  A three-dimensional chiral helimagnet is analyzed using a mean-field (MF)
analysis and a classical Monte Carlo (MC) simulation at finite temperatures. We
consider a Hamiltonian containing Heisenberg exchange and uni-axial
Dzyaloshinskii-Moriya interactions on a simple cubic lattice. Magnetization
curves calculated by the MF theory are qualitatively consistent with those
observed in experiments. A comparison between lattice and continuum models
clarifies the region where the continuum approximation can be applied. By
combining the MF theory with the classical MC method, it is also clarified that
results are quantitatively much improved by including spin correlations in the
layer perpendicular to the helical axis. On the basis of our simple model,
interaction parameters in $CrNb_3S_6$ are estimated. These values of exchange
interactions justify a physical picture that the spins are strongly coupled in
the two-dimensional layer and are weakly interacted with those in the helical
chain.
