1.A coexistence phase of antiferromagnetism and superconductivity was recently observed in a series of heavy fermion compounds (see, e.g., review [1]). In Ce based heavy fermion compounds, the coexistence phase of antiferromagnetism and superconductivity is often achieved by the change in the ground state due to the application of an external hydrostatic pressure. For example, CeIn 3 [2], CeRhIn 5 [3], and Ce 2 RhIn 8 [4] are considered as such compounds.A phenomenological two liquid model was pro posed in [5] on the basis of experimental data. This model made it possible to describe the thermody namic, magnetic, and transport properties of many heavy fermion materials. Its main idea is connected with the existence of the coherence temperature T* below which the thermodynamic characteristics are determined by two different contributions. The first contribution is due to the presence of Kondo impuri ties. The second contribution is determined by the hybridization processes of localized electrons with the conduction electrons leading to the formation of the heavy fermion coherent state. The temperature T* is related to the parameter ⑀ = J sd ρ(E F ), where J sd is the integral of the s-d exchange interaction and ρ(E F ) is the density of states on the Fermi level. For a series of heavy fermion compounds, the parameter ⑀ is directly related to the type of phase transition at low tempera tures [6]. In [7], a mechanism was proposed according to which the transition from the antiferromagnetic phase to the superconducting phase with increasing external pressure is explained by the growth of ⑀.In the phenomenological approach, the problem of the microscopic mechanisms determining the struc ture of the phase diagram of, e.g., CeRhIn 5 , remains open. Furthermore, an important question of whether different interactions or the same interaction induces transitions to the superconducting and antiferromag netic states is not considered. The possibility of imple menting the coexistence phase of antiferromagnetism and superconductivity in heavy fermion systems was considered on the microscopic level in [8,9].In this work, we show that the microscopic mecha nism of forming the coexistence phase of antiferro magnetism and superconductivity with the d wave superconducting order parameter can be related to the presence of the exchange interaction in the subsystem of the localized moments. The calculations were per formed on the basis of the effective periodic Anderson model, which takes into account the superexchange interaction in a system of localized f electrons. The conditions under which the coexistence phase of anti ferromagnetism and superconductivity corresponding to that observed experimentally is implemented were obtained. The proposed model reflects well the fea tures of the electron structure of Ce based heavy fer mion intermetallides (e.g., CeRhIn 5 ), since the same Ce 4f electrons in them are responsible for the estab lishment of the antiferromagnetic ordering and super conductivity [10]. An important conclusion obtai...
