Dipolar Sums in the Primitive Cubic Lattices

Dipole-wave sums, important in many magnetic and electric problems involving dipole-dipole interactions, are defined, and numerical values are given at sets of independent points in k-space equivalent to a 512-fold sampling of the first Brillouin zone of each of the three primitive cubic lattices. Strong size, shape, and position dependence of these sums is shown to occur in a pathological region about the origin in k-space. The dipole-wave sums are shown to be related to dipole-field factors at points within the unit cell. The dipolar anisotropy energy in the antiferromagnet MnO is discussed as an illustration of the use of dipole-wave sums.