Hall effect magnetic field dependence

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. 

Soule D. Magnetic field dependence of the hall effect and magnetoresistance in graphite single crystals. Physical Review. 1958 112(3) 698-707. 

Further information on the transport processes in a-Si H and on the influence of doping can be obtained, e.g., from measurements of the drift mobility (Allan et al., 1977 Moore, 1977), of the photoconductivity (Rehm et al., 1977 Anderson and Spear, 1977), as well as of the magnetic field dependence of the photo- and dark conductivity (Weller et al., 1981). In this chapter, however, we shall confine ourselves mainly to results of conductivity and thermopower measurements. Some results from Hall effect and photoconductivity studies are also discussed. 

Fig. 37. Band edge profile of a (In,Mn)As/GaSb heterostmcture. Eq. E. and Ep denote band edges of conduction band, valence band, and Fermi level, respectively, (b) Temperature dependence of the magnetization observed during cooldown in the dark (open circles) and warmup (solid circles) under a fixed magnetic field of 0.02 T. The effect of light irradiation at 5 K is also shown by an arrow, (c) Magnetization curves at 5 K observed before (open circles) and after (solid circles) light irradiation. Solid line shows a theoretical curve, (d) Hall resistivity />Hall observed at 5 K before (dashed line) and after (solid line) light irradiation (Koshihara...

Fig. 38. Hall resistance Rnall of an insulated gate (ln.Mn)As field-effect transistor at 22.5 K as a function of the magnetic field for three different gate voltages. /tnaii s proportional to the magnetization of the (In.Mn)As channel. Upper right inset shows the temperature dependence of / Hall- Let inset shows schematically the gate voltage control of the hole concentration and the conesponding change of the magnetic phase (Ohno et al. 2000).

Special attention is paid to transport properties (resistance and Hall effect) because they are very sensitive to external parameters being the base for working mechanisms in many types of sensors and devices. The magnetic field and temperature dependences of resistance and Hall effect are considered in the framework of the percolation theory. Various types of magnetoresistances such as giant and anisotropic ones as well as their mechanisms are under discussion. 

The multiphysics and multiscale character of the important features of Hall-Heroult cell operation makes difficult laboratory scale experimentation that is relevant to industrial pot operations. For example, cell C E is influenced by the cell-scale flow of the metal and electrolyte, which is determined in turn by the magnetic field which depends on the entire cell current. CE also depends on the finer scale flow due to release of the carbon dioxide bubbles from the anodes. It is generally not possible to examine these two effects simultaneously in the laboratory. Also, the generally hostile environment inside Hall-Heroult cells makes experimentation difficult, and the high cost of modification of full-scale pots further complicates industrial trials. In this environment, numerical or mathematical modeling of pots would be expected to be a useful tool. 

Figure 40. The dependence of the Hall coefficient (a) and the relative effective conductivity (b) on the concentration and on the magnetic field when the Hall factors of components differs essentially, and their conductivities are equal (x = 1, y = 10-10)).

As the magnetic field increases, the sudden jump in dependence of the Hall coefficient at p 0 departs from the percolation threshold p = pc (Fig. 40a). Furthermore, in the dependence of the effective conductivity on magnetic field a minimum exists near the percolation threshold the depth of which tends to zero as H —> oo (Fig. 40b). This is caused by the appearance of rotating currents induced by the difference in the Hall coefficients of the components. Certain terms in formula (322) correspond to these rotating currents. 

Levin (1979) has studied the ternary compound CeCo2Si2. He reported the dependence of the spontaneous Hall effect and the magneto-resistance on the applied field. He observed anomalous galvanomagnetic effects due to an asymmetric distribution of charge carriers caused by their spin-orbit interaction with magnetic defects (Co clusters). 

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