Generalized phonon-connected relations in the Hall resistivity of cadmium

An analysis of Hall resistivity data for Cd and Cd-alloy crystals previously published by Lilly and Gerritsen has led to the following, rather unexpected results. The coefficient (A₁) of the term in first order in H, the magnetic field parallel to the hexagonal axis, varies as A₁∝ρ₁₁^-1e^-43/T in the temperature range 8≤T≤200 K (ρ₁₁ is the resistivity parallel to 〈112̄0〉). The difference between the measured Hall resistivity and A₁H passes zero for all samples at T≈11 K. This temperature can be connected to the onset of strong, specific phonon modes. A further relation, that may have less physical significance is that in the temperature range $10<T<20$ K, where the Hall resistivity passes through a maximum, the field Hₘ at the maximum varies as Hₘ∝ρₘ^-1e^-109Tₘ, The temperature 109 K compares to the temperature ΘR=112 K that has to be used in the Bloch-Gr\"uneisen relation to describe ρ₁₁(T) for temperatures above {≈} 8 K.