Variation of the Helicomagnetic Turn Angle in Dysprosium

Abstract

An explanation of the temperature variation of the helicomagnetic turn angle $\ensuremath{\omega}$ is sought for dysprosium. A Gibbs function is introduced which includes the basal exchange parameter ${J}_{0}$, the first- and second-nearest-neighbor exchange parameters ${J}_{1}$ and ${J}_{2}$, the dependence of ${J}_{1}$ and ${J}_{2}$ on the axial lattice parameter $c$, the axial stress, and the lattice entropy. The evaluation of these parameters leads to good fits with both $\ensuremath{\omega}$-versus-$T$ and $c$-versus-$T$ data. It also correctly predicts a shift of the N\'eel point ${T}_{N}$ under pressure of -0.57\ifmmode^\circ\else\textdegree\fi{}K ${\mathrm{kbar}}^{\ensuremath{-}1}$, and a value of the initial turn angle ${\ensuremath{\omega}}_{i}$ of 49\ifmmode^\circ\else\textdegree\fi{} as ${T}_{N}$ approaches zero. It is tentatively concluded, to first order, that variations in $\ensuremath{\omega}$ are due to the dependence of the exchange parameters on interlayer spacing. Values of the exchange parameters and their derivatives are: ${J}_{0}=200$\ifmmode^\circ\else\textdegree\fi{} K, ${J}_{1}=33$\ifmmode^\circ\else\textdegree\fi{} K, ${J}_{2}=\ensuremath{-}13$\ifmmode^\circ\else\textdegree\fi{} K, $\frac{\ensuremath{\partial}{J}_{1}}{\ensuremath{\partial}c}=260$\ifmmode^\circ\else\textdegree\fi{} K/\AA{}, and $\frac{\ensuremath{\partial}{J}_{2}}{\ensuremath{\partial}c}=60$\ifmmode^\circ\else\textdegree\fi{} K/\AA{}. These conform to the general requirements for a spiral magnetic structure and an oscillating Ruderman-Kittel-Kasuya-Yosida indirect exchange interaction.