Abstract
We study theoretically the lattice instability in the spin gap systems under magnetic field. With the magnetic field 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 first order phase transition with this lattice distortion.
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