First principles theory of spin waves in Fe, Co, and Ni

Using constrained local spin density functional theory it is possible to directly calculate the adiabatic magnon dispersion curve. Small amplitude magnons with wavelengths between 2 and 32 atomic layers were constructed and the energy change with respect to amplitude within the frozen potential approximation was calculated. The resulting dispersion curves give the spin wave stiffness for [111] face-centered-cubic Co and Ni in fair agreement with experiment. In Fe the stiffness was calculated along [100] and [110] directions. The two values of stiffness were found to be nearly equal to each other and roughly half the measured value. It was found that the calculated Fe stiffness did not change upon addition of gradient corrections to the local density approximation, indicating that the source of discrepancy is not likely a failure of the local density approximation. It is argued that the adiabatic approximation is more likely the source of discrepancy since the magnetic interactions in Fe are longer ranged than those in Co or Ni, thus making the dynamical retardation effect more important in Fe.