Surface pinning in an amorphous ZrTiCuNiBe alloy

Abstract

We have measured the amplitude and the phase of an electromagnetic ͑EM͒ field radiated from a superconductor ͑amorphous ZrTiCuNiBe alloy͒ in the mixed state due to the interaction of the flux lattice with an elastic wave. The results point to an essential contribution of a surface pinning into the flux lattice dynamics. We propose a model that describes radiation of the EM field from superconductors with nonuniform pinning. The model allows us to reconstruct the viscosity and the Labusch parameters from the experimental data. The behavior of the Labusch parameter can be qualitatively explained in terms of the collective pinning theory with the allowance of thermal fluctuations. Soft type-II superconductors were studied intensively during last four decades with the goal to investigate various aspects of vortex matter dynamics ͑see the comprehensive review by Brandt 1 ͒. Nevertheless, many questions that require further investigation remain. Among these questions is the problem of relation between the surface and the bulk pinning. Up to now the dynamics of the vortex state in such an exclusively nonuniform situation was studied by the surface impedance method. 2 In this paper, on the example of amorphous Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be 22.5 alloy we demonstrate abilities of a method based on excitation of vortex lattice oscillations by a high-frequency sound wave.The essence of the method is the following. A superconductor situated in the lower half space ͑z Ͻ 0͒ is subjected by a constant magnetic field H ʈ z. A transverse elastic wave propagating along H and polarized in x direction produces transverse ͑with respect to H͒ oscillations of the vortex lattice caused by pinning and viscous friction, and, consequently, induces an electromagnetic ͑EM͒ field. An antenna receives the EM field ͑with E y and H x components͒ radiated through the elastically free surface of the sample ͑the surface perpendicular to the direction of propagation of the elastic wave͒. While a similar experimental setup was already applied for the study of type-II superconductors, 3,4 the key point is measuring both the amplitude and the phase of the EM field ͑more accurately, the changes of these quantities͒.In the uniform case and in the local limit ͑q Ӷ l −1 , q is the wave number and l is the mean-free path͒ the components of the EM field at z = 0 are given by a simple expression, 5,6where u͑z͒ = u 0 cos qze i t is the displacement in the elastic wave, k 2 is the square of the complex wave number of the EM field in a conductor, and c is the light velocity. Equation ͑1͒ is applicable for the normal as well as the superconducting state of the metal. In the normal state k 2 = k n 2 =4 i 0 / c 2 ͑ 0 is the static conductivity in the normal state͒ is imaginary valued quantity. In the superconducting state at small magnetic fields͑ L is the London penetration length͒ is real valued. At such fields the phase of the EM signal is a constant and we use its value as the reference point. In the well-developed Shubnikov statewhere Ͼ 0 is the viscosity p...

Pinning in nomagnetic borocarbides

“…This question is studied in detailed in Ref. 5. It is shown that the nonuniformity of 0 ͑the decrease of the conductivity of a layer near the surface͒ increases the phase angle, fixed in the normal state.…”

“…In addition, in these fields X͑H͒ is close to 1, and the relation ͑3͒, as already mentioned earlier, is very sensitive to the possible corrections which were neglected, including also to thermal fluctuations, which decrease the effective magnitude of pinning. 5 Figure 5 demonstrates the "quality" of the description of the amplitude of the peak effect near H C2 by the CP theory at various temperatures. This description is fully acceptable.…”

Magnus force and acoustic Stewart-Tolman effect in type-II superconductors

“…The fulfillment of this condition can be considered as an independent test for the measuring procedure proposed. If this condition fails it can be due to a strong non-uniformity of the conductivity near the surface of the sample (see [5]), and in this case one cannot use the relations (6), (7) for the analysis of the results of the measurements. In the experiments presented in this paper the above mentioned condition was fulfilled with the accuracy ∼ 5%.…”

Transverse acousto-electric effect in superconductors

“…In particular, under the influence of the ultrasound wave, the inertial motion of normal electrons as well as superconducting electrons leads to nonzero bulk currents via the Tolman-Stewart effect. The oscillating current radiates electromagnetic waves [6,7] so that the superconductor exhibits nonzero acousto-electric effect.…”

“…The standard time-dependent Ginzburg-Landau theory (TDGL), which contains the assumption of local equilibrium, and is formulated in the laboratory frame, is a powerful tool to study phenomena in the vicinity of the superconducting-normal phase transition. To study gyroscopes [1], gravitational wave antennae [2] and the interaction of the superconducting condensate with strong sound waves [3,4,5,6,7,8,9,10,11,12,13], where the atomic lattice is in motion, an extension to TDGL is needed to accommodate the dynamical system.…”