Quadrupole Effects of Vacancy Orbital in Boron-Doped Silicon

We have investigated low-temperature properties at a longitudinal elastic constant C L[111] of a boron-doped silicon crystal grown by a floating zone (FZ) method. The softening of C L[111] depending on magnetic fields indicates that a magnetic charge state V + of a vacancy orbital accommodating three electrons is stable. Appreciable anisotropy in the softening of C L[111] at magnetic fields along the [111] and [1\bar10] axes up to 10 T is described in terms of a quadrupole susceptibility for the vacancy orbital consisting of a Γ 8 quartet ground state and Γ 6 doublet excited state due to the spin–orbit interaction.