The magnetic susceptibility, elastic constant, specific heat and magnetization of the magnetic semiconductor TmTe have been measured in detail. A phase transition which is likely to be an antiferro quadrupolar ordering was found to occur at 1.8 K. The specific heat measurements under magnetic fields along the three main crystal axes revealed the unusual characters of this phase transition. The (H - T) phase diagram below 5 T is very similar to that of the antiferro quadrupolar ordering in CeB6. Above 5 T, however, the phase line for H ∥  begins to close toward T = 0 K. The physical properties in the paramagnetic region at high temperatures are discussed in the mean field approximation. The theoretical fitting of the elastic softening indicates the antiferro inter-ionic quadrupolar interactions. However, the mean field theory can not explain the specific heat results.
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