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

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