# Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments

## Abstract

The relativistic effect on electromagnetic forces yields two types of forces which depend on the velocity of the relevant particles: (i) the usual Lorentz force exerted on a moving charged particle and (ii) the apparent Lorentz force exerted on a moving magnetic moment. In sharp contrast with type (i), the type (ii) force originates due to the transverse field induced by the Hall effect (HE). This study incorporates both forces into a Drude-type equation with a fully spin-polarized condition to investigate the effects of self-consistency of the source and the resultant fields on the HE. We also examine the self-consistency of the carrier kinematics and electromagnetic dynamics by simultaneously considering the Drude type equation and Maxwell equations at low frequencies. Thus, our approach can predict both the dc and ac characteristics of the HE, demonstrating that the dc current condition solely yields the ordinary HE, while the ac current condition yields generation of both fundamental and second harmonic modes of the HE field. When the magnetostatic field is absent, the simultaneous presence of dc and ac longitudinal currents generates the ac HE that has both fundamental frequency and second harmonic.

- Authors:

- Division of Material Science, Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama 338-8570 (Japan)

- Publication Date:

- OSTI Identifier:
- 22611558

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Advances; Journal Volume: 6; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CARRIERS; CHARGED PARTICLES; CURRENTS; ELECTRIC FIELDS; HALL EFFECT; LORENTZ FORCE; MAGNETIC MOMENTS; MAXWELL EQUATIONS; RELATIVISTIC RANGE; SPIN; SPIN ORIENTATION; VELOCITY

### Citation Formats

```
Sakai, Masamichi, E-mail: sakai@fms.saitama-u.ac.jp.
```*Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments*. United States: N. p., 2016.
Web. doi:10.1063/1.4954808.

```
Sakai, Masamichi, E-mail: sakai@fms.saitama-u.ac.jp.
```*Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments*. United States. doi:10.1063/1.4954808.

```
Sakai, Masamichi, E-mail: sakai@fms.saitama-u.ac.jp. Wed .
"Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments". United States.
doi:10.1063/1.4954808.
```

```
@article{osti_22611558,
```

title = {Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments},

author = {Sakai, Masamichi, E-mail: sakai@fms.saitama-u.ac.jp},

abstractNote = {The relativistic effect on electromagnetic forces yields two types of forces which depend on the velocity of the relevant particles: (i) the usual Lorentz force exerted on a moving charged particle and (ii) the apparent Lorentz force exerted on a moving magnetic moment. In sharp contrast with type (i), the type (ii) force originates due to the transverse field induced by the Hall effect (HE). This study incorporates both forces into a Drude-type equation with a fully spin-polarized condition to investigate the effects of self-consistency of the source and the resultant fields on the HE. We also examine the self-consistency of the carrier kinematics and electromagnetic dynamics by simultaneously considering the Drude type equation and Maxwell equations at low frequencies. Thus, our approach can predict both the dc and ac characteristics of the HE, demonstrating that the dc current condition solely yields the ordinary HE, while the ac current condition yields generation of both fundamental and second harmonic modes of the HE field. When the magnetostatic field is absent, the simultaneous presence of dc and ac longitudinal currents generates the ac HE that has both fundamental frequency and second harmonic.},

doi = {10.1063/1.4954808},

journal = {AIP Advances},

number = 6,

volume = 6,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}