Voigt effect on arvau

Wikipedia / Voigt effect

The Voigt effect is a magneto-optical phenomenon which rotates and elliptizes linearly polarised light sent into an optically active medium. The effect is named after the German scientist Woldemar Voigt who discovered it in vapors. Unlike many other magneto-optical effects such as the Kerr or Faraday effect which are linearly proportional to the magnetization (or to the applied magnetic field for a non magnetized material), the Voigt effect is proportional to the square of the magnetization (or square of the magnetic field) and can be seen experimentally at normal incidence. There are also other denominations for this effect, used interchangeably in the modern scientific literature: the Cotton–Mouton effect (in reference to French scientists Aimé Cotton and Henri Mouton who discovered the same effect in liquids a few years later) and magnetic-linear birefringence, with the latter reflecting the physical meaning of the effect.

(same as for the Kerr effect in the case of a paramagnetic material.

Detailed calculation and an illustration are given in sections below.

Theory

As with the other magneto-optical effects, the theory is developed in a standard way with the use of an effective dielectric tensor from which one calculates systems eigenvalues and eigenvectors. As usual, from this tensor, magneto-optical phenomena are described mainly by the off-diagonal elements.

the electric field the magnetization at saturation. We emphasized with the fact that it is because the light propagation vector is perpendicular to the magnetization plane that it is possible to see the Voigt effect.

Dielectric tensor

Following the notation of Hubert,. At the present moment, there is no evidence that this approximation is not valid, as the observation of Voigt effect is rare because it is extremely small with respect to the Kerr effect.

Eigenvalues and eigenvectors

are:

Reflection geometry

Continuity relation

is the induction defined from Maxwell's equations

Calculation of rotation angle

Transmission geometry

The calculation of the rotation of the Voigt effect in transmission is in principle equivalent to that of the Faraday effect. In practice, this configuration is not used in general for ferromagnetic samples since the absorption length is weak in this kind of material. However, the use of transmission geometry is more common for paramagnetic liquid or cristal where the light can travel easily inside the material.

). For convenience, the field will be added at the end of calculation in the magneto-optical parameters.

At the position

Illustration of Voigt effect in GaMnAs

As an illustration of the application of the Voigt effect, we give an example in the magnetic semiconductor where a large Voigt effect was observed.) for a material with an in-plane magnetization, exhibits a biaxial anisotropy with the magnetization aligned along (or close to) <100> directions.

A typical hysteresis cycle containing the Voigt effect is shown in figure 1. This cycle was obtained by sending a linearly polarized light along the [110] direction with an incident angle of approximately 3° (more details can be found in ), and measuring the rotation due to magneto-optical effects of the reflected light beam. In contrast to the common longitudinal/polar Kerr effect, the hysteresis cycle is even with respect to the magnetization, which is a signature of the Voigt effect. This cycle was obtained with a light incidence very close to normal, and it also exhibits a small odd part; a correct treatment has to be carried out in order to extract the symmetric part of the hysteresis corresponding to the Voigt effect, and the asymmetric part corresponding to the longitudinal Kerr effect.

In the case of the hysteresis presented here, the field was applied along the [1-10] direction. The switching mechanism is as follows:

We start with a high negative field and the magnetization is close to the [-1-10] direction at position 1.
The magnetic field is decreasing leading to a coherent magnetization rotation from 1 to 2
The magnetization stay close to the state 3 while rotating coherently to the state 4, closer from the applied field direction.
Finally the magnetization rotates coherently from the state 5 to the state 6.