Quantum magnetism of perfect spin tetrahedra in Co$_{4}$B$_{6}$O$_{13}$

Co$_{4}$B$_{6}$O$_{13}$ contains undistorted tetrahedral clusters of magnetic 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 expretimental results very well.