Nearly antiferromagnetic Fermi-liquid description of magnetic scaling and spin-gap behavior

We present a Fermi-liquid description of magnetic scaling and spin-gap behavior in strongly correlated electron systems. We show that a gap in the spin-excitation spectrum is a natural consequence of the existence of a second energy scale of magnetic origin, in systems of itinerant, but nearly localized electron spins, such as are found in the cuprate superconductors and heavy-electron systems. A second energy scale leads to a frequency-dependent restoring force ${\mathit{f}}^{\mathit{a}}$(q,ω) that becomes stronger as the frequency increases. A spin gap at Q=(π/a,π/a) is a consequence of these frequency-dependent vertex corrections; it takes on a constant value when the antiferromagnetic correlation length becomes a constant. We show that the spin-spin response function reduces to that recently introduced by Barzykin to describe the damping by particle-hole excitations of the spin-wave spectrum found in the N=∞ quantum nonlinear σ model. We discuss fully doped and underdoped cuprate superconductors, the appearance of a pseudogap of magnetic origin in the quasiparticle density of states in the underdoped system, and the constraints nuclear magnetic resonance and neutron-scattering experiments impose on the magnitude and temperature dependence of the Fermi-liquid parameters.