On the anomalous Hall effect

[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.

Thanks in advance!

 

[BigJDubs]

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.