Collective Modes near the Spin-Flip Continuum and Spin Depolarization due to Indirect Exchange

In the indirect exchange model, the spin-wave dispersion relation undergoes anomalous behavior as it enters the continuum of electron spin-flip excitations. This anomaly consists of two Kohn-type singularities of opposite strength located very close together, causing a bump in the dispersion relation rather than the usual isolated kink. The single-particle renormalization constant diverges logarithmically at these singularities, and thus the spin-wave picture is inadequate in this region. The line shape is distorted by the strong frequency dependence near the absorption edge and the peak shifts either up or down depending on the sign of the exchange interaction between the localized spins and the conduction electrons. At zero temperature the ground state does not have the local spins fully aligned but slightly depolarized due to virtual excitations of conduction electrons. The total fractional deviation is given approximately by the Curie-to-Fermi-temperature ratio. Effects of a short-range repulsion between conduction electrons have also been studied. In general, the spin-wave spectrum curvature, Curie temperature, and zero temperature deviation are increased by powers of the spin-susceptibility enhancement factor.