F-sum rule for the spin conductivity in itinerant magnets

We derive a rigorous f-sum rule for the spin conductivity D(ω), valid in the paramagnetic regime of any itinerant system with nearest-neighbor hopping, assuming only that the potential energy conserves the total spin at each site. Two such itinerant systems are the double-exchange and Hubbard models. According to the f-sum rule, the integral over D(ω) is proportional to the average, electronic kinetic energy and is inversely proportional to the static susceptibility. The elastic value D(0) can be obtained directly from the width of the quasielastic peak in neutron-scattering measurements. For infinite dimensions dynamical mean-field theory implies that D(ω) is proportional to the optical conductivity σ(ω) and that implies the f-sum rule for D(ω) reduces to the well-known optical sum rule for σ(ω). Our results place severe constraints on the appropriate model to describe the magnetoresistive manganites.