-like chains, as well labyrinth structures.