Hall resistance

Here p and pj are the transverse and longitudinal resistivities with respect to the magnetization direction, respectively. The off-diagonal element pn represents the spontaneous or anomalous Hall resistivity (AHR) [3]. Conventionally, the anisotropy of the resistivity is expressed by the SMA ratio... 

Should the force be directed so as to deflect the path of the moving charge, an additional resistance, usually called the Hall resistance, would be observed. It should be noted that the magnitude of the effect is very small, invariably much less than 1% of the initial resistance. A secondary effect occurs in magnetic metals, however, and results in a modified magnetoresistivity curve. 

The solid line in fig. 9 shows M determined by the transport measurements, where the Hall resistance is almost proportional to the perpendicular component of M, as described in the next section. The good agreement between M determined by SQUID and transport measurements indicates that one can correctly determine M of (Ga,Mn)As by magnetotransport measurements. 

Fig. 12. Hall resistance Rnal of (a) (Ga,Mn)As/(In,Ga)As and (b) (Ga,Mn)As/GaAs as a function of the magnetic field for various angles between the field and the sample surface normal. (Ga,Mn)As films in (a) and (b) are under tensile and compressive strain, respectively. Clear hysteresis and angle independent heights of the hysteresis in (a) show that magnetic easy axis is perpendicular to the sample surface, whereas the easy axis in (b)...

Due to the presence of the anomalous Hall effect (known also as the extraordinary or spin Hall effect), magnetotransport measurements provide valuable information on the magnetism of thin films. The Hall resistance / Haii is empirically known to be a sum of ordinary and anomalous Hall terms,... 

Figure 13a presents the Hall resistance /(Hall at various temperatures plotted as a function of the magnetic field for the same sample, for which magnetization data were collected in fig. 11 (200-nm thick Gao.947Mno.o53As). The inset shows the temperature... 

Fig. 17. Magnetotransport properties of a 200-nm thick film of Ga -x Mnr As with x = 0.0S3 at 50 m K in high magnetic fields, (a) Hall resistance, which is a linear function of the magnetic field in the high-field region (inset), (b) Sheet resistance negative magnetoresistance tends to saturate in the high-field region (Omiya et al. 2000).

Fig. 19. Magnetic field dependence of the diagonal resistivity p (open circles) and magnetization Afnaii (close circles) determined from the ratio of the Hall and diagonal resistivities, Afnall = PHM/CP< where c = 6.3, for a 1.3-rrm thick film of lni tMnr As with x = 0.013. The solid line is a fit by the modified Brillouin function B (y), where S = 5/2 and y = SgpgB/(T + T0) with T0 = 1.5 K. The inset shows the hysteresis observed in the Hall resistivity at 3.5 K (Ohno et al. 1992).

Fig. 29. Thickness dependence of Che ratio of Hall resistance and sheet resistance ftHall/ sheei> which is proportional to magnetization perpendicular to the film plane, as a function of the magnetic field at 10 K. The inset shows the thickness dependence of 7c (Matsukura et al. 1998a).

Fig. 31. Hall resistance / Hall (circles) and sheet resistance / sheci (triangles) versus magnetic field B at 25 K for a (Gao.95Mno.os)As/(Alo. i4Gao.86)As/(Gao.97Miio.o3)As trilayer structure. Closed and open symbols show the major and minor loops, respectively. Dashed arrows indicate sweep directions of the magnetic field. The minor loop of f Hail is skewed by the presence of a ferromagnetic coupling between the two (Ga,Mn)As layers (Chiba...

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).

The vanishing electrical resistance and the plateaus in the I lull resistance are remarkable phenomena. It is even more remarkable, as pointed out by Halperin iSee reference), that, on each plateau, the value of ihe Hall resistance satisfies a remarkably simple condition. That is. Ihe reciprocal of the Hall resistance is equal to an integer multiplied bv the square of the charge on the electron and divided by Planck s constant (the fundamental constant of quantum mechanics). Bach plateau is characterized hy a different integer. Essentially, in snch a system, the Hall resistance is reduced to ilie formula... 

The degree of precision of the quantized Hall effect has amaz-cd even the experts. Measured values of the Hall resistance at various integer plateaus are accurate to about one part in six million. The effect can be used to construct a laboratory standard of electrical resistance that is much more accurate than Ihe standard resistors currently in use. Authorities also observe that, if the quantized Hall effect is combined with a new calibration ol an absolute resistance standard, it should he able lo yield an improved measurement of the fundamental dimensionless constant of quantum electrodynamics. Ihe fine-structure constant or. 

Should the force be directed so as to deflect the path of the moving charge, an additional resistance, usually denoted as the Hall resistance, would be observed. 

In ferromagnetic materials, including the granular metals, the Hall resistivity follows the equation ... 

Temperature dependence of the Hall resistivity is described by the same —1/2 law ... 

Let us address the parametrical dependence of the Hall resistance on longitudinal resistance (the parameter is temperature) for the above samples with xexponential function (R oc R xx), it was found that the exponent m varies from 0.44 to... 

Fig. 11.16. The magnetic field dependence of the Hall resistivity ph (solid circles) and magnetization M (line) at T = 300K. The inset plots extraordinary Hall coefficient it, at T = 77K [46],...

Consideration of a system with widespread granule sizes shows that in the case when the temperature dependence of resistance of a nanocomposite is described by the —1/2 law, the characteristic temperature To oc X 3/2. The temperature dependence of the Hall resistance is described by the same law (see Eq. (18)) ... 

K. von Klitzing, G. Dorda, and M. Pepper, M. (1980). New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45 494 97 (1980). 

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