Spin diffusion in the double-exchange model far above the Curie temperature

Spin diffusion within the double-exchange model is studied in the limits W<<T<<JHS (intermediate temperatures) and W<<JHS<<T (infinite temperature), where W is the electron bandwidth, T is the temperature, S is the local spin, and JH is the Hund's coupling. In both limits, T is still far above the Curie temperature TC∼W. All dynamical properties are obtained from the spin-current correlation function C(x), where x denotes time. While C(x) is real (even) at infinite temperature, it contains both real (even) and imaginary (odd) parts at intermediate temperatures. Upper and lower Tchebycheff bounds are used to evaluate the real part of C(x) in each limit. From C(ω), we construct the spin conductivity D(ω), which has Gaussian peaks at ω=0 and ± 2JHS, all with the same width ∼W. Whereas the central peak is produced by the hopping of electrons between sites, the side peaks are produced by the mutual precession of the local and itinerant spins at every site. At infinite temperature, each of the side peaks has half the weight of the central peak. But at intermediate temperatures, the side peaks are reduced by T/(JHS)<<1 as the spin precession becomes energetically prohibitive. A rigorous f-sum rule relates the integral over D(ω) to the average kinetic energy at any temperature. In the zero-frequency limit, the spin-diffusion coefficient Ds=(1/2)D(ω=0) yields the relaxation time τr(k)=1/(Dsk2) for a magnetic disturbance with wavevector k. Whereas Ds reaches a maximum at half-filling (an average of one electron per site) for infinite temperature, it vanishes at half-filling for intermediate temperatures because an electron cannot hop to a neighbouring site without sacrificing enormous Hund's energy. The predictions of this work are compared with recent neutron-scattering measurements on the manganites. (author)