Anomalous Hall Effect in Single-Crystal Dysprosium

The "anomalous" or magnetization-dependent contribution to the Hall effect in single-crystal dysprosium has been investigated from 340 down to 4^∘{}K. In the paramagnetic region, with H applied along 〈112̄0〉 directions, the Hall resistivity, defined by ρH≡R₀B+Rₛ4πMₛ, is linear in H and exhibits a temperature dependence principally due to that of the magnetic susceptibility. The resulting anomalous coefficient Rₛ=-18×10^-12 {Ω} cm/G and normal coefficient R₀=-0.3×10^-12 {Ω} cm/G are both temperature-independent above 190^∘{}K. Below the N\'eel temperature (178^∘{}K), the anomalous coefficient changes sign, passes through a maximum near 120^∘{}K (where Rₛ=+21×10^-12 {Ω} cm/G), and decreases essentially to zero at 30^∘{}K. The temperature dependence of Rₛ below 105^∘{}K is well represented by the first power of the magnetic (spin disorder) resistivity, ρₘ. Such a dependence is in agreement with the f-spin-s-orbit interaction model due to Maranzana, considering only scattering from the thermally disordered spin system as calculated by Irkhin and Abelskii. The contributions to ρH predicted by other mechanisms are evaluated and discussed. The second independent component of ρH allowed in hcp symmetry and characterized by H applied along $〈0001〉$ was determined in the paramagnetic range. High-temperature values of Rₛ and R₀ are -23×{}10^-12 {Ω} cm/G and -3.7×{}10^-12 {Ω} cm/G, indicating appreciable anisotropy between c-axis and basalplane components. Results could not be continued into the ordered temperature range, because of the enormous magnetic anisotropy.