Second Anisotropy Constant in Cubic Ferromagnetic Crystals

Abstract

The second anisotropy constant, ${K}_{2}$, is evaluated at 0\ifmmode^\circ\else\textdegree\fi{}K for cubic, ferromagnetic crystals using two-particle dipole- and quadrupole-like interactions as perturbations on a molecular field Hamiltonian. In second- and third-order perturbation, the energy denominators are modified to take into account the effect on the molecular field of the exchange interaction of consecutively reversed spins. The expression for ${K}_{2}(0)$ is used in conjunction with that for ${K}_{1}(0)$ to calculate the values of the pseudodipolar and pseudoquadrupolar coupling constants for iron, cobalt, and nickel. For bcc Fe, $\frac{D}{J}=0.0793$ and $\frac{Q}{J}=0.00157$, where $JS=2.87\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ erg; for fcc Co, $\frac{D}{J}=0.113$ and $\frac{Q}{J}=0.000865$, where $JS=2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ erg; and for fcc Ni, $\frac{D}{J}=\ensuremath{-}0.0768$ and $Q=0$, where $JS=2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ erg, although the application of the model to nickel is not entirely satisfactory. These values are used to predict the size of the third anisotropy constant and the paramagnetic resonance linewidth.