Ab Initio Study of Electric Transport and Interlayer Exchange Coupling in Fe-Si-Fe Systems

We present a first principles study of the magnetoresistance (MR) perpendicular to the planes of atoms and the interlayer exchange coupling (IEC) in Fe-Si-Fe trilayers. In both cases the dependence on the number of spacer layers is investigated, whereby the spacer thickness ranges between 3 and 21 Å for the IEC and extends to 33 Å for the MR in order to obtain the asymptotic behavior. Additionally, the influence of alloy formation at the interfaces on the MR and the IEC is examined. The calculations of the electronic structure are performed within the fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method and the transport properties are derived from the Kubo-Greenwood equation. Our results give evidence that inter-diffusion is one of the origins of the small MR, which is observed experimentally in Fe/Si/Fe trilayers. AFM coupling occurs for spacers thicker than 4 Å which is in accordance with the experimental findings. It seems that interdiffusion stabilizes AFM coupling in Fe-Si-Fe trilayers.     

Universality of “level curvature” distribution for large random matrices: systematic analytical approaches

We perform an extensive analytical study of distributions of “level curvatures” (the second derivatives of eigenvalues with respect to a perturbation parameter) for different classers of random matrice. First, we consider the case of three Gaussian ensembles: GUE, GOE and GSE. This part of our calculation is complementary to that done recently by von Oppen [22, 23], but evaluation goes along different lines and allows to treat all the three cases uniformly. In the second part of the paper we exploit completely another method allowing to treat the problem analytically for the broad class of disordered systems subject to time-reversal symmetry breaking perturbation. That gives us a possibility to prove the conjecture by Zakrzewski and Delande [17] for the ensemble of symmetric sparse random matrices.     

Berechnung des oberflächensenkrechten kritischen Magnetfeldes für supraleitende Filme

On the basis of the BCS theory a simplified system of equations for the calculation of the perpendicular critical magnetic field,H _c⊥, for superconducting films is derived with the help of “the method of the correlation function”, developed by Lüders. In the vicinity ofT=T _c for all film thicknesses and mean free paths the problem becomes mathematically equivalent to the calculation of the residual resistance of the film. The results are in good agreement with the experiments of Harper and Tinkham and of others. Further limiting cases are investigated: on the one hand specular reflection and weakly diffuse surface scattering, on the other hand diffuse reflection and very thin films.     

On the dynamic mean field theory of spin glasses

We derive in detail Sompolinsky's mean field theory of spin glasses using a diagram expansion of the effective local Langevin equation of Sompolinsky and Zippelius. We use a simpler generating functional than in the literature, on which the quenched average is very easily done. We pay special attention to the existence of an external field. We show that there are two different types of singularities for ω=0 in the equations. The first type, which leads to Parisi'sq(0), is connected with the local magnetisation. The second type, which leads toq′(x), is connected with the nonergodic behaviour. We show that the continuous limit of discrete Sompolinsky solutions has to be taken in order to be in accordance with the fluctuation dissipation theorem on infinite time scales. We discuss carefully the question of dynamical stability. We show that Sommers' solution is unstable only on an infinite time scale and thus remains an acceptable equilibrium theory with a broken symmetry. We argue that for ω=0 a formal violation of the fluctuation dissipation theorem is physically expected if the relaxation times are of the order of the switching time of the external field. From this point of view the spin-glass state is a steady state but not a real equilibrium state.     

Random versus nonrandom competing bonds for spin glasses with long-range interactions

The mapping of random onto nonrandom competing bonds recently suggested is here implemented for spin glasses of long-ranged interactions. Exact results are obtained which support previous conclusions from high-temperature series.     

Theory of a Heisenberg spin glass

For the quantum mechanical long-range random Heisenberg model we derive mean field equations in analogy to the TAP equations. The complete solution requires a self-consistent calculation of the dynamical local susceptibility. We discuss a variational approximation above and below the critical point.     

Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of () at =0 above the AT line to a power law behaviour ()(–i) ^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to ^1/v , where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as ^1–1/v . The average relaxation time diverges as ^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i) ^v at and below the AT line.