Spin diffusion in the double-exchange modelfar above the Curie temperature

Abstract

Spin diffusion within the double-exchange model is studied in thelimits W<<T<<JHS (intermediate temperatures) and W<<JHS<<T (infinite temperature), where W is theelectron bandwidth, T is the temperature, S is the local spin,and JH is the Hund's coupling. In both limits, T is stillfar above the Curie temperature TC~W. All dynamicalproperties are obtained from the spin-current correlation functionC(x), where x denotes time. While C(x) is real (even) atinfinite temperature, it contains both real (even) and imaginary(odd) parts at intermediate temperatures. Upper and lowerTchebycheff bounds are used to evaluate the real part of C(x) ineach limit. From C(ω), we construct the spin conductivityD(ω), which has Gaussian peaks at ω = 0 and ±2JHS, all with the same width ~W. Whereas thecentral peak is produced by the hopping of electrons between sites,the side peaks are produced by the mutual precession of the localand itinerant spins at every site. At infinite temperature, each ofthe side peaks has half the weight of the central peak. But atintermediate temperatures, the side peaks are reduced by T/(JHS)<<1 as the spin precession becomes energeticallyprohibitive. A rigorous f-sum rule relates the integral overD(ω) to the average kinetic energy at any temperature. Inthe 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 Dsreaches a maximum at half-filling (an average of one electron persite) for infinite temperature, it vanishes at half-filling forintermediate temperatures because an electron cannot hop to aneighbouring site without sacrificing enormous Hund's energy. Thepredictions of this work are compared with recent neutron-scatteringmeasurements on the manganites.