We study the magnetic excitations in the spiral phase of the two-dimensional Hubbard model using a functional-integral method. On the one hand, spin waves are strongly renormalized and a line of near zeros is observed in the spectrum around the spiral pitch ±Q. The possibility of disordered spiral states is examined by studying the one-loop corrections to the spiral order parameter. On the other hand, an imaginary mode is present simultaneously with the Goldstone modes. The spiral phase thus shows an intrinsic instability towards an inhomogeneous state [phase separation, charge-density wave (CDW), ...] at weak doping. Though phase separation is suppressed by weak long-range Coulomb interactions, the CDW instability only disappears for sufficiently strong Coulomb interaction.

• Received 24 February 1995

DOI:https://doi.org/10.1103/PhysRevB.52.R11557