Magnetic Long-Range Order and Colossal Magnetoresistance Effect in Double Exchange Ladders

By applying Bogoliubov's inequality to double-exchange (DE)
ladders, we show that the ferromagnetic (FM) order is absent in the new DE systems at finite temperature. The incorporations of Jahn-Teller electron-phonon coupling, orbital degeneracy and on-site Coulomb interaction with the DE interaction do not preserve these orders. The long-wavelength thermal fluctuations of the spins overcome the DEFM correlation and destroy the FM orders. The implication of the absence of FM order on the transport of the DE ladders is discussed.