Charged magnetic domain lines and the magnetism of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>oxides

The breakdown of the antiferromagnetism in the high-${T}_{c}$ oxides is studied taking into account the 3d charge fluctuations. We point out a tendency towards the formation of charged magnetic domain lines if holes are introduced in such a state, which can be viewed as a generalization of soliton of the Su, Schrieffer, and Heeger to two dimensions. In the ground state these domain lines line up, explaining the incommensurate spin phase observed in the high-${T}_{c}$'s superconductors.

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