Three compounds of general formula (NBu4)[MIIRuIII(ox)3] have been synthesized; NBu4 + stands for tetra-n-butylammonium, M for Mn, Fe, and Cu, and ox2- for the oxalate dianion. The X-ray powder patterns for the three derivatives have revealed that these compounds are isostructural with (NBu4)[MnIICrIII(ox)3], whose crystal structure was known, and the cell parameters have been refined in the R3c space group. The (NBu4)[MIIRuIII(ox)3] compounds are new examples of two-dimensional bimetallic assemblies with oxalate bridges. The temperature (T) dependences of the magnetic susceptibility (χM) in both the dc and ac modes and the field dependences of the magnetization have been investigated. The local spins are S Ru = S Cu = 1/2, S Mn = 5/2, and S Fe = 2. The RuIII−MII interaction has been found to be antiferromagnetic for M = Fe and Cu and ferromagnetic for M = Mn. The two compounds (NBu4)[FeIIRuIII(ox)3] and (NBu4)[CuIIRuIII(ox)3] exhibit a ferrimagnetic behavior, characterized by a minimum in the χM T versus T plots. (NBu4)[FeIIRuIII(ox)3] exhibits a long-range magnetic ordering at T c = 13 ± 1 K. A slight frequency dependence of the out-of-phase ac magnetic response has been observed. The field dependence of the magnetization in the magnetically ordered state has revealed a rather strong coercivity, with a coercive field of 1.55 kOe at 2 K. A theoretical model has been used to determine the magnitude of the RuIII−MII interactions, with M = Mn and Fe. This model is based on a quantum−classical spin approach together with Monte Carlo simulations. The interaction parameters have been found as J = 1.04 cm-1 for (NBu4)[MnIIRuIII(ox)3] and −9.7 cm-1 for (NBu4)[FeIIRuIII(ox)3], with a spin Hamiltonian of the type −J∑ i,j S Ru, i · S M, j . The magnetic properties of these compounds have been discussed. In particular, it has been emphasized that the symmetry rules governing the nature and the magnitude of the interaction between two 3d magnetic metal ions seem not to be valid anymore for 4d ions such as RuIII.

We study the planar antiferromagnetic Heisenberg model on a decorated hexagonal lattice, involving both classical spins (occupying the vertices) and quantum spins (occupying the middle of the links). This study is motivated by the description of a recently synthesized molecular magnetic compound. First, we trace out the spin 1 2 degrees of freedom to obtain a fully classical model with an effective ferromagnetic interaction. Then, using high temperature expansions and Monte Carlo simulations, we analyse its thermal and magnetic properties. We show that it provides a good quantitative description of the magnetic susceptibility of the molecular magnet in its paramagnetic phase.The Heisenberg model [1] has a long history and has been extensively studied throughout these last thirty years. While it is exactly solvable in one dimension [2] in some of its versions, it is only through approximate methods that quantitative information can be obtained in higher dimensions. High and low temperature expansions [3,4], Monte Carlo simulations [5,6] and renormalisation group calculations [7,8] have been widely developed and give now a precise account of the critical regime of the model. However, little has been done in the various specific contexts which are now realized in the magnetic molecular materials.For instance, the compound (, exhibits a transition at T c = 15K towards an ordered state. The structure of this material can be schematically described by a superposition of layers of hexagonal lattices with the Mn II ions occupying the vertices and the Cu II ions occupying the middle of the links, as shown in Fig. 1. The interplane-coupling is small, so that the spin system can be considered two-dimensional. In the plane, the nearest neighbour Mn-Cu ions interact through an antiferromagnetic coupling. It is interesting to determine the extent to which such a simple microscopic model with no other interaction included, can quantitatively describe the magnetic and thermal properties of such a complex molecular architecture. Of course, the isotropic O(3) model is critical only at zero temperature [10] and the symmetry breaking at T c = 15K has presumably its origin in a slight spin anisotropy and/or a small interplane coupling. However, one expects for T ≫ T c that the properties of the material are well described by the two-dimensional isotropic antiferromagnetic spin 1 2 -spin 5 2 interaction. This is the problem we investigate in this paper. We denote by S where J is positive, H is the external magnetic field, < i, j > stands for a pair of nearest neighbour spins, N S is the number of sites and N L is the number of links on the honeycomb lattice (N L = 3/2N S ). The spin where we have defined α 1 = S βg 1 µ B , α 2 = 1 2 βg 2 µ B , Ds = NS j=1 sin θ j dθ j dϕ j and X stands for the length of vector X. The indices i and j now label the classical spins located at the vertices of the honeycomb lattice.

Various types of mixed spin two-dimensional Heisenberg networks are investigated by means of Monte Carlo simulations. This study aims at interpreting quantitatively the thermodynamical properties of two-dimensional molecule-based magnets recently synthesized. The proposed model requires that: (i) one of the two magnetic centers has a spin large enough to be treated as a classical spin; (ii) the zero field Hamiltonian is isotropic; (iii) the quantum spins have only classical spins as neighbours. The quantum Hamiltonian is then replaced by a classical one with effective ferromagnetic interactions. The temperature dependence of both the specific heat and magnetic susceptibility are calculated. The effect of the lattice geometry is analysed.