Thermodynamics of the re-entrant regime of type II two-dimensional superconductivity in a strong transverse magnetic field

The thermodynamics (including energy gap and critical temperatureT _c ) of a two-dimensional type II BCS superconductor subjected to a strong transverse magnetic fieldH in the re-entrant regime is studied. There are qualitative differences with the re-entrant 3D case; in particularT _c grows unboundedly likeB/lnB asB (filling factor 1) for fixedN. The thermodynamics atT=0 is completely described by the evaluation of the magnetic Gibbs free energy as a function of andH. A first order magnetic phase transition (failure of H/ B>0 for around each lowlying Landau level) found for the normal phase for unbroadened Landau levels, is washed out in the superconducting phase.     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.     

The magnetic structures of NdCu2 determined by single crystal neutron diffraction

We investigated the magnetic structure of NdCu₂ by means of neutron diffraction as a function of temperature between 1.5 K and 8 K in zero external field. The diffraction data were obtained on two single crystals with different orientations using the triple-axis-spectrometer TAS6 at the DR-3 reactor at Risø. Two magnetic phases were observed between 1.5K andT _N =6.5K. From 1.5 K to 4.1 K the magnetic reflections can be described by the commensurate wave vector =(3/5 0 0) and its higher harmonics 3 and 5. Below 2.5K the structure is completely squared-up. For 4.1 KT6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector=(3/5 0 0) and its higher harmonies 3 and 5M. Below 2.5 K the structure is completely squared-up. For 4.1 K T 6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector ^*=(0.62 0.044 0). In both phases the Nd-moments are oriented along the easyb-direction.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Magnetic after-effect in Mn ferrite

The ballistic method was used to study the disaccommodation of magnetic inductionB in Mn_1.36Fe_1.64O₄ in a d.c. magnetic fieldH 0·040–5·5 Oe. The experimental results were interpreted from the point of view of the irreversible displacements of walls. It was shown that under certain assumptions it is possible to derive the statistical distribution of Bloch wall energies from the experimental curves for substances in which there exists magnetic diffusion aftereffect.     

A comparison of high-T c superconductors: Specific heat in magnetic fields at very low temperatures

We discuss specific-heat,C(T), results on YBa₂Cu₃O_7–(=0.13, 0.99) and Bi₂Sr₂CaCu₂O₈. For completion, we compare these with literature data on La_1.85Sr_0.15CuO₄ and La₂CuO₄ by emphasizing the data at lowest temperatures,T0.45K. The strong upturn inC(T)/T found atB=0 is predominantly associated with a splitting of nuclear states by quadrupolar interactions. The shift of this upturn towards higher temperatures, when magnetic fields up to 8 T are applied, indicates additional hyperfine splitting. For YBa₂Cu₃O_6.87 and Bi₂Sr₂CaCu₂O₈, subtraction of the nuclear specific heat from the raw data reveals a spin-glass derived contribution ^*(T,B), with ^* being strongly depressed upon both warming and applying externalB-fields. The probable source for ^* T are impurity phases (in YBa₂Cu₃O_7–) and/or frustrated Cu²⁺ moments created by lattice defects. Any intrinsic linear specific heat, ⁱ , due to, e.g., spinon excitations or normal electronic carriers, would have to imply ⁱ <1 mJ/K² mole_f.u. for each of these two compounds.Dedicated to Prof. Dr. G. von Minnigerode on the occasion of his 60th birthday     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

Flux diffusion in high-T c superconductors

In type-II superconductors in the flux flow (J J _c ), flux creep (J _c J _c ), and thermally activated flux flow (TAFF) (J J _c ) regimes the inductionB(r,t), averaged over several penetration depths , in general follows from a nonlinear equation of motion into which enter the nonlinear resistivities (B, J ,T) caused by flux motion and (B, J ,T) caused by other dissipative processes.J andJ are the current densities perpendicular and parallel toB,B=|B|, andT is the temperature. For flux flow and TAFF in isotropic superconductors with weak relative spatial variation ofB, this equation reduces to the diffusion equation plus a correction term which vanishes whenJ =0 (this means B××B=0) or when – = 0 (isotropic normal conductor). When this diffusion equation holds the material anisotropy may be accounted for by a tensorial . The response of a superconductor to an applied current or to a change of the applied magnetic field is considered for various geometries. Such perturbations affect only a surface layer of thickness where a shielding current flows which pulls at the flux lines; the resulting deformation of the vortex lattice diffuses into the interior until a new equilibrium or a new stationary state is reached. The a.c. response, in particular the frequency with maximum damping, depends thus on the geometry and size of the superconductor.     

Electron-electron interaction and magnon scattering in the d-electron dominated resistivity of Ni80−xFe x Si8B12 glasses

Our investigation of the electrical resistivity (T) betweenT=0.1 K and 295 K revealed for all Fe-concentrations, 2.4x16, a minimum of betweenT _min=7 K and 15 K. Above the minimum, scattering from structural disorder prevails in the paramagnetic alloy (x=2.4), while in the ferromagnetic glasses (x5.6) coherent magnon scattering appears to dominate. With one exception, (TT _min) increases as down to the lowest temperatures for all investigated Fe-contents (x10.4) in zero magnetic field as well as in applied 6 T. The value of the slopes, 6.3(6) ( cm)^–1 K^–1/2, agrees with the universal scaling behaviour reported recently by Cochrane and Strom-Olsen for systems with strong electron-electron interaction. A large, linear rise of (T<T _min,B=0) observed in the most diluted sample (x=2.4) is tentatively attributed to quantum localization in the non-reentrant spin glass phase. The magnitude of the temperature effects on (T) above as well as belowT _min indicates significantd-band contributions to the conductivity.     

Hydromagnetic flow in a rotating channel permeated by an inclined magnetic field in the presence of an oscillator

A steady hydromagnetic flow of a viscous incompressible electrically conducting fluid confined between a perfectly conducting rotating parallel plate channel due to a constant pressure gradient permeated by an inclined magnetic field with the positive direction of the axis of rotation in the presence of an oscillator along the axis of rotation is investigated. The influence of these parameters, viz.M ² (the Harmann number) andK ² (the rotation parameter), describes a new relationG _MK ² =16K ⁴–M ⁴sin⁴ which defines the fundamental relation between the hydromagnetic force and the coriolis force. It is noticed that the laminar flow breaks down when the velocity is very large, i.e.,u+iv= and it becomes turbulent when the frequency is very high, i.e.,T=1/2. The rate of heat transfer is analysed when the frequency is very high, i.e.,T=1/2.     

Gravitation and universal Fermi coupling in general relativity

The generally covariant Lagrangian densityG = + 2K _matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg _ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form _kl ⁱ = _kl ⁱ for the coefficients _kl ⁱ of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , g_ik, and the coefficients _kl ⁱ . Then the _kl ⁱ are determined by the Palatini equations. From these equations and from the symmetry _kl ⁱ = _lk ⁱ for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10^–81erg cm³     

Critical current density of a YBa2Cu3O7 film: Comparison between experiment and collective pinning theory

With the vibrating reed technique we have measured the critical current densityJ _c of a Y 123 200 nm thin film as a function of magnetic field perpendicular to the CuO₂ planes (O T<B8 T) and temperature (20KT60 K). At fieldsB<0.1 TJ _c is magnetic field independent and decreases at higher fields. A comparison with theory indicates that a crossover from a single pinning to a small bundle collective pinning regime may explain the observed behaviour. According to our estimate the main pinning centers are weak point pins due to oxygen vacancies. From the temperature dependence ofJ _c atB0 we obtain a temperature dependence of the thermodynamical critical fieldB _c (1–T/T _c )² forT20 K which agrees with the anomalous temperature dependence ofB _c2 observed recently in highly anisotropic high temperature superconductors.     

Nonequilibrium thermodynamics of lasing and bistable optical systems

A simple model of nonlinear optical systems exhibiting instability—such as in laser action and in bistable absorption—is presented that provides a prototype of nonequilibrium thermodynamics on a statistical basis. The adiabatic reduction of the atomic degrees of freedom in a revised Langevin treatment establishes a fully consistent framework in which the active electromagnetic field mode is in contact with two thermal reservoirs (the cavity and the atoms) as well as being acted upon by an external field. The results are summarized by the first and second laws,dE=W+Q _c +Q _A anddS Q_c/¯T_c+Q_A/¯T_A, with the statistical mechanical representations of the entities therein exhibiting the nature of the mode; i.e., (a) a heat-engine structure operating between two reservoirs of temperatures¯T _c > 0 and¯T _A < 0 for the laser, and (b) a nonlinear response against external work balanced by a single reservoir (¯ T _c = ¯T _A ) for the absorptive bistability.Originally presented at the Taniguchi Symposium, October 1979.⁴⁴     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Variance calculations and the Bessel kernel

In the Laguerre ensembleof n xN Hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted var_N f, asN . Furthermore, this statistic often contains an additional parameter a for which the limit is most interesting and most difficult to compute numerically. We derive exact expressions for both lim_N var_N f and lim , lim_N var_N f.     

Nuclear physics with ion traps at ISOLDE: present and future

Nuclear physics experiments with ion traps started at the on-line separator ISOLDE/CERN, Geneva, with the installation of the tandem Penning trap mass spectrometer ISOLTRAP. With this device the massM of a stored ion is determined by measuring its cyclotron frequency _c=(q/M)B in a magnetic fieldB. Mass measurements with a resolving powerR=_c/_c(FWHM)1×10⁶ and accuracies of M/M10^–7 were performed on more than sixty unstable isotopes of the elements Rb, Sr, Cs, Ba, Fr, and Ra.     

Far-infrared spectroscopy of the supreconductor YBa2Cu4O8

The frequencies of allB _1u (z) phonon modes predicted by a group-theoretical analysis were measured and found to agree well with recent lattice dynamical calculations for this compound. We report also the determination of two superconducting gap values in YBa₂Cu₄O₈ through phonon self-energy effects in the normal and superconducting conducting state. The gap-to-T _c ratios obtained from an analysis of these effects are 2 ₁/kT _c 2.5 and 5.82 ₂/kT _c 9.2. This coincides with previous results of both phononic and electronic Raman scattering where values of 2.1 and 6.3 were found. We further find anomalous softenings of two phonon modes 40 Kabove T _c , which correlate with an observed deviation from the linear temperature dependence of the average plasma frequency _p (T).     

Boundedness for large |x| of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity

We consider time-dependent perturbationsu of R. Finn's stationary PR-solution of the Navier-Stokes equations, which converges to a constant vectorv as |x|. For a given time interval [,T], we find a radiusK such thatu is essentially bounded on [,T]×{|x|K}.     

The magnetic behavior of CeB6: Comparison between elastic and inelastic neutron scattering,initial susceptibility and high-field magnetization

We report measurements of the elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization on thoroughly prepared poly- and single crystalline samples of CeB₆. Part of these experiments have been performed at temperatures down to 60 mK and magnetic fields up to 70 kØe. Our neutron-diffraction data provide the first proof that CeB₆ is an antiferromagnet belowT _N2K as has been suggested by previous bulk experiments. The reduced value of the low-temperature magnetic moment both below and aboveT _N points to the existence of a Kondo effect of the ₇ crystal-field (CF) ground state of Ce³⁺. From the low-temperature width of the quasielastic neutron line, the Kondo temperature is inferred to beT _K3 K. The thermal variation of the initial susceptibility (forT>20K) is semiquantitatively explained invoking, besides the Kondo effect, a ₇- ₈ CF splitting of 70 K and magnetic interactions, which are about 10 times stronger between ₈ states than those between ₇ states. This large ₈- ₈ exchange interaction is also assumed to account for the most striking result of this work, i.e. the lack of any CF-transition peak up to 44 meV in our inelastic neutron-scattering spectra.     

Anisotropic low-temperature heat transport in YBa2Cu3O6.9 single crystal

We report measurements of the low-temperature thermal conductivity of YBa₂Cu₃O_7– (0.1) single crystals (T _c =84 K) both parallel ( ^{a, b} ) and perpendicular ( ^c ) to the CuO₂ planes. Whereas ^c (T) is found to be identical, within experimental resolution, with the phonon contribution _ph (T), ^{a, b} (T) contains an additional term linear in temperature,AT. We ascribeAT to the contribution of unpaired electronic carriers residing in the chain layers. Measurements performed in external magnetic fieldsB8 T support this interpretation. Our observations can be explained by an internal multilayer (IML) model in which it is assumed that strong superconductivity is generated within the CuO₂ layers and weak superconductivity is induced in the chain layers by the proximity effect. The fit of the experimental results to the IML model reveals that approximately 15% of the electronic carriers remain unpaired in YBa₂Cu₃O₇ belowT=1 K.