  In frustrated systems, some or many states are competed due to frustration of
exchange interactions, and this competition often results in exotic states,
such as spin liquid and chiral orders. We consider a pyrochlore oxide, a
three-dimensional frustrated system, and study its $S=\frac{1}{2}$ effective
model, consisting of the Heisenberg-type and Dzyaloshinsky-Moriya-type
superexchange interactions between the nearest-neighbor transition-metal ions.
We show that by using new multiorbital effects of the $t_{2g}$ orbitals on
coefficients of those interactions, we can change the effective dimensionality
from three-dimensional to two-dimensional, and control the competition between
chiral orders and spin liquid. We also show that the new multiorbital effects
are vital to stabilize three-in-one-out chiral order, distorted
four-in-four-out chiral order, and distorted three-in-one-out chiral order, and
can be used to hold macroscopic degeneracy, resulting in the spin liquid, even
with the finite Dzyaloshinsky-Moriya interactions. Those results open up new
multiorbital physics in spin systems, and make the essential step for the
realistic mechanism for the spin liquid in pyrochlore oxides.
