Quantum magnetism of perfect spin tetrahedra inCo4B6O13

${\text{Co}}_{4}{\text{B}}_{6}{\text{O}}_{13}$ contains undistorted tetrahedral clusters of magnetic ${\text{Co}}^{2+}$ ions. The high-field magnetization of this magnet exhibits a periodic undulation indicating quantization of the total spin number per cluster. Measurements of magnetic susceptibility and specific heat reveal that the ground state is composed of several different singlet states, reflecting the high symmetry of the spin tetrahedron. An exact diagonalization calculation taking account of single-ion-type anisotropies and Dzyaloshinsky-Moriya interactions reproduces the experimental results very well.