  We study the Kondo lattice model with the Heisenberg-type RKKY-exchange
coupling among localized f-spins in the presence of a magnetic field. By means
of an extended dynamical mean field theory combined with the non-crossing
approximation, we investigate the one-particle spectral function and the
dynamical spin correlation function in the Kondo insulating phase. It is shown
that the magnetic field and the RKKY exchange interaction both cause the
instability to the antiferromagnetic order with enhanced transverse spin
fluctuations, which give rise to a strong renormalization of quasi-particles as
the system approaches the quantum critical point. This leads to a tendency to
retain the Kondo insulating gap up to rather large fields.
