Experimental study of the Fermi surfaces of niobium and tantalum

The Fermi surfaces of niobium and tantalum have been investigated experimentally utilizing the techniques of the de Haas-van Alphen effect at magnetic fields up to 31 kOe and magnetothermal oscillations at magnetic fields up to 110 kOe. Oscillations associated with extremal orbits on two Fermi-surface sheets of each element have been observed. The Fermi surface is found to have qualitatively the same topology in both metals: a set of six closed surfaces substantially distorted from ellipsoidal shape and centered at N in the bcc Brillouin zone; and a multiply connected jungle-gym surface consisting of interconnecting arms along 〈100〉 directions with intersections at Γ and H. The agreement between these data and recent augmented-plane-wave (APW) energy-band calculations is excellent. The minimum cross sections of the 〈100〉 arms of the jungle gym have areas of 0.138 Å⁻² in Nb and 0.263 Å⁻² in Ta; and the principal cross sections of the distorted ellipsoids are 0.636, 0.757, and 0.857 Å⁻² in Nb, and 0.434, 0.580, and 0.59 Å⁻² in Ta. A third surface of holes centered at Γ is predicted by band-structure calculations, but has not been observed unambiguously in the present work. Effective masses have been measured at several orientations, and comparison with the APW calculations yield average mass-enhancement factors of 1.75 for Nb and 1.85 for Ta, in fair agreement with predictions based on phonon enhancement.