de Haas-van Alphen Effect in Antiferromagnetic Chromium

De Haas-van Alphen torque oscillations have been studied in single-domain crystals of Cr in magnetic fields to 33 kG and have been analyzed by computer calculation of their Fourier transform. Extensive data in all major symmetry planes and several nonsymmetry planes confirm the tetragonal symmetry of the Fermi surface in the antiferromagnetic state. The frequency resolution is sufficient to isolate several families of data, a number of which can be represented well by simple geometrical Fermi-surface models. Band calculations for paramagnetic Cr indicate a Fermi surface which contains a closed hole sheet at the point $N$ of the Brillouin zone and a closed electron sheet located along $\Gamma H$. For simplicity, it is assumed that the electron and hole octahedra at $\Gamma$ and $H$, respectively, are destroyed by the interaction which stabilizes the antiferromagnetic state. The surviving Fermi-surface sheets at $N$ and along $\Gamma H$ are truncated by energy gaps due to the antiferromagnetic Q vector, as proposed by Lomer. Several of the resulting surfaces resemble those obtained from the geometrical analysis of the data. By adjusting the dimensions and shape of the hole surfaces at $N$, it is possible to interpret three families of data with an accuracy of ∼10% in area. Applying a similar procedure to the electron surface along $\Gamma H$ yields ∼20% agreement with a fourth family of data. The many remaining frequencies receive either a tentative assignment or none at all.