Hall Effect Phenomena

The anomalous Hall Effect phenomenon has a long history behind it which is connected to the history of magnetism and electricity. In 1879 Erwin H. Hall, made a historic discovery [1] at the University of Baltimore, that when a conductor or semiconductor with current flowing in one direction was introduced to a perpendicular magnetic field H, a voltage could be measured at right angles to the current path. Later in 1881 he reported that this effect was ten times larger in ferromagnetic iron [2]. It is remarkable, though, that the first Hall discovery was made almost three decades prior to the electron discovery by J.J. Thomson in 1897. Since the transverse resistance (or Hall resistance), defined as UH/I, is proportional to H/n, where n is the sheet carrier density of the sample, the Hall effect provides a simple sophisticated method, that has been extensively used, to compute the carrier type (electron or hole), density, and the mobility of materials. The ability to calculate the carrier concentration in nonmagnetic conductors and semiconductors has played a critical role for the birth of semiconductor physics and solid state electronics. The second Hall discovery in ferromagnetic conductors is known as the anomalous Hall Effect (AHE) (Figure 1).