  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.
