Magnetoresistance

The classical transverse magnetoresistance (MR) is mainly due to the bending of the charge carrier trajectory by the Lorentz force. It is proportional to the square of the field, with the proportionality constant expressed as a function of charge transport scattering time [23]. In crystalline 3D metals the dominant 

Even in typical disordered metals, the classical model for MR breaks down due to quantum corrections to conductivity, especially at low temperatures [13]. In the presence of weak disorder, carriers get localized by repeated back-scattering due to constructive quantum interference, and this is called weak localization (WL). A weak magnetic field can destroy this interference process and delocalize the carrier. As a result, a negative MR (resistivity decreases with field, usually less than 3%) can be observed at temperatures around 4 K. Another quantum correction to low temperature conductivity is due to e-e interaction contributions. This is mainly due to the fact that carriers interact more often when they diffuse slowly in random disorder potentials. The resistivity increases (usually less than 3%) with field due to e-e interaction contributions. Hence, the total low-field magnetoconductance (MC, Act) due to additive contributions from WL and e-e interactions is given by 

The e-e interaction contribution shows a universal scaling behavior in the MC [15]. The scaling behavior is given by 

In unoriented metallic conducting polymers like PANI-CSA, PPy-PFf, PEDOT-PF6, etc. [ r(300 K) 300 S/cm, pT 3], the sign of MR is positive at all fields and temperatures. In these systems, the conductivity is not large 

EuIn2P2 magnetic susceptibility shows a clear magnetic transition at about 24 K. In Fig. 11.5 c, magnetic susceptibility as a function of the a, a-h, and c direction were obtained on a plate crystal. The a axis exhibits the largest susceptibility and is the easy magnetization direction. The c axis is the hard magnetization direction. 

In all cases, the high-temperature magnetic susceptibility data are consistent with Eu being all Eu.  

While our original goal of this study, to produce large crystals of Eui4MnPn for detailed characterization, has been unsuccessful to date, we have discovered a number of new compounds with unique magnetic and electronic properties, illustrating the complexity of synthesis and the richness of solid-state structures. 

This work illustrates the point that new and unexpected magnetic and electronic behavior can be found where it is least expected, providing further justification for synthetic exploration. 

We thank Marilyn Olmstead, Han-Oh Lee, Peter Klavins, and Zachary Fisk for useful discussions. We acknowledge the funding of the NSF (DMR- 0120990). JJ was supported in part by a Tyco Fellowship. 

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Special applications, such as in high-magnetic fields, require special thermometers. The carbon-glass and strontium-titinate resistance thermometers have the least magnetoresistance effects. 

Metallic multilayers. In Section 7.4, we have met the recent discovery of multilayers of two kinds of metal, or of a metal and a non-metal, that exhibit the phenomenon of giant magnetoresistance. This discovery is one reason why the preparation and exploitation of such multilayers have recently grown into a major research field. 

Key Words—Carbon nanotubes, scanning tunneling microscopy, spectroscopy, magnetoresistance, electrical resistivity, magnetic susceptibility. 

Song et al. [16] reported results relative to a four-point resistivity measurement on a large bundle of carbon nanotubes (60 um diameter and 350 tm in length between the two potential contacts). They explained their resistivity, magnetoresistance, and Hall effect results in terms of a conductor that could be modeled as a semimetal. Figures 4 (a) and (b) show the magnetic field dependence they observed on the high- and low-temperature MR, respectively. 

Fig. 6. The magnetic field dependence of the magnetoresistance at different temperature for the same microbundle measured in Fig. 5 (after Langer et aL[ 9 ).

The same k p scheme has been extended to the study of transport properties of CNTs. The conductivity calculated in the Boltzmann transport theory has shown a large positive magnetoresistance [18], This positive magnetoresistance has been confirmed by full quantum mechanical calculations in the case that the mean free path is much larger than the circumference length [19]. When the mean free path is short, the transport is reduced to that in a 2D graphite, which has also interesting characteristic features [20]. 

We will discuss below the reeent experimental observations relative to the eleetrieal resistivity and magnetoresistance of individual and bundles of MWCNTs. It is interesting to note however that the ideal transport experiment, i.e., a measurement on a well eharacterised SWCNT at the atomic scale, though this is nowadays within reaeh. Nonetheless, with time the measurements performed tended gradually eloser to these ideal eonditions. Indeed, in order to interpret quantitatively the eleetronie properties of CNTs, one must eombine theoretieal studies with the synthesis of well defined samples, which structural parameters have been precisely determined, and direet electrical measurements on the same sample. 

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