Nonlinear Hall resistivity inYBa2Cu3

P. J. M. Wöltgens

¹

,

Cees Dekker

²

,

H. W. de Wijn

³

Abstract

The Hall electric field E y is observed to be a strongly nonlinear function of the current density J x in the vicinity of the vortex-glass transition of YBa2Cu307-«5 films in a magnetic field. Much like the longitudinal electric field E x , E y appears to scale critically with J x , with a Hall-related critical exponent A = 3.4 ± 0.3. Furthermore, the Hall resistivity p xy -E y /J x and the longitudinal resistivity p xx = E x /J x are found to obey p xy oc p xx ±0 ' 2 over a wide range of current densities and temperatures. The results quantitatively verify recent theoretical predictions.PACS numbers: 74.60. Ge, 73.50.Jt, 74.76.Bz In this Letter, we report on the first observation of nonlinear Hall resistivity in YE^CusOr-^ films in the vicinity of the vortex-glass transition in a high magnetic field, i.e., the Hall electric field E y is a nonlinear function of the driving longitudinal current density J x . At the vortex-glass transition temperature T g , YE^CusOy-s films pass from a vortex liquid to a vortex glass state [1]. As it appears, the Hall resistivity becomes increasingly of nonlinear character upon approaching T g from above, and turns entirely nonlinear below T g .Entering the nonlinear regime implies, as quite general arguments show [1], that the length scales on which the system is probed becomes of the order of the vortex-glass correlation length, which diverges at T g . It therefore puts theories of the Hall effect relying on vortex dynamics to a particularly severe test. This, in fact, is the objective of this Letter. Contrary to the nonlinear Hall effect, the linear Hall effect, which is only observed at sufficient distance from the transition and at sufficiently low currents, has recently attracted considerable attention. The focus of the interest has been on the intriguing sign change that occurs upon cooling from the normal to the vortex liquid state [2][3][4][5][6][7][8]. Of particular relevance here furthermore is the finding by Luo et al. [9] that in the linear regime the Hall resistivity p xy -E y /J x as a function of the temperature follows a power-law dependence on the longitudinal resistivityTwo theories are available for the Hall effect in superconductors in the nonlinear regime. First, inspired by the results of Luo et al [9], Dorsey and Fisher (DF) [10] devised a critical scaling model, elaborating on the fact that the Hall effect in superconductors is an expression of the particle-hole asymmetry. In the vicinity of the vortexglass phase transition [1], this asymmetry is assumed to scale with a power of the vortex-glass correlation length. The linear Hall resistivity then exhibits a critical scaling behavior, in consistency with experiment [9], Furthermore, DF made an explicit prediction for the Hall effect, which may serve as an independent test of their theory: "The nonlinear Hall electric field E y should exhibit universal scaling, and right at the transition should vanish with a universal power of the current density J x ." An alternative, but not necessarily incompatible, ...

Theory of the supercyclotron resonance and Hall response in anomalous two-dimensional metals

“…The Hall conductivity σ H o of the Bogoliubov quasiparticles is typically negligible due to their approximate particle-hole symmetry. Dominance of the first term, proportional to the Hall conductivity σ H n of the vortex cores, leads to the relation ρ yx ∼ ρ 2 xx obtained by Vinokur et al [10], and observed in some thermally activated flux flow [14][15][16][17][18][19]. This scaling arises because -as shown by Bardeen-Stephen [5] and rederived below -ρ xx ∼ x, the fraction of the area occupied by mobile vortex cores, is strongly temperature and field dependent, while σ H n is not.…”

“…InO x is therefore far from the 'Nozières-Vinen' free flow regime. A condition analogous to (3) must also hold for the systems mentioned above where a ρ yx ∼ ρ 2 xx scaling was previously observed [14][15][16][17][18][19]. The supercyclotron resonance will be easiest to observe in materials that instead exhibit free flux flow, with negligible pinning, so that ρ yx ∼ ρ xx .…”

“…The electric field term, which is in fact E − ∇µ in general, drops out because E is held fixed and χ J φ ∇µ = 0 at any nonzero temperature (where the response at low wavevector k is nonsingular, so that χ J φ ∇iµ ∼ k i → 0). Putting (14) and (15) together gives the results for Ω and Ω H stated in (2) above. Finally, the inclusion of correlations between distinct vortex cores and finite size corrections to Green's functions in the cores (i.e.…”

Universality of frequency and field scaling of the conductivity measured by ac susceptibility of aYBa2Cu3Kötzler1, Nakielski2, Baumann3 et al. 1994Phys. Rev. B696360View full textAdd to dashboardCite

“…The widely observed scaling feature of the electrical conductivity in the presence of a transverse magnetic field B and the universality of the critical exponents obtained in such scaling analyses on thin YBa 2 Cu 3 O 7 -films [1][2][3][4][5][6][7][8][9][10][11] serve as the best evidences for the existence of a continuous thermodynamic phase transition to a genuine superconducting phase occuring at some transition line T g (B). Considering the interplay between the elastic properties of the vortex lattice and the disordering potential exerted on the vortices by density fluctuations of pointlike pinning centers on a microscopic level, the possibility of a glassy vortex state with infinite barriers for vortex motion, U (j → 0) and, hence, zero linear resistance, ρ(j → 0) = 0, was argued previously for 3-dimensional lattices (see e.g.…”

Scaling behavior of anomalous Hall effect and longitudinal nonlinear response in high-Tcsuperconductors

“…P.J.M. Wöltgens et al 20 measured the nonlinear Hall resistivity in YB 2 Cu 3 O 7Ϫ␦ film near the vortex-glass transition. Their results firmly indicated that the Hall resistivity has a similar scaling relation as for longitudinal resistivity which has been discussed extensively by M.P.A.…”