Neutron paramagnetic form factor

Neutron paramagnetic form factor 99 3.4. The electronic polaron model 127... 

Under a uniform magnetic field H a paramagnetic material develops a macroscopic magnetization given by in = xH. The magnetization is not uniform on the microscopic scale, because it reflects the spatial distribution of the electrons which are polarized by the field. In a crystalline material the magnetic moment distribution m r) is a periodic function of the lattice, and the neutron paramagnetic form factor measures its Fourier transform m(G), where <7 is a reciprocal lattice vector (Moon 1986, Stassis... 

Stassis and co-workers (Stassis et al. 1985, 1986) have measured the neutron paramagnetic form factors of three superconducting heavy-fermion systems, CeCu2Si2, UPtj and UBei3, both above and below their critical temperatures. The material CeCu2Si2 has 1 K. The form factor x(G) at 4.2 K is well fitted by the theoretical atomic form factor for Ce state, i.e. one electron in the 4f sheU, as shown in fig. 10. The form factor remains the same at 300 K where the susceptibility is Curie-Weiss, and at 0.1 K where the material is superconducting. This indicates that the same set of electrons are polarized by the magnetic field at all three temperatures. The resistivity maximum of this material appears at about 20 K and the Curie temperature is... 

Fig. 10. The neutron paramagnetic form factor of CeCu2Si2 (Stassis et al. 1985). The magnetic scattering amplitude is proportional to the form factor x(G)- The solid curve is the theoretical form factor for Ce state, which is the Fourier transform of the magnetic moment distribution for one 4f electron.

Fig. 13. The neutron paramagnetic form factor of CeSn3 between 40 and 300 K (Stassis et al. 1979a). The ratio between the magnetic scattering amplitude F (0) and the nuclear scattering amplitude f a measure...

Fig. 14. The neutron paramagnetic form factor of CeSnj at 4.2 K, obtained for a 4 mm (open circles) and a 2 mm (solid circles) thick crystal with the field parallel to the [110] direction (Stassis et aL 1979a). The triangles are calculated values assuming that the induced moment consists of a 4f and a Ce5d component of e, symmetry. The solid lines represent the theoretical 4f form factor.

Unlike the neutron paramagnetic form factor, the de Haas van Alphen effect does not give direct information on the wave function of the electrons. A model of the Fermi surface, such as that obtained from a band calculation, is needed to sort out the various pieces. On the other hand, the experiment usually provides such a large amqpnt of specific information that only a highly realistic model can have any chance to fit the observed frequencies and their dependences on the field direction. 

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