  Magnetic properties under the external field are investigated in low-carrier
two-band systems, which may explain the nontrivial phase boundary found in
temperature vs. magnetic field diagram discovered in some materials, such as
filled-skutterudite compound CeOs$_{4}$Sb$_{12}$. Analysis is made both for the
periodic Anderson model with the small-dispersive $f$ band and the simplified
two parabolic band model in the vicinity of the Fermi level. The magnetic
susceptibilities are calculated by using the random phase approximation. It is
shown that the maximum value of the magnetic susceptibility perpendicular to
the external field is enhanced and yields the anomalous phase boundary. By
applying the magnetic field, the phase boundary shifts to higher temperature
region in the insulating state with a small band gap. On the other hand, the
similar phase boundary also appears in the semi-metallic states, in which the
structure of the density of states in the vicinity of the Fermi level and the
finite temperature effect are essential.
