de Haas—van Alphen Effect and Electronic Band Structure of Nickel

We present here a de Haas-van Alphen (DHVA) investigation of nickel utilizing low-frequency field-modulation techniques in magnetic fields extending to 38 kG and at temperatures down to 0.3\ifmmode^\circ\else\textdegree\fi{}K. Two distinct sets of DHVA-frequency branches were obtained with the magnetic field in either the ($1\overline{1}0$) or the (100) crystallographic symmetry plane. The assignment of these to sheets of the nickel Fermi surface is discussed in terms of the general features of band-structure models recently proposed for ferromagnetic nickel. The low-frequency branches are assigned to the [111]-directed necks of the spin-$\ensuremath{\uparrow}$ $s$-band electron sheet. The high-frequency branches are shown to arise from a $d$-band hole pocket derived from a pure ${X}_{5}$ level in the spin-$\ensuremath{\downarrow}$ band. No evidence was obtained for $d$-band hole pockets derived from the ${X}_{2}\ensuremath{\downarrow}$ and ${L}_{3}\ensuremath{\downarrow}$ levels. Since the singal-to-noise ratio for detecting the high-frequency branches was large, the fact that we did not observe any DHVA oscillations assignable to either the ${X}_{2}\ensuremath{\downarrow}$ or ${L}_{3}\ensuremath{\downarrow}$ pockets makes their existence doubtful.