Doped antiferromagnet: The instability of homogeneous magnetic phases

The Schwinger-boson--slave-fermion mean-field theory is applied to the complete (to order t²/U) two-dimensional t-J model at low doping and at zero temperature. A multiple Hubbard-Stratonovich transformation defines the order parameters and keeps track of their random-phase-approximation (RPA) fluctuations. The lowest mean-field state is a long-range-ordered spiral state. We find that for any t/J at infinitesimal doping, this state and other homogeneous magnetic states are unstable against local enhancements of the spiral's pitch. The instability manifests itself at the mean-field level by a negative compressibility, and at the RPA level by negative eigenvalues of the Gaussian determinant. We discuss the implications of this instability on theory and experiments.