Variation of the Helicomagnetic Turn Angle in Dysprosium

An explanation of the temperature variation of the helicomagnetic turn angle $\omega$ 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 $\omega$-versus-$T$ and $c$-versus-$T$ data. It also correctly predicts a shift of the Néel point $T_N$ under pressure of -0.57°K ${\mathrm{kbar}}^{-1\mathrm{}}$, and a value of the initial turn angle ${\omega }_i$ of 49° as $T_N$ approaches zero. It is tentatively concluded, to first order, that variations in $\omega$ are due to the dependence of the exchange parameters on interlayer spacing. Values of the exchange parameters and their derivatives are: $J_0=200\mathrm{}$° K, $J_1=33\mathrm{}$° K, $J_2=-13\mathrm{}$° K, $\frac{\partial J_1}{\partial c}=260\mathrm{}$° K/Å, and $\frac{\partial J_2}{\partial c}=60\mathrm{}$° K/Å. These conform to the general requirements for a spiral magnetic structure and an oscillating Ruderman-Kittel-Kasuya-Yosida indirect exchange interaction.