Isomorphism Between The Electro-Elastic Modeling Of The Spin Transition And Ising-Like Model With Competing Interactions: Elastic Generation Of Self-Organized Spin States

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.