"Magnetic order" in usual materials is described by electron's magnetic dipole moment, i.e., spin. We are interested in, exotic, new type of magnetism in the system with strong quantum fluctuations.

  One of a example here is a state which breaks spin rotational symmetry keeping zero magnetic dipolar moments. For spin S=1 case, we study quadrupolar ordering of the spin whose order parameters are written as S_iS_j (i, j=x, y, z). This phase is called as "spin nematic phase" after "nematic order" in liquid crystal.

  We have investigated this spin nematic ordered state in detail. We have fined that the low temperature specific heat is proportional to temperatures by calculating the energy of Goldstone's modes associated with the spin rotational symmetry. We also calculated the magnetic susceptibility and NMR relaxation rate. All the results are consistent with the recent experimental results in triangular spin liquid material NiGa₂S₄.