In the present work, two models based on the mean field approximation and density functional theory are developed for two independent subsystems – the “local-spin exchange” and “conduction band” – in order to analysis the elimination of exchange anisotropy, where the possibility of Kondo-like behavior in gadolinium-element can be investigated. These models allow us to describe the coupled spin-lattice subsystems in direction to remove the intra-layer loop of exchange of “hexagonal” to lower symmetry of “rhombohedral” (crystallography slip). The intra-layer “a–b” loop exchange, which is the cause of exchange anisotropy, was calculated by the exchange eigenvalue–eigenfunction Jij( − ′) between two completely separate magnetic ions (Rij ≥ 3.6 Å ≫ R4f ≈ 0.36 Å) in the metallic Gd-element, where there is no crystal field effect (L = 0) and to a good approximation no notable hybridization in the mean field approximation. In this regard, the pressure induced phase transition of Gd from hexagonal to rhombohedral as the result of the first principle density functional theory by using the Wien2K package within the PBE + U approximation, is investigated. We observed the leakage of d orbitals into f orbitals in the electronic structure of the Gd rhombohedral phase, as well as the coincidence of all three principal directions in the eigenvalue (λmin(K)). Both phenomena can predict the appearance of Kondo-like behavior in Gd.