The specific heat and the magnetization of the Fe4 and the Fe8 SMMs

We study the thermal properties of the quantum and classical models of the Fe4 and Fe8 SMMs in the presence of an arbitrary constant magnetic field, obtaining the β-expansions of the Helmholtz free energy of the models up to orders β26, β25 and β26 for the spin-5 (Fe4), the spin-10 (Fe8) and their classical models respectively. These expansions are functions of the arbitrary set of parameters in their Hamiltonians. We show that the specific heat per site of the Fe8 SMM can be well approximated by its classical analogue with a precision of up to 2%, but the same is not true for the spin-5 Fe4 SMM. The three components of the quantum magnetization per site of these two SMMs are all well represented by their respective classical functions. We also show that the value of the x component of the magnetization per norm of the spin-S operator differs very little for the two SMMs (S=5,10) when these are compared at different temperatures (TFe8=113TFe4) and magnetic fields (hFe8=113hFe4). The same is also true for the z component of the magnetization. Finally, we calculate the average of the quantum specific heat per site of these SMMs for a powder sample distributed either on a plane or in three-dimensional space.