# Why Is the Anomalous Hall Coefficient Temperature Dependent?

• I
• ubergewehr273
In summary, the anomalous Hall coefficient has a strong temperature dependence due to the dependence of magnetization on temperature, and is much larger than the ordinary Hall coefficient due to relativistic effects in ferromagnetic materials.
ubergewehr273
Hi!

Reading through this paper, the Hall resistivity in ferromagnetic materials is given by $$\rho_H = R_0 B + 4 \pi R_s M$$

It is mentioned that ##R_s## (anomalous Hall coefficient) is significantly larger than ##R_0## (ordinary Hall coefficient) and has a strong dependence on temperature. However, I'm unable to understand why this is the case. Temperature dependence is taken care of by the magnetization ##M## of the material i.e. decreases as the temperature increases. So why does ##R_s## have to be temperature dependent? All the texts that I've referrred seem to suggest that this is just experimental observation, which I'm not really satisfied with.

Also, why does ##R_s \gg R_0## have to hold true? I'd really appreciate if someone could explain this to me.

The temperature dependence of the anomalous Hall coefficient (R_s) is due to the fact that the magnetization of the material varies with temperature. Since the magnetization M is a part of the Hall resistivity equation, then the Hall resistivity (ρ_H) is also affected by the changes in temperature. This is why R_s is significantly larger than R_0 and has a strong dependence on temperature. As for why R_s is so much larger than R_0, this is because the anomalous Hall effect is a consequence of relativistic effects in ferromagnetic materials, which makes the Hall resistivity much larger than that of the ordinary Hall effect. The anomalous Hall effect is caused by the interaction of the spin of the electrons with the magnetic field, while the ordinary Hall effect is caused by the Lorentz force on the charge carriers in the material.

## What is the anomalous Hall effect?

The anomalous Hall effect is a phenomenon observed in certain materials where an electric current perpendicular to a magnetic field produces a voltage perpendicular to both the current and the field. This effect is not explained by the classical Hall effect and is believed to be caused by the presence of spin-orbit coupling in the material.

## What causes the anomalous Hall effect?

The anomalous Hall effect is believed to be caused by the presence of spin-orbit coupling in the material. This means that the motion of electrons is affected by their spin, or intrinsic magnetic moment, as well as their position. This leads to a deflection of the electrons in a magnetic field, resulting in the observed voltage perpendicular to both the current and the field.

## What are some applications of the anomalous Hall effect?

The anomalous Hall effect has potential applications in spintronics, a field of electronics that utilizes the spin of electrons in addition to their charge. It can also be used in the development of new materials for magnetic storage and sensing devices.

## How is the anomalous Hall effect measured?

The anomalous Hall effect is typically measured by applying a magnetic field perpendicular to a sample of the material and measuring the voltage perpendicular to both the current and the field. The magnitude of the voltage is then compared to the magnitude of the current to determine the strength of the effect.

## What are some current research areas related to the anomalous Hall effect?

Current research on the anomalous Hall effect is focused on understanding the underlying mechanisms that cause the effect, as well as exploring new materials and structures that exhibit this phenomenon. There is also ongoing research into potential applications of the anomalous Hall effect in spintronics and other fields.

• Atomic and Condensed Matter
Replies
1
Views
818
• Atomic and Condensed Matter
Replies
1
Views
1K
Replies
1
Views
1K
• Classical Physics
Replies
1
Views
810
• Programming and Computer Science
Replies
1
Views
2K
• Beyond the Standard Models
Replies
11
Views
3K
• Atomic and Condensed Matter
Replies
1
Views
4K
Replies
3
Views
1K
• Beyond the Standard Models
Replies
10
Views
2K
• Other Physics Topics
Replies
10
Views
2K