Magnetic lattice period

If the on-site repulsion is large (U>4t), then two electrons cannot be accommodated on the same site, and the band fills up to 7c/b (Fig. 5c). The magnetic lattice period is twice the normal period, and one has a Mott-Hubbard semiconductor, in which Bragg or Umklapp scattering occurs at 4kp. 

From the above discussion it becomes clear that xi9) can have a maximum at q O only if there exist large, nearly parallel sheets of Fermi surface. The q for the stable magnetic structure is measured by the average separation of the two nesting sheets of Fermi surface. Since the Fermi surface geometry is not simply related to the lattice periodicity, this explains why the periodicity of the spin structure is not necessarily commensurate with the lattice. 

The R ions form a periodic lattice, which leads for the 4f electrons together with the conduction electrons to the formation of quasi-particle bands, i.e. the electrons are in a coherent state. Since the magnetic moments either vanish (in the non-magnetic Kondo state) or form themselves a periodic magnetic structure (Kondo systems with magnetic order) there is no elastic scattering of the conduction electrons and therefore Pn,(0) = 0. This is different at high temperatures, where even in a periodic lattice one has disordered moments, which scatter elastically. The coefficient Ai can be calculated analytically. One finds A = j j + with the resistivity in the unitarity limit... 

We now describe the system of atomic moments or spins 5j in more detail on a specific model, the n vector model. We assume that the magnetic atoms are located on a periodic lattice. Each magnetic atom (i) carries a spin S( this is a vector, with n components 5(1, Sa... 5( . In our considerations, we ignore all quantum effects the components Sia are just numbers. There is one constraint—i.e., the total len 5 of each spin is fixed. We choose the following normalization ... 

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

Hohenberg and Kohn have proved generally that the total ground state energy E of a collection of electrons in the presence of an externally applied potential (e.g. the valence electrons in the presence of the periodic potential due to the cores in a lattice), when no net magnetic moment is present, depends only on the average density of electrons n(R). By this proof, n(R) becomes the fundamental variable of the system (as it is in the Thomas-Fermi theory ). Variational minimization of the most general form of E, with respect to n lends to the Hartree-Fock equations formalism. 

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

---