Oscillatory Magnetostriction and the Stress Dependence of the Fermi Surface of Aluminum

We have measured the absolute amplitude of the torque and the oscillatory magnetostriction of single crystals of aluminum between 1.2 and 4.2 K and in fields up to 22 kOe. From these results we determined the uniaxial stress dependence of six different orbits. The values for $\left(\frac{1}{A}\right)\left(\frac{\partial A}{\partial \sigma }\right)$, where $A$ is the orbit area and $\sigma$ is a tension in the positive [001] direction were found to range from -2.2×${10}^{-5\mathrm{}}$ ${\mathrm{bar}}^{-1\mathrm{}}$ for the ${\gamma }_2$ orbits to +15.0×${10}^{-5\mathrm{}}$ ${\mathrm{bar}}^{-1\mathrm{}}$ for the ${\alpha }_1$ orbits. The experimental values are in close agreement with the results of a four-OPW (orthogonalized-plane-wave) calculation in which we use the pseudopotential matrix elements and the Fermi energy determined by Ashcroft and take the stress dependence of the pseudopotential to be given by the Heine-Animalu form factor with a local correction for volume changes. By fitting our stress-dependence data to the theoretical calculation we were also able to deduce the slopes of the actual form factor at the two smallest reciprocal-lattice vectors. The values we obtained for the slopes are not very different from those of the Heine-Animalu form factor. Our experimentally determined values for the slopes are $\frac{\partial V}{\partial q}=0.15\mathrm{}\pm 0.07$ a.u. at $\overrightarrow{\mathrm{q}}=\left(\frac{2\pi }{a}\right)(1, 1, 1)$ and $\frac{\partial V}{\partial q}=0.05\mathrm{}\pm 0.01$ a.u. at $\overrightarrow{\mathrm{q}}=\left(\frac{2\pi }{a}\right)(0, 0, 2)$.