Permanent Magnetic Moments

In many actinide solids, as we shall see, the experimentally determined magnetic properties are explained well by assuming the permanent magnetic moment due to Hund s rules. The f-electrons are considered atomic, and their interaction with the environment is through crystal field forces or weak exchange forces with conduction electrons. Here, the magnetic properties are explained in the atomic limit. 

One important point is whether narrow bands would display permanent magnetic moments and undergo magnetic collective phenomena. This depends clearly upon their bandwidth and will lead again to the problem localization vs itineracy. In band calculations, new ways have to be looked for, since the set of hypotheses examined previously, which hold for non-magnetic solids, must be corrected for spin-polarization. 

B. A permanent magnetic moment and, possibly, collective magnetic phenomena. 

Ferrite compounds with the inverse spinel structure are similar to magnetite, with different ions substituting for the iron atoms. As with FeO (cf. Figure 6.62), the oxygen ions have no permanent magnetic moment. Tetrahedral sites in the FCC oxygen array are occupied by half of the trivalent cations, and octahedral sites are occupied equally by divalent cations and the remaining trivalent cations. 

Analogous quantities to die electric moments can be defined when the external perturbation takes the form of a magnetic field. In this instance die first derivative defines the permanent magnetic moment (always zero for non-degenerate electronic states), the second derivative the magnetizability or magnetic susceptibility, etc. 

FERROELECTRIC EFFECT. The phenomenon whereby certain crystals may exhibit a spontaneous dipole moment twhich is called ferroelectric by analogy with ferromagnetic—exhibiting a permanent magnetic moment). The effect in the most typical case, barium manate. seems to he due to a polarization catastrophe, in which the local electric fields due lo the polarizuiion itself increase faster than die elastic restoring forces on the ions in Ihe crystal, thereby leading to an asymmetrical shift in ionic positions, and hence lo a permanent dipole moment. Ferroelectric crystals... 

Since (2p r ) can accommodate a total of four electrons, the two electrons of Oz that go in (2p r ) will go into different v orbitals, with spins parallel (Hund s rule) The ground state of Oa has two unpaired electrons. Thus, the oxygen molecule has a permanent magnetic moment, and we say that it is paramagnetic. 

Then the van Vleck formula applies for the magnetization of a paramagnetic system in the absence of a permanent magnetic moment ... 

The further layout of the experiment consists of a first sextupole SI as a spin selector, a microwave cavity, and a second sextupole S2 as a spin analyzer (cf. Fig. 8). Since the magnetic field in SI is higher on the outside, the low-field seekers (1,1) and (1,0) will be focused, while the high-field seekers will move towards the magnet poles and annihilate there. We further assume that the states with Mp = 0 that have no permanent magnetic moment will loose their orientation in the field-free region before SI, so that after SI only atoms in the state (1,1) will remain. 

Magnetic (Natural) Multipoles. Magnetic dipole. In 1905 Langevin, when aiming at an explanation of Curie s law, i.e. of the temperature dependence of magnetic susceptibility in paramagnetics, attributed a priori and classically a permanent magnetic moment to the microsystems. 

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