Arrhenius Monte Carlo study of two-step spin crossover: Equilibrium and relaxation paths

Abstract

We analyze the static and dynamical properties of cooperative two-step spin-crossover solids adopting an Ising-like model where the states $+1$ and $\ensuremath{-}1$ represent the high-spin (HS) state and the low-spin (LS) state, respectively. The model consists of two equivalent sublattices with a ``ferro'' intrasublattice interaction which causes the uniform order of HS or LS in a sublattice and an ``antiferro'' intersublattice interaction which tends to have an opposite state in each sublattice, which is a key ingredient of the two-step transition. At high temperatures both sublattices are in the HS state, and in the LS state at low temperatures. At intermediate-temperatures, the system may show an intermediate temperature phase where the sublattices have different states. By means of a mean-field analysis and a Monte Carlo method, we analyze the stability of this intermediate antiferromagnetic (AF) phase in the equilibrium phase diagram. We find that the temperature region of the AF phase increases linearly with the ``antiferromagnetic'' interaction. Dynamical properties of this model are also investigated in detail by using a Monte Carlo method. For the spin-crossover problem, the adequate choice of the transition rates is of Arrhenius type, rather than of Glauber or Metropolis. This suited choice allows us to obtain nonlinear sigmoidal (S-shaped) relaxation curves of the HS fraction at low temperatures, in good agreement with the experimental shapes. A plateau appears in the relaxation from the HS state in the low-temperature phase as a reminiscence of the thermal plateau obtained at the equilibrium. We also find that the metastability changes nonmonotonically with temperature. We then investigate its mechanism from a viewpoint of the contour diagram of the free energy in the mean-field metastable states and the flow of the order parameters on the diagram. This nonmonotonic behavior of the lifetime of the metastable state is explained as a result of the double role of the temperature in this model.