We consider the formation of defects in a non equilibrium second order phase transition induced by an instantaneous quench to zero temperature in a type II superconductor. We perform a full non-linear simulation where we follow the evolution in time of the local order parameter field. We determine how far into the phase transition theoretical estimates of the defect density based on the gaussian approximation yield a reliable prediction for the actual density. We also characterize quantitatively some aspects of the out of equilibrium phase transition.

We study a model of a Spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an inter-chain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic Spin-Peierls compound CuGeO3The recent discovery of the first inorganic SpinPeierls(SP) compound CuGeO 3 has renewed the interest in the subject of quasi-one-dimensional spin-phonon coupled systems 1 . In spite of the intense experimental and theoretical activity devoted to the study of this system neither the excitations in the low temperature phase nor the mechanism of the Spin-Peierls transition itself are well understood yet. Most studies have used as a model Hamiltonian a Heisenberg antiferromagnetic chain with alternating coupling and next nearest neighbors (nnn) interaction 2,3 . The Spin-Peierls transition is supposed to arise from a competition between the elastic energy cost necessary to dimerize the chain and the magnetic energy gain in this process. The dynamics of the phonons are then supposed to be independent of the magnetic subsystem and an extreme adiabatic approximation is assumed.In spite of the success to reproduce both thermodynamical as well as dynamical properties of Spin-Peierls systems by this approach, there are now several indication that the Spin-lattice interaction in CuGeO 3 is strong enough to make insufficient this approximation. No soft phononic mode related to dimerization has been found 4 . This fact point toward an order-disorder type transition where nonlinear excitations (domain wall) different from phonons drive the structural transition. Otherwise, the phase diagram of the system in presence of a magnetic field is now well established. Above a critical value of the magnetic field the system undergoes a transition from the uniform dimerized into an incommensurate phase. The incommensurate lattice pattern has been measured by X-ray experiments and interpreted as soliton lattice structure 5 . The role of solitons in CuGeO 3 was indeed previously emphasized 6 . They could give an unified picture of the above features. They could also be relevant to explain the rapid reduction of the SP temperature by doping and the apparition of an antiferromagnetic phase 6,7 .It seems then natural to build the excitation spectrum of SP systems on the basis of some kind of solitonic excitation (in this work we use the term soliton in the general sense of a finite energy localized configuration which is simultaneously magnetic and structural excitations, we call kinks the 1D solitons). The pr...

We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of competing spontaneous and explicit dimerization relevant for spin-Peierls compounds. The bosonized theory is a two-frequency sine-Gordon field theory. We analyze the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverges for vanishing dimerization. The internal oscillations of the magnon give rise to a series of excited states until another magnon is emitted and a two-magnon continuum is reached. We discuss, for weak dimerization, the manner in which the magnon forms as a result of a spinon-spinon interaction potential.

We analyze the excitation spectra of a spin-phonon coupled chain in the presence of a soliton. This is taken as a microscopic model of a Spin-Peierls material placed in a high magnetic field. We show, by using a semiclassical approximation in the bosonized representation of the spins that a trapped magnetic state obtained in the adiabatic approximation is destroyed by dynamical phonons. Low energy states are phonons trapped by the soliton. When the magnetic gap is smaller than the phonon frequencies the only low energy state is a mixed magneto-phonon state with the energy of the gap. We emphasize that our results are relevant for the Raman spectra of the inorganic Spin-Peierls material CuGeO3.The discovery in 1993 by Hase et al [1] of the first inorganic Spin-Peierls compound CuGeO 3 has opened the possibility of study the physics of this collective phenomena in a deep way. Several experimental proves have given an exhaustive information about the excitation spectra of this system and its evolution with an applied magnetic field. The effect of non-magnetic impurities has been investigated also.Theoretical studies have focused on simplified magnetic model. The excitation spectra in the low temperature phase have been analyzed using a dimerized and frustrated Heisenberg chain as a minimal model for this material [3][4][5]. The logic underlying these studies are: the competition between magnetic and elastic energies resolves in the low temperature phase in the dimerization of the lattice. Once this process takes place, phononic and magnetic excitation completely decouple and the magnetic excitations are the same as the chemical dimerized system. This point of view is based on an adiabatic approximation supposing that the energy scale of the magnetic process are high enough respect to the phononic ones. As it has been recently emphasized [6], this relation is not fulfilled for CuGeO 3 where the phonons relevant for the dimerization process are about one order of magnitude more energetic than the magnetic gap. The adiabatic approximation is questionable for this system. An antiadiabatic approach has been developed. The frustrated interaction arises, in this context, from the integration of the in-chain phonons and the explicit dimerization from the interchain interaction treated in a mean field approximation [7]. The same frustrated-dimerized Hamiltonian is therefore obtained but with a reinterpretation of the parameters. What is clearly missed in these studies is a general understanding on how spin and phonons mix as elementary excitation and how the spectra of Spin-Peierls systems is built as a result of this mixing. Some recent numerical results have partially addressed this question [8].In this paper, we analyze the excitation spectra of onedimensional spin-phonon system by semiclassical techniques on the bosonized representation of the spins subsystem. We focus on the properties of this system in a high magnetic field. In the dimerized phase the system is in a singlet ground state. Coupling with a magnetic field...

We report on the observation of the rearrangement of vortices in the ns time scale following a fast magnetic field variation due to selective local heating of a high Tc superconducting film. Detailed simulations describing the measured photoinduced voltage signals along the film lead to a better understanding of vortex dynamics in fast regimes, where mean vortex velocities reach 10 4 m/s.PACS numbers: 74.60. Ge, 74.60. JgVortex dynamics in type II superconductors continues to be a stimulating research area. Striking memory effects and dynamical ordering of vortex matter in the low frequency domain have been observed recently [1], and may lead in the future to switching devices [2]. However, the high frequency response of vortex matter is still an open question that needs to be addressed.In the past, the use of conventional techniques has limited the observations of magnetic properties to the low frequency domain. These techniques have long intrinsic response and initial data-acquisition times, somewhere between fractions of seconds and minutes [3]. The study of short time vortex dynamics with novel nonconventional techniques is a requirement for the development of future fast devices.In this letter we report on the rearrangement of vortices in a high T c superconducting sample over nanosecond time scales observed following a fast magnetic field variation due to partial heating.The sample is a GdBa 2 Cu 3 O 7−x film of thickness δ = 300 nm on NdGaO 3 substrate. The sample was patterned (see Fig. 1) using laser ablation in a strip (∼ 10 × 2 mm 2 ), and voltage contact pads were provided by gold sputtering, to reduce contact resistance below 1 Ω. The T c of the film is 91 K with a ∆T c = 1.5 K (10% -90% criterion) determined by ac susceptibility.For the experimental observations we used a high bandwidth electronic detection method coupled with a pulsed magnetic field generator and a synchronized pulsed laser, based on a previously designed short-time magnetometer (∼ 200 µs ) [4]. The excimer laser provided 45 ns FWHM pulses at 308 nm and uniformly illuminated the target area.Briefly, the technique consists in the preparation of the thermomagnetic initial state by stabilizing the sample temperature below the irreversibility line and applying a transverse pulsed magnetic field H a at a high rate (dH/dt ∼ 1000 T/s) to reduce the uncertainty in the time origin. The laser pulse is triggered at a controlled delay, t d , at different stages of the propagation of the magnetic field front. Flux penetration can be followed, as will be described below, by measuring the voltage signal across the pair of contacts provided in the film. The optical heating lowers the pinning force on the vortex structure (at the location where the laser spot was positioned) below that corresponding to the critical state at uniform temperature. This allows the fast penetration of vortices and triggers the flux redistribution in the whole sample. Flux motion is detected as a voltage pulse, superposed to signal induced by the application of the magn...