Second Anisotropy Constant in Cubic Ferromagnetic Crystals

The second anisotropy constant, $K_2$, is evaluated at 0°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 $K_2\mathrm{}\left(0\right)\mathrm{}$ is used in conjunction with that for $K_1\mathrm{}\left(0\right)\mathrm{}$ to calculate the values of the pseudodipolar and pseudoquadrupolar coupling constants for iron, cobalt, and nickel. For bcc Fe, $\frac{D}{J}=0.0793\mathrm{}$ and $\frac{Q}{J}=0.00157\mathrm{}$, where $JS=2.87\mathrm{}\times {10}^{-14\mathrm{}}$ erg; for fcc Co, $\frac{D}{J}=0.113\mathrm{}$ and $\frac{Q}{J}=0.000865\mathrm{}$, where $JS=2.0\mathrm{}\times {10}^{-14\mathrm{}}$ erg; and for fcc Ni, $\frac{D}{J}=-0.0768\mathrm{}$ and $Q=0\mathrm{}$, where $JS=2.5\mathrm{}\times {10}^{-14\mathrm{}}$ 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.