de Haas-van Alphen effect study of dislocations in copper

The influence of lattice dislocations on conduction electrons has been studied both theoretically and experimentally in copper single crystals. A first-principles de Haas-van Alphen (dHvA) dephasing calculation was made, using the dislocation strain field with a realistic dislocation array. Both the Dingle temperature $X$, which characterizes the amplitude reduction, and the dHvA relative phase shift were measured using dHvA wave-shape analysis. Breaking the cubic symmetry by introducting a forest of edge dislocations allows a test of the sensitivity of previously equivalent neck orbits to the relative orientation with respect to the dislocation lines. Both magnitude and anisotropy agree with the theory. Orbits in contact with the Brillouin zone were found to have larger $X$. A slight field dependence predicted by the dephasing calculation was observed. The large discrepancy observed among different $\frac{1}{\tau }$ results obtained from dHvA, radio-frequency size effect, and resistivity measurements is due to the different sensitivity of each method to small-angle scattering by the long-range strain field around dislocations. It is shown how to separate dislocation effects from mosaic-structure effects also present in these strained crystals.