  Pressure effects on the charge and spin dynamics in the bilayer manganite
compounds $La_{2-2x}Sr_{1+2x}Mn_2O_7$ are studied theoretically by taking into
account the orbital degrees of freedom. The orbital degrees are active in the
layered crystal structure, and applied hydrostatic pressure stabilizes the
$3d_{x^2-y^2}$ orbital in comparison with $3d_{3z^2-r^2}$. The change of the
orbital states weakens the interlayer charge and spin couplings, and suppresses
the three dimensional ferromagnetic transition. Numerical results, based on an
effective Hamiltonian which includes the energy level difference of the
orbitals, show that the applied pressure controls the dimensionality of the
spin and charge dynamics through changes of the orbital states.
