Magnetization dynamics in Fe$_x$Co$_{1-x}$ in presence of chemical disorder
In this paper, we present a theoretical formulation of magnetization dynamics in disordered binary alloys based on Kubo linear response theory interfaced with the combination of seamlessly three approaches; density functional based tight-binding linear muffin-tin orbitals, generalized recursion and Augmented space formalism. We apply this method to study the magnetization dynamics in chemically disordered Fe$_x$Co$_{1-x}$ ($x$ = 0.2, 0.5, 0.8) alloys. We reported that the magnon energies decrease with an increase in Co concentration. Significant magnon softening has been observed in Fe$_{20}$Co$_{80}$ at the Brillouin zone boundary. The magnon-electron scattering increases with increasing Co content which in turn modifies the hybridization between the Fe and Co atoms. This reduces the exchange energy between the atoms and soften down the magnon energy. The lowest magnon lifetime in found in Fe$_{50}$Co$_{50}$, where disorder is maximum. This clearly indicates that the damping of magnon energies in Fe$_x$Co$_{1-x}$ is governed by the hybridization between Fe and Co whereas the magnon lifetime is controlled by disorder configuration. Our atomistic spin dynamics simulations show a reasonable agreement with our theoretical approach in magnon dispersion for different alloy compositions.