sin(2 phi) current-phase relation in SFS junctions with decoherence in the ferromagnet

We propose a theoretical description of the sin(2 phi) current-phase relation in SFS junctions at the 0-$\pi$ cross-over obtained in recent experiments by Sellier et al. [Phys. Rev. Lett. 92, 257005 (2004)] where it was suggested that a strong decoherence in the magnetic alloy can explain the magnitude of the residual supercurrent at the 0-pi cross-over. To describe the interplay between decoherence and elastic scattering in the ferromagnet we use an analogy with crossed Andreev reflection in the presence of disorder. The supercurrent as a function of the length R of the ferromagnet decays exponentially over a length xi, larger than the elastic scattering length $l_d$ in the absence of decoherence, and smaller than the coherence length $l_\phi$ in the absence of elastic scattering on impurities. The best fit leads to $\xi \simeq \xi_h^{({\rm diff})}/3$, where $\xi_h^{({\rm diff})}$ is exchange length of the diffusive system without decoherence (also equal to $\xi$ in the absence of decoherence). The fit of experiments works well for the amplitude of both the sin(phi) and sin(2 phi) harmonics.Comment: 7 pages, 3 figures, article rewritte

N\'eel ordered versus quantum disordered behavior in doped spin-Peierls and Haldane gap systems

I consider a theoretical description of recent experiments on doping the spin-Peierls compound CuGeO$_3$ and the Haldane gap compounds PbNi$_2$V$_2$O$_8$ and Y$_2$BaNiO$_5$. The effective theory is the one of randomly distributed spin-$1/2$ moments interacting with an exchange decaying exponentially with distance. The model has two phases in the (doping, interchain coupling) plane: (i) A N\'eel ordered phase at small doping; (ii) A quantum disordered phase at larger doping and small interchain interactions. The spin-Peierls compound CuGeO$_3$ and the Haldane gap Nickel oxides PbNi$_2$V$_2$O$_8$ and Y$_2$BaNiO$_5$ fit well into this phase diagram. At small temperature, the N\'eel phase is found to be reentrant into the quantum disordered region. The N\'eel transition relevant for CuGeO$_3$ and PbNi$_2$V$_2$O$_8$ can be described in terms of a classical disordered model. A simplified version of this model is introduced, and is solved on a hierarchical lattice structure, which allows to discuss the renormalization group flow of the model. It is found that the system looks non disordered at large scale, which is not against available susceptibility experiments. In the quantum disordered regime relevant for Y$_2$BaNiO$_5$, the two spin model and the cluster RG in the 1D regime show a power law susceptibility, in agreement with recent experiments on Y$_2$BaNiO$_5$. It is found that there is a succession of two distinct quantum disordered phases as the temperature is decreased. The classical disordered model of the doped spin-$1$ chain contains already a physics relevant to the quantum disordered phase.Comment: 21 pages, 12 figures, revised versio

Magnetization and overlap distributions of the ferromagnetic Ising model on the Cayley tree

We analyze the magnetization and the overlap distributions on the ferromagnetic Cayley tree. Two quantities are investigated: the asymptotic scaling of all the moments of the magnetization and overlap distributions, as well as the computation of the fractal dimension of the magnetization and overlap probability measures

Microscopic theory of equilibrium properties of F/S/F trilayers with weak ferromagnets

The aim of this paper is to explain the non monotonic temperature dependence of the self-consistent superconducting gap of ferromagnet/superconductor/ferromagnet (F/S/F) trilayers with weak ferromagnets in the parallel alignment (equivalent to F/S bilayers). We show that this is due to Andreev bound states that compete with the formation of a minigap. Using a recursive algorithm we discuss in detail the roles of various parameters (thicknesses of the superconductor and ferromagnets, relative spin orientation of the ferromagnets, exchange field, temperature, disorder, interface transparencies).Comment: 13 pages, 11 figures, modifications in the presentatio

Level spacing statistics of bidimensional Fermi liquids: II. Landau fixed point and quantum chaos

We investigate the presence of quantum chaos in the spectrum of the bidimensional Fermi liquid by means of analytical and numerical methods. This model is integrable in a certain limit by bosonization of the Fermi surface. We study the effect on the level statisticsof the momentum cutoff $\Lambda$ present in the bidimensional bosonization procedure. We first analyse the level spacing statistics in the $\Lambda$-restricted Hilbert space in one dimension. With $g_2$ and $g_4$ interactions, the level statistics are found to be Poissonian at low energies, and G.O.E. at higher energies, for a given cut-off $\Lambda$. In order to study this cross-over, a finite temperature is introduced as a way of focussing, for a large inverse temperature $\beta$, on the low energy many-body states, and driving the statistics from G.O.E. to Poissonian. As far as two dimensions are concerned, we diagonalize the Fermi liquid Hamiltonian with a small number of orbitals. The level spacing statistics are found to be Poissonian in the $\Lambda$-restricted Hilbert space, provided the diagonal elements are of the same order of magnitude as the off-diagonal matrix elements of the Hamiltonian.Comment: figures available on reques

Antiferromagnetism in a doped spin-Peierls model: classical and quantum behaviors

We address the problem of antiferromagnetism in a two dimensional model of doped spin-Peierls system, at the classical and quantum levels. A Bethe-Peierls solution is derived for the classical model, with an ordering temperature proportional to the doping concentration. The quantum model is treated in a cluster renormalization group showing a finite randomness behavior and an antiferromagnetic susceptibility at low temperature.Comment: 17 pages, 10 figure

Magnetization Distribution on Fractals and Percolation Lattices

We study the magnetization distribution of the Ising model on two regular fractals (a hierarchical lattice, the regular simplex) and percolation clusters at the percolation threshold in a two dimensional imbedding space. In all these cases, the only fixed point is $T=0$. In the case of the two regular fractals, we show that the magnetization distribution is non trivial below $T^{*} \simeq A^{*}/n$, with $n$ the number of iterations, and $A^{*}$ related to the order of ramification. The cross-over temperature $T^{*}$ is to be compared with the glass cross-over temperature $T_g \simeq A_g/n$. An estimation of the ratio $T^{*}/T_g$ yields an estimation of the order of ramification of bidimensional percolation clusters at the threshold ($C = 2.3 \pm 0.2$).Comment: Jour. Phys. I (France

Contribution of weak localization to non local transport at normal metal / superconductor double interfaces

In connection with a recent experiment [Russo {\it et al.}, Phys. Rev. Lett. {\bf 95}, 027002 (2005)], we investigate the effect of weak localization on non local transport in normal metal / insulator / superconductor / insulator / normal metal (NISIN) trilayers, with extended interfaces. The negative weak localization contribution to the crossed resistance can exceed in absolute value the positive elastic cotunneling contribution if the normal metal phase coherence length or the energy are large enough.Comment: 9 pages, 7 figures, minor modification