Paramagnetism Pauli

Most metals show paramagnetic behaviour. It is rather small and independent of temperature and is quite different from the Curie law behaviour of a normal paramagnetic ion. The cause of the weak paramagnetism was explained by Pauli in terms of the Fermi-Dirac statistics of electrons in solids. It is known as Pauli paramagnetism. 

All electrons not in the conduction band will be in filled shells, paired, and not magnetically active. 

The band model just outlined would lead to the expectation that all metals would show Pauli paramagnetism. However, three 3d transition metals, iron, cobalt and nickel, together with a few lanthanides, are ferromagnetic metals. The simple band picture must be expanded to account for this complication. 

When the density of states at the Fermi surface is calculated with a high precision, it is found that only the three metals iron, cobalt and nickel will have sufficient exchange energy to retain a ferromagnetic state. The experimental value of the magnetic moment (Table 12.4) is also calculated to be equal to the number of holes in the d band. Thus, the d band of iron contains 7.78 electrons, (2.22 holes). 

Such a shift in metals is large enough for the re-occupancy of energy levels (Fig. 7.8). The difference in populations (n — na) generates the magnetisation 

---

Pauling s rules Pauli paramagnetism Pavabid Pavements Pavidon Paving... 

Na3Hg, as a typical example of the first group, exhibits Pauli paramagnetism (/mol 3 x 10-5) at higher temperatures with a weak but significant temperature dependence [4], In particular the a/p phase transition for Na3Hg at 309 K is reflected in a x change of about 5%. 

Maki K (1964) Pauli paramagnetism and the superconducting state n. Prog Theor Phys 32 29-36... 

In other solids, Pauli paramagnetism is found to be explained in the band limit. In others, still, an intermediate behaviour is encountered. 

The density of states at the Fermi-level N(pp) is responsible for many electronic properties, e.g. the electronic contribution to the low-temperature specific heat of a solid, and the Pauli paramagnetic moment of conduction electrons. The specific heat contribution may be written as ... 

Fig. 13. Modification of N(E) under the effect of a perturbing agent and equalization of the electron population to the same (Fermi) level. The picture illustrates qualitatively (N(E)a E for simplicity) the statistical procedure in the derivation of Pauli paramagnetism and in the Stoner theory...

A net magnetic moment is obtained which gives rise to Pauli paramagnetism ... 

To derive the magnetic susceptibility the argument then follows lines which are similar to the treatment of Pauli paramagnetism. Essentially (see Fig. 13), the two populations must have the same pp, and this causes a disequilibrium leading to a net magnetic moment (n+ - n ). The paramagnetic susceptibility is given as ... 

In one sample, the crossover from the metallic (Pauli paramagnetic) region to the diamagnetic state occurred at 32 K. The diamagnetism measured was rather weak, on the order of 1% Meissner fraction, as compared to a pure superconductor (-1/47T, the full Meissner effect). 

Pauli paramagnetism + 10 Independent None Spin and orbital motion of delocalised electrons... 

Takeda, 1983) shows that Fe in this oxide is in the high-spin state down to 4K. CaFeOj, on the other hand, shows disproportionation of Fe to Fe and Fe below 290 K. In the last but one column containing S = j cations, metallic and Pauli paramagnetic LaNiOj should be separated from antiferromagnetic YNiOj and LuNiOj, indicating that in LaNiOj b > b and in YNiOj b < b . Similarly, LaCoOj should be separated from LaRhOj because the latter is a narrow gap semiconductor with a filled t2g n ) band and an empty eg a ) band. 

The large phase shifts t 2 give a large enhancement of the resistivity when transitional metals are dissolved in other metals. A survey for solid metals is given by Friedel (1956), and for solutions of Fe and Co in liquid germanium and tin by Dreirach et al (1972). The resonance will also enhance the electronic specific heat and the Pauli paramagnetism, but these quantities cannot be treated quantitatively without including correlation as shown in Chapter 3. 

We emphasize that the use of g in these equations may be justified only if /—a, because of the Edwards cancellation theorem (Section 6). We should expect a metal-insulator transition to occur for some value of in the neighbourhood of For several liquid systems there is experimental evidence that the interference term in (52) is absent. Thus for liquid TeTl alloys, with variation of composition and temperature, for a less than the Ioffe-Regel value e2/3hai the conductivity is proportional to the square of the Pauli paramagnetic susceptibility and then to 2. These results are due to Cutler (1977). Warren (1970a, b, 1972a, b) examined... 

We note that when moments do not appear an enhancement of the Pauli paramagnetism x is expected of the form... 

---