Giant Hall Effect in Nonmagnetic Granular Metal Films

Abstract

Nearly 3 orders of magnitude enhancement in the Hall coefficient is observed in Cu x -͑SiO 2 ͒ 12x granular films. This large enhancement of the Hall coefficient not only is significantly larger than the prediction of the classical percolation theory, but also occurs at a metal concentration identified to be the quantum percolation threshold. Measurements of the electron dephasing length and magnetoresistance, plus the TEM characterization of microstructures, yield a physical picture consistent with the mechanism of the local quantum interference effect. DOI: 10.1103/PhysRevLett.86.5562 PACS numbers: 72.20.My, 71.30. +h, 72.80.Tm, 73.50.Jt As a basic material constant, the Hall coefficient is generally indicative of the density and sign of the charge carriers. Thus, in granular metals, as the metal concentration decreases, the lower carrier density is expected to yield an enhanced Hall coefficient which peaks at the percolations threshold with a factor of ϳ30 for ϳ1 mm thick films [1,2]. Recently, however, it was found that in the magnetic ͑NiFe͒-SiO 2 , and Fe-SiO 2 granular films [2-5], the extraordinary Hall coefficient was enhanced by a factor of 10 4 when the metal volume fraction is close to x 0.53 (the classical percolation threshold). An especially intriguing feature of this discovery is that, even after magnetic saturation, the ordinary Hall coefficient was still observed to increase by almost 3 orders of magnitude [4], suggesting a magnetic-independent mechanism could be operative.In this Letter, we focus on the origin of the ordinary giant Hall effect (GHE) by studying the nonmagnetic Cu-SiO 2 granular system. We find the same 3 orders of magnitude enhancement in the Hall coefficient. By carrying out measurements on the electron dephasing length and the magnetoresistance (MR), and by characterizing our samples by transmission electron microscope (TEM) pictures, we find the Hall coefficient to peak at the quantum percolation threshold. Based on the picture that inhomogeneities (due to the small substructures) inside a dephasing length would necessarily cause local quantum interference and thereby modify the effective local properties, we show that all experimental data can be quantitatively accounted for within this simple framework. In particular, when the small substructures are suppressed through annealing, the GHE is shown to disappear, in agreement with the theoretical prediction [6].Cu-SiO 2 granular films with different metal volume fractions were fabricated by using the cosputtering technique with a glass or Kapton substrate, at a temperature of 50 ± C. The base pressure of the chamber was kept below 2 3 10 27 Torr. The films deposited on the glass were used for transport measurements and the films on Kapton were for composition determination. The metal volume fraction x for all the films was obtained from energydispersive x-ray spectroscopy analysis. The dc resistance was measured by using the standard four-probe technique, and the Hall resistance was measured by using the five-contacts me...

Hall Resistivity of Granular Metals

“…(4)- (8) with experimental data may serve as a good check of the theory developed here. The logarithmic dependence ρ xx = a + b ln T of granular metals has been observed experimentally [8], and ρ xy can also be measured [9]. Our theory may also be applied to indium tin oxide(ITO) materials (see e.g.…”

Quantum interference and the giant Hall effect in percolating systems

“…The origin of this ordinary GHE was investigated by using nonmagnetic CuSiO 2 granular films, with the result that not only the maximum enhancement magnitude coincided with the ordinary GHE observed in magnetic composites, but more importantly the mechanism was also found to be correlated with quantum interference. 8 In particular, the maximum enhancement was found at the quantum-percolation threshold, determined experimentally by the Ioffe-Regel criterion of klϳ1, 3 where k is the electronic wave vector and l the mean free path. The enhancement was also found to vanish when the feature size of the granular film was increased ͑through annealing͒ to being comparable to the electron dephasing length.…”

“…This is also in good correspondence with what has been observed experimentally in granular CuSiO 2 . 8 A simple explanation is that the overall Hall effect is sensitive only to the mean of P( H ). Therefore, while the distribution itself can vary as L (T) varies, its mean may nevertheless remains similar.…”

“…This sensitivity on the feature size was indeed demonstrated experimentally through sample annealing, which showed that as the feature size increases to the level comparable to or larger than the measured dephasing length, the GHE disappears. 8 Below we focus on the calculation of the Hall effect in 3D percolating networks based on the above picture. In the composition range xϳx q the local Hall coefficient, calculated on the basis of L (T)Ϸa few 's, is shown to be dominated by wave scattering and interference, and can be of either positive or negative sign with roughly equal probability.…”

“…Numerical results based on our picture are shown to give a good account for the GHE found in nonmagnetic CuSiO 2 granular composites. 8 Consider a 3D sample of disordered metal-insulator composite in the percolating regime, characterized by an average geometric feature size defined by the small insulating ͑or metallic͒ particles and their separations, which form the conducting channels. At finite temperatures, the existence of a dephasing length L (T) means that the wave effects are negligible on a scale larger then L (T).…”