Spin-fluctuation limit

Figure 15 (a) The 4.2 K Mossbauer spectra of [(Fe(IV)=0)(TMC)(NCCH3)](0Tf)2 in acetonitrile recorded in (A) zero field and (B)a parallel field of 6.5 T. The solid line represents a spin Hamilton simulation with the parameters described in the text, (b) Mossbauer spectra of [Fe(lV)=(0)(TMCS)] recorded at temperatures and applied fields that are indicated. The solid lines represent spin Hamiltonian simulations with parameters described in the text. The spectra were simulated in the slow (at 4.2 K) and fast (at 30 K) spin fluctuation limit. The applied field was directed parallel to the observed y radiation. The doublet drawn above the topmost experimental spectrum (0 T, 4 K) represents a 7% Fe(ll) contribution from the starting complex. (From J. U. Rohde et al. (2003) Science 299 1037-1039. Reprinted with permission from AAAS)... 

As discussed in more detail in section 4 the exaet result for g (z) to leading order in l/Nf ean be ealeulated analytically for the ease [/ = oo. In the spin fluctuation limit -6f PNfA the corresponding spectral function has a Lorentzian peak of halfwidth NfA near z = 6f and sharp rise near the Fermi energy, whieh eorresponds to the onset of the Kondo peak, which has most of its weight in the BIS spectrum slightly above Sp. An analogous ealculation can be carried out for g (z). This shows in addition to the P-peak near + U a sharp P-peak just above the Fermi level. The position and width nk Ty lN[ of this Kondo or Abrikosov-Suhf... 

The integral equations (61) have to be solved numerically. In addition to the f-spectral function the temperature dependence of the specific heat and the magnetic susceptibility (Kojima et al. 1984, Bickers et al. 1985, Cox 1985) have been calculated. In the spin-fluctuation limit the f-spectral functions show the Kondo... 

The shape of the spectrum for 1/ < c has been discussed in detail by Gunnarsson and Schonhammer (1985a). In the spin fluctuation limit and to lowest order in l/Nf the dominating contribution for small e is... 

However, the intra-atomic Coulomb interaction Uf.f affects the dynamics of f spin and f charge in different ways while the spin fluctuation propagator x(q, co) is enhanced by a factor (1 - U fX°(q, co)) which may exhibit a phase transition as Uy is increased, the charge fluctuation propagator C(q, co) is depressed by a factor (1 -H UffC°(q, co)) In the case of light actinide materials no evidence of charge fluctuation has been found. Most of the theoretical effort for the concentrated case (by opposition to the dilute one-impurity limit) has been done within the Fermi hquid theory Main practical results are a T term in electrical resistivity, scaled to order T/T f where T f is the characteristic spin fluctuation temperature (which is of the order - Tp/S where S is the Stoner enhancement factor (S = 1/1 — IN((iF)) and Tp A/ks is the Fermi temperature of the narrow band). 

The main equation for the d-electron GF in PAM coincides with the equation for the Hubbard model if the hopping matrix elements t, ) in the Hubbard model are replaced by the effective ones Athat are V2 and depend on frequency. By iteration of this equation with respect to Aij(u>) one can construct a perturbation theory near the atomic limit. A singular term in the expansions, describing the interaction of d-electrons with spin fluctuations, was found. This term leads to a resonance peak near the Fermi-level with a width of the order of the Kondo temperature. The dynamical spin susceptibility in the paramagnetic phase in the hydrodynamic limit was also calculated. 

We applied the generating functional approach to the periodic Anderson model. Calculation of the electron GFs gdd, 9ds, 9sd and gss reduces to calculation of only the d-electron GF. For this, an exact matrix equation was derived with the variational derivatives. Iterations with respect to the effective matrix element Aij(to) allow to construct a perturbation theory near the atomic limit. Along with the self-energy, the terminal part of the GF Q is very important. The first order correction for it describes the interaction of d-electrons with spin fluctuations. In the paramagnetic phase this term contains a logarithmic singularity near the Fermi-level and thus produces a Kondo-like resonance peak in the d-electron density of states. The spin susceptibility of d-electrons... 

Recall (above) that in ZF, fast field fluctuations in a Gaussian distribution result in muon spin relaxation at a rate determined solely by AVv, so that ZF (in that limit) cannot separate the distribution width from the fluctuation rate, but LF in principle can. For a Lorentzian distribution, the ZF fast-fluctuation limit relaxation rate A(0) 4a/3 depends... 

Mossbauer spectroscopy was the distinct difiference in dynamical properties of the Dy + moments in cr- and am-DyAg with the fluctuation rate being at least one order of magnitude lower in the amorphous compoimd. The static limit (on the Mossbauer time scale) was reached in am-DyAg well above 7c- M-SR is a complementary technique to study spin dynamical properties with a quite different time window. It is usually possible to follow the temperature dependence of spin fluctuations deep inside the paramagnetic regime (see the examples discussed in sects. 4 and 5.3). 

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