Chiral magnets are magnetically ordered insulators having spin scalar chirality, and magnons of chiral magnets have been poorly understood. We study the magnon dispersion and specific heat for four chiral magnets with Q=0 on the pyrochlore lattice. This study is based on the linear-spin-wave approximation for the S=1/2 effective Hamiltonian consisting of two kinds of Heisenberg interaction and two kinds of Dzyaloshinsky-Moriya interaction. We show that the three-in-one-out type chiral magnets possess an optical branch of the magnon dispersion near q=0, in addition to three quasiacoustic branches. This differs from the all-in/all-out type chiral magnets, which possess four quasiacoustic branches. We also show that all four chiral magnets have a gapped magnon energy at q=0, indicating the absence of the Goldstone type gapless excitation. These results are useful for experimentally identifying the three-in-one-out or all-in/all-out type chiral order. Then, we show that there is no qualitative difference in the specific heat among the four magnets. This indicates that the specific heat is not useful for distinguishing the kinds of chiral orders. We finally compare our results with experiments and provide a proposal for the three-in-one-out type chiral magnets.
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