Correlation effects in the cohesion and magnetic properties of transition metals

The variational method of Stollhoff and Fulde is applied to a model Hamiltonian describing the $d$ band of a transition metal to obtain the correlated ground state. The model used includes the Coulomb and exchange intra-atomic energies and is rotationally symmetric in orbital and spin space. The calculated cohesion energy has a minimum for a half-filled $d$ band, which is connected with gradual localization of a magnetic moment in the presence of the Hund's-rule exchange interaction. At the same time the charge fluctuations are strongly suppressed and spin fluctuations enhanced. We have found a corrected Stoner criterion which gives a ferromagnetic ground state for realistic values of the model parameters for $3d$ metals, and is in agreement with the exact result of Kanamori at very low electron and hole concentrations.