Question

Why does hall coefficient decrease with temperature?

Answer 1

As you know hall coefficient depends on the carrier density and type of carriers,So in metals electrons scattering increases with phonons with increase in temperature so the free electron density changes.  Hall coefficient is the ratio of mobility to conductivity tensor and relaxation time for isotropic tau(k) on Fermi sphere so its simply inverse of carrier density so assuming We have perfect Fermi  sphere then conductivity in metal decreases so if you consider a metal with no structural phase transition up to the temperature you are talking about then n(carrier density is fixed) then all the dependence you get from relaxation time and effective mass so there are some approx methods to get resulting temperature dependence from Boltzmann transport theory....