Oscillatory Field Dependence of the Knight Shift in a Monocrystal of Tin

Abstract

A detailed experimental investigation of the magnetic-field dependence of the Knight shift in a monocrystal of white tin has been performed. The measurements were made at 1.2\ifmmode^\circ\else\textdegree\fi{}K and in magnetic fields ranging from 10.5 to 16.2 kG. The Knight shift is found to oscillate at the de Haas-van Alphen (dHvA) frequency, and in the range of fields investigated, exhibits two periods of 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ and 5.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ ${\mathrm{G}}^{\ensuremath{-}1}$. The values and angular variations of these periods are in satisfactory agreement with the data on the tin Fermi surface obtained from other experiments and from a pseudopotential calculation of the band structure. The magnetic-field dependence of the amplitude of the oscillations has been investigated for both periods. The amplitude of the shorter-period component increases, and that of the longer-period component decreases, with increasing magnetic field. The decrease in amplitude of the longer-period oscillation is attributed to the effects of magnetic breakdown. The observed amplitudes are in satisfactory agreement with the assumption that the Knight-shift oscillations are due to oscillations in the ground-state wave functions of the contributing electrons rather than oscillations in the susceptibility as has been previously suggested. Measurements of the dHvA susceptibility oscillations in the same sample used for the Knight-shift measurements give further support to this viewpoint, since the field variation of the amplitude of the susceptibility oscillations is drastically different from the corresponding field dependence of the oscillatory Knight shift.