Instability in the Spin - Ladder System under

We study theoretically the lattice instability in the spin gap systems under magnetic eld. With the magnetic eld larger than a critical value h c1 , the spin gap is collapsed and the magnetization arises. We found that the lattice distortion occurs in the spin-ladder at an incommensurate wavevector corresponding to the magnetization, while it does not occur in the Haldane system. At low temperatures the magnetization curve shows a rst order phase transition with this lattice distortion.