De Haas-van Alphen Effect and Fermi Surface in Palladium

Abstract

A detailed study of the de Haas-van Alphen (dHvA) effect in Pd by the field modulation technique is presented. The dHvA oscillations were observed in magnetic fields up to 53 kG at temperatures between 1 and 2\ifmmode^\circ\else\textdegree\fi{}K. Two distinct sets of oscillations were observed with the field in either the (110) or the (100) planes. These are interpreted by a rigid-band model using the known Cu band structure. The oscillations correspond to (1) electrons in the $s$ band and (2) small pockets of holes in one of the $d$ bands. The electron surface is closed and it is centered at $\ensuremath{\Gamma}$. The hole surfaces, also closed, are located at $X$; and they are approximately ellipsoidal with their major axis along [100]. The electron surface contains 0.36\ifmmode\pm\else\textpm\fi{}0.01 electrons/atom while the hole ellipsoids contain only 5.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ holes/atom. The average effective mass $m=2.2{m}_{0}$ for the electrons, and the smallest hole mass ${m}_{100}=(0.63\ifmmode\pm\else\textpm\fi{}0.05){m}_{0}$. There is also a second $d$-band hole surface which is open along [100]. The total number of holes is thus 0.36\ifmmode\pm\else\textpm\fi{}0.01 per atom, since Pd is a compensated metal. This model also provides a complete interpretation of the galvanomagnetic data. The effects of spin-orbit coupling on the $d$-band surfaces are discussed in terms of a semiempirical calculation by Mueller. Since the known Cu band structure explains almost every detail of the present experiment, it provides direct evidence that the band structures of certain transition metals have many common features.