Localized magnetism

We now come back to the important example of two spin 1/2 nuclei with the dipole-dipole interaction discussed above. In simple physical tenns, we can say that one of the spins senses a fluctuating local magnetic field originatmg from the other one. In tenns of the Hamiltonian of equation B 1.13.8. the stochastic fiinction of time F l t) is proportional to Y2 (9,( ))/rjo, where Y, is an / = 2 spherical hannonic and r. is the... 

If energy of the proper frequency is supplied, a transition between these quantum states occurs with the absorption of an amount of energy equal to the separation of the states. The frequency of the absorbed radiation lies in the radio-frequency range and depends on the local magnetic field at the atom in question. 

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

Compute the dip angle of the magnetic field vector after correction for the drill collar field, it should check with the local magnetic field data. What do you conclude if it does not ... 

All nuclei in molecules are surrounded by electrons. When an external magnetic field is applied to a molecule, the electrons moving around nuclei setup tiny local magnetic fields of their own. These local magnetic fields act in opposition to the applied field so that the effective field actually felt by the nucleus is a bit weaker than the applied field. 

We said previously that differences in chemical shifts are caused by the small local magnetic fields of electrons surrounding the different nuclei. Nuclei that are more strongly shielded by electrons require a higher applied field to bring them into resonance and therefore absorb on the right side of the NMR chart. Nuclei that are less strongly shielded need a lower applied field for resonance... 

Each electronically distinct 1H or 13C nucleus in a molecule comes into resonance at a slightly different value of the applied field, thereby producing a unique absorption signal. The exact position of each peak is called the chemical shift. Chemical shifts are caused by electrons setting up tiny local magnetic fields that shield a nearby nucleus from the applied field. 

Anderson PW. 1961. Localized magnetic states in metals. Phys Rev 124 41-53. 

The third prominent interaction in iron Mossbauer spectroscopy is the magnetic hyperfine interaction of the Fe nucleus with a local magnetic field. As explained in detail in Chap. 4, it can be probed by performing the Mossbauer experiment in the presence of an applied external magnetic field. 

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