Dislocations and the de Haas-van Alphen Effect in Copper

Abstract

Experiments have been carried out to determine the effect of lattice dislocations in pure copper single crystals on the de Haas-van Alphen (dHv A) scattering (Dingle) temperature $X$. The measurements were made on copper samples of measured dislocation density under stringent experimental conditions, including a magnetic field homogeneity of better than 2 ppm and an orientation of the sample symmetry direction along the field to within 0.05\ifmmode^\circ\else\textdegree\fi{}. The results for the [111] neck and belly orbits in copper showed a linear dependence of $X$ on the dislocation density $D$ over the range $D\ensuremath{\simeq}0.5\ifmmode\times\else\texttimes\fi{}{10}^{7} \mathrm{to} 7\ifmmode\times\else\texttimes\fi{}{10}^{7}$ ${\mathrm{cm}}^{\ensuremath{-}2}$, with slopes given by $\frac{{X}_{n}}{D}\ensuremath{\simeq}0.32\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ K ${\mathrm{cm}}^{2}$ and $\frac{{X}_{b}}{D}\ensuremath{\simeq}0.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ K ${\mathrm{cm}}^{2}$. Two approaches have been suggested to explain the results: (i) The scattering temperature is inversely proportional to the electron relaxation time and is therefore a direct measure of electron scattering from dislocations; (ii) $X$ is due to phase cancellation in the dHv A signal from orbits moving within the spatially varying elastic strain field of the dislocation array. The experimental results are discussed in terms of these two points of view.