Effect of the additional second neighbor hopping on the spin dynamics in   the t-J model
  The effect of the additional second neighbor hopping t' on the spin dynamics in the t-J model is studied within the fermion-spin theory. Although the additional second neighbor hopping t' is systematically accompanied with the reduction of the dynamical spin structure factor and susceptibility, the qualitative behaviors of the dynamical spin structure factor and susceptibility are the same as in the case of t-J model. It is also shown that the integrated dynamical spin structure factor is almost t' independent in the underdoped regime. 
Xianglin Le, Feng Yuan, and Shiping Feng