Influence of the additional second neighbor hopping on the spin response   in the t-J model
  The influence of the additional second neighbor hopping t' on the spin response of the t-J model in the underdoped and optimally doped regimes 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 behavior of the dynamical spin structure factor and susceptibility of the t-t'-J model is the same as in the case of t-J model. The integrated dynamical spin structure factor spectrum is almost t' independent, and the integrated dynamical spin susceptibility still shows the particularly universal behavior as $I(\omega,T)\propto {\rm arctan}[a_{1}\omega/T+a_{3}(\omega/T)^{3}]$. 
Xianglin Ke, Feng Yuan, and Shiping Feng