Abstract
The effect of the extra second neighbor hopping t′ on the incommensurate spin correlation in the t-J model in the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighbor hopping t′ is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamical spin structure factor, for the physical reasonable small value of t′ the qualitative behavior of the incommensurate spin correlation in the t-t′-J model is the same as in the case of t-J model.
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