As part of a project on the Hall Effect in metals, we would like to find out whether the Hall Coefficient of copper depends on its temperature, and if so how.
We passed a current I through a copper foil inside a magnetic field. We measured the Hall Voltage as a function of the current in the foil, using
$$ V_{\text{Hall}} = \left({B R_H\over\delta}\right)I $$
where $B$ is the magnetic field perpendicular to the foil, $R_H$ is the Hall coefficient, $I$ is the current through the foil and $\delta$ is the thickness of the foil. We also know that raising the temperature raises the resistivity $\rho$, but we do not know the dependence of $R_H$ on $\rho$.
By plotting the graph of $V_{\text{Hall}}$ as a function of $I$, we expected to find the known value of $R_H$ for copper. However, we found a somewhat larger value (by about 15-20%). We were wondering if a possible explanation could be the rise in temperature, caused by the very large currents (5-10Amps) used in the experiment.
Best Answer
You seem to be onto something. This research paper on arXiv suggests a linear relation between the Hall coefficient and temperature for a certain strongly disordered metal; the analysis probably does not apply in your case with copper, but was included because it is interesting, is current research and deals with the relation between the hall coefficient and temperature. This german experiment directly deals with the temperature dependence of the Hall coefficient of copper samples, relevant to your case; the result seems to indicate that the Hall coefficient is not temperature-dependent, but further mentions that inaccuracies in determining the hall coefficient of zinc samples may have something to do with certain contact effects and impurities:
These effects and some impurities most likely affected measurements, more likely than temperature.