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Notes on magnetism II - Magnetic ions in crystals

Talking about the magnetism of ions in crystals naturally brings us out of the atomic physics picture which we previously based ourselves in when discussing the free atom and ions (see previous note by clicking me! ). Also, for sure we should turn to the many-electron scheme instead of a single-electron one. However, to build up the final multi-electron picture, we can potentially take the single-electron pathway. This is quite similar to the situation of independent atoms, where we have been mentioning the coupling between angular momentum of multi-electrons. The pathway we take thereby is also a single-electron one. For example, based on Hund's rule, we talk about filling electrons one-by-one to various energy levels to finally build up the ground state. Here, for discussing the magnetism of ions in crystals, Hund's rule can still be used in some situations. However, attention should be paid and we will revisit this issue later by inspecting a specific example. To start,

Notes on magnetism I - magnetism of free atoms and ions

To understand the magnetism of free atoms and ions, we may go through several stages, as follows, Hartree approximation - electrons are treated in a non-interactive manner. Beyond Hartree - interaction between electrons is taken into account. Spin-orbital coupling. Hyperfine interaction - the interaction between electrons and nucleus. Stage-1: At this stage, the single electron Schrodinger equation can be solved in the spherical potential field and one can get quantized energy levels indexed by quantum number \(n\), \(l\) and \(m\). Hydrogen atom is the simplest and the most special case - the Coulomb potential is rigorously inverse proportional to \(r\) and therefore energy levels with the same \(n\) but different \(l\) are degenerate. For general cases, e. g. hydrogen-like atoms, the effective Coulomb potential is not rigorously inverse proportional to \(r\), as the result of screening effect from the atom core charge (nucleus + electrons). This results in the splitting o

Demo for Coriolis force

First, a comprehensive GIF animation demonstrating the basic ideas of Coriolis force is presented. Then detailed explanation and derivation is presented in the embedded document.