Dynamic susceptibility and photoemission in thet-t’-Jmodel

We consider the slave-fermion–Schwinger-boson decomposition of a t-J model for a two-dimensional antiferromagnet in which the next-nearest-neighbor hopping is taken into account by an explicit t’ term. This technique is particularly suitable to describe systems with low hole density, as in the parent phases of high-${\mathit{T}}_{\mathit{c}}$ superconducting (HTSC) materials, and we examine the experimental consequences of the model. Using mean-field states which admit finite spiral and off-diagonal order, we compute first the dynamic susceptibility χ(q,ω) from fluctuations in the boson (spin) degrees of freedom, and investigate a selected parameter regime for the model to seek features consistent with inelastic neutron scattering experiments on underdoped HTSC crystals. We find peaks in the scattered intensity at incommensurate wave vectors (π±2${\mathit{k}}_0$,±π) and (π,±π±2${\mathit{k}}_0$), but within our approximation the q-integrated susceptibility as a function of frequency and temperature resembles that from spin-wave theory, which does not contain the scaling behavior over all values of ω/T found experimentally. We show also the form of the nuclear magnetic resonance relaxation time ${\mathit{T}}_1^{\mathrm{-}1}$(T), which measures the zero-frequency limit of the susceptibility. The imaginary part of the physical electron Green function is a convolution of both fermionic (hole) and bosonic Green functions, and so incorporates the effect of spin dynamics on the charge motion. We calculate the photoemitted intensity, a direct experimental measurement of this quantity, focusing on its behavior near the hole pockets at (±π/2,±π/2) which characterize this type of model. The peak photocurrent occurs not at the hole Fermi surface, but at points separated from it by ${\mathbf{k}}_0$ due to the boson incommensuration.