Exchange Energy And Magnetism Of Rare - Earth Metals

In our study of Ferromagnetism, we have used the Heisenberg model as a general frame work. The indirect exchange model of Ruthermann - Kittel interaction (originally proposed for atomic nuclei) is applied to the case of Rare - earth Ferromagnetic systems. This exchange energy (between spins) is calculated as a second order perturbation. The behaviour of the Weiss Mean Field (WMF) which is an approximation of the exchange interaction and the energy spectrum of the spin are presented in graphical form. Calculation of the WMF and the energy against the Fermi Wave Vector (KF) are performed for simple cubic lattice (SC), Body-Centred Cubic lattice (BCC) and Face-Centred Cubic lattice (FCC) configuration along the [100] direction. The results obtained are in good agreement with those found in the literature. The extension to Hexagonal Closed Pack (HCP) which is the common structure in Rare - earth metals is the major contribution of this project. The plots of the WMF and energy against KF along [100], [110] and [111] directions give regions of positive values, thereby satisfying the main condition for Ferromagnetic properties.

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