Monte Carlo simulations for 1- and 2D spin crossover compounds using the atom–phonon coupling model Aurelian Rotaru a,b , Adrian Carmona a , Flavien Combaud a , Jorge Linares a, * , Alexandru Stancu b , Jamil Nasser c a ‘‘Groupe d’Etude de la Matière Condensée” (GEMaC), CNRS-UMR 8635, UVSQ, 78035 Versailles Cedex, France b Faculty of Physics, Department of Physics, Alexandru Ioan Cuza University, Iasi, Bdul Carol I, nr 11, 6600, Romania c Laboratoire LISV, Université de Versailles St. Quentin, 45 Av. des Etats-Unis, 78035 Versailles Cedex, France article info Article history: Available online 10 December 2008 Keywords: Spin crossover First order phase transition Atom–phonon coupling abstract In this contribution we have simulated, using the Monte Carlo–Metropolis technique, the thermal behav- ior of an one dimensional and of a square lattice spin crossover system. In the one dimensional case, a long-range interaction parameter must be included in order to obtain a thermal hysteresis. For the square lattice we have tacked into account the nearest as well the next-near- est neighbors. We show the role of the elastic constant ratio on the hysteresis width. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Spin crossover phenomenon occurs in some six-coordinate first-row transition metal complexes as a result of an electronic instability that is driven by temperature, pressure or electronic radiation. These external constraints induce structural changes at molecular as well as lattice level [1–3]. This contribution concerns the iron(II) (3d 6 ) spin crossover compounds that are the most investigated systems. These kind of compounds changes from dia- magnetic (S = 0) to paramagnetic (S = 2) spin states. A first-order phase transition is observed in some spin crossover compounds at the solid state, and this particular behavior is the fingerprint of an interaction between the molecules. Many models have been proposed to explain this spin crossover phenomenon [4–7]. Re- cently it has been shown that the behavior of the spin crossover compounds, either diluted or undiluted, can be obtained by using a microscopic model based on an atom–phonon coupling mecha- nism [8,9]. In this model the spin crossover compounds molecules are modeled as atoms with two electronic states: a ground state (LS) and one excited state (HS) which are interconnected by springs. The gap energy between these LS and HS states is D. The basic idea of this model is to assume that the elastic constant of the spring depends on the electronic state of the two near-neigh- bor coupled molecules; the interactions intensities have been eval- uated from phonon contribution. The thermal variation of the high spin fraction is obtained from the competition between the elec- tronic parameter D, which is favoring the (LS) state and the pho- nons which are favoring the (HS) state. This model has been solved in the mean field approximation [8,9]. In this contribution we have used the Monte Carlo–Metrop- olis numerical simulations in order to reproduce the behavior of 1D and 2D spin crossover compounds. In the next section we present the atom–phonon coupling mod- el and we are introducing the reduced parameters. The results of the Monte Carlo–Metropolis simulations are presented in Section 3. New considerations for 2D spin crossover compounds are shown in Section 4. 2. Atom–phonon coupling model It is considered the one dimensional [8,9] case where the mol- ecules are coupled to each other by springs. The molecules have two electronic levels (LS) and (HS) and the difference in energy is D. To each molecule we have associated a fictitious-spin ^ r with eigenvalues 1 (corresponding to the fundamental level LS) and +1 (corresponding to the HS level). The degeneracy of LS level is 1 and that of the HS level is r. So, in function of the electronic state of the neighbor molecules we have three types of elastic constants: (see Fig. 1): k when both molecules are in the (LS) state, m when both are in the (HS) state and l when one atom is in the (LS) level and the other in the (HS) level. In the mean field approximation this leads to the naturally introduction of long and short-range interaction. The total Hamiltonian of the chain is the sum: H ¼ H spin þ H phon , where H spin ¼ X D 2 ^ r i ; ð1Þ is the spin Hamiltonian and 0277-5387/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2008.10.053 * Corresponding author. E-mail address: jlinares@physique.uvsq.fr (J. Linares). Polyhedron 28 (2009) 1684–1687 Contents lists available at ScienceDirect Polyhedron journal homepage: www.elsevier.com/locate/poly