``Flux'' state in double exchange model

We study the ground state properties of the double-exchange systems. The phase factor of the hopping matrix elements arises from $t_{2g}$ spin texture in two or more dimensions. A novel ``flux'' state is stabilized against the canted antiferromagnetic and spiral spin states. In a certain range of hole doping, the phase separation occurs between the ``flux'' state and antiferromagnetic states. Constructing a trial state which provides the rigorous upper bound on the ground state, we show that the metallic canted antiferromagnetic state is not stable in the double exchange model.