Conduction electron polarisation

Core-polarisation and conduction-electron polarisation effects can be studied as can exchange polarisation of diamagnetic atoms in magnetic hosts. The lattice dynamics of the metal lattice are examined via the temperature dependence of the /-factor. Many metals approximate closely to the Debye model, and a Debye temperature has some significance. Impurity doping can... 

This implies that the magnetic field at the iron is produced by the short-range core-polarisation effects, and that the conduction-electron polarisation is negligible because of there being little 4 density at the Fermi surface. This is consistent with the successful interpretations of the hyperfine field values using a 3(/-model only. 

The magnetic field at Ni at 4-2 K in iron-nickel alloys falls smoothly from 235 kG at 4 at. % Ni to 77 kG at 100 at. % Ni [8, 11]. The main contribution to the field is from conduction-electron polarisation. The rare-earth/nickel alloys (see table) do not show a significant field at 4-2 K [8]. 

More detailed measurements on the Pt/Fe system have covered compositions in the range 3-50 at. % Pt [81]. The 3 at. % alloy gave Hm = —1260 kG at 4-2 K and (99 keV) = -0-60(15) n.m. The value of the field is almost independent of composition within the range specified. Neutronscattering data have shown that there is no localised magnetic moment on the Pt atoms, so that the field is generated entirely by conduction-electron polarisation, approximately 0-07 unpaired conduction electrons being required per Pt atom. A similar mechanism is believed to act in the cobalt and nickel alloys [84]. 

Magnetic hyperfine splitting is seen at nominally diamagnetic Au in ferromagnetic alloys, presumably as a result of conduction-electron polarisation. The 6i-contribution to the conduction band becomes partially spin-unpaired by interaction with the magnetic atoms. The lines are usually only partly resolved, and the first magnetic data were not analysed successfully... 

A systematic study of the Eu/Yb and Eu/Ba alloys has been made [52, 53]. In the ytterbium system, the Curie temperature falls from 90 to 5 K and the saturation field also falls from 265 to 160 kG as the ytterbium content increases from 0 to 92 at. %. The relationships are linear apart from a discontinuity at 50 at. % where there is a phase change. Similarly for barium the Curie temperature falls from 90 to 40 K and the field from 265 to 206 kG as the barium content rises to 50 at. %. However, the chemical isomer shift is not significantly altered. The sign of the magnetic field is known to be negative from neutron diffraction data. Calculations suggest that a contribution of —340 kG to the field in europium metal arises from core polarisation, that +190 kG comes from conduction-electron polarisation by the atoms own 4/-electrons, and that —115 kG comes from conduction-electron polarisation, overlap, and covalency effects from neighbouring atoms. 

The saturation magnetisation 0, in pb per atom, of many materials often corresponds to non-integral values of s. This is due to contributions other than s being involved, for example polarised conduction electrons. It is, therefore, general practice to substitute the experimental value of the saturation magnetisation at 0 K, /3b, for 2s in Eq. (8.3) which leads to (Miodownik 1977)... 

The electronic polarisability of a spherical atom may be calculated in a number of simplified ways. In the oldest approximation, an atom is regarded as a conductive sphere of radius R, when the polarisability may be shown to be 4k 0R3, a quantity that is closely related to the actual volume of a molecule. In the more realistic semi-classical Bohr model of a hydrogen atom, the application of a field normal to the plane of the electron orbit, radius R, will produce a small shift, — x, in the orbit, as shown in Fig. 2.2. To a first approximation the distance of the orbit from the nucleus will still be R and the dipole moment p. induced in the atom will have magnitude ex. At equilibrium, the external field acting on the electron is balanced by the component of the Coulombic field from the positive nucleus in the field direction ... 

Since K depends on the wavefunction density at the nucleus, the effect is dominated by s-electrons which is certainly true in metals with unpaired s-electrons. If the Pauli susceptibility and electron density can be independently measured then the Knight shift will give an independent measure of the s-component of the conduction electron spin density. These shifts are positive and are much larger than chemical shift effects, some typical values being Li — 0.025%, Ag — 0.52% and Hg — 2.5%. In other metals the situation is more complicated when the s-electrons are paired but there are other electrons (e.g. p but especially d). As only s-electrons have significant density at the nucleus the effects of these other electrons are much smaller. The hyperfine fields of these electrons induce polarisation in the s-electrons that subsequently produce a shift, termed core polarisation. 

The Jaccarino and Peter effect is the production of superconductivity in certain ferromagnetic metals through the application of an external magnetic field that compensates for the polarisation of the conduction electrons. It is also known as the compensation effect. 

Fig. 8.6 The energy diagram of an organic semiconductor, a The energy levels of the neutral isolated molecules. Sq Is the electronic ground state, S], S2. .. S are the electronic singlet excited states, Iq is the molecular ionisation energy, Aq the electron affinity of the isolated molecule, b The energy bands of the ionised states of the ideal crystal. /, is the energy of holes, VB = valence band = transport level of the holes Eg = is the energy of the conduction electrons, CB = conduction band = transport level of the electrons. P/, and Pg are the mean polarisation energies of the holes...

The origin of the distortion is the reaction (the response ) of the conduction electrons in the 1-d metal to a periodic modulation of the periodic potential. The amplitude n of the electron density in the 1-d metal exhibits an increasing and divergent component when the wavevector of the potential Vq(q) of the periodic modulation of the lattice potential (which is due to the phonons), i.e. the wavevector q of the periodic perturbation, has the value q = 2kp. Figure 9.10 shows the so-called polarisation function or density-response function x( ). It describes the redistribution 8n(q) of the electron density n(q) in the presence of this periodic potential Vq(q) ... 

Azz is the component of the hyperfine tensor in the Bq direction. Avesr is called the Overhauser shift. It is analogous to the Knight shift Avnmr of tho nuclear-spin resonance frequency v mr in the presence of conduction electrons with a polarisation P. ... 

---