Magnetic dipole interactions in crystals

The influence of magnetic dipole interactions (MDI5) on the magnetic properties of local-moment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues [lambda] and eigenvectors [mu] of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius rsurrounding a given moment [mu][subi] for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and non-Bravais spin lattices. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFM5) are given. The angular orientation of the ordered moments in the noncollinear coplanar AFM structure of GdB[sub 4] with a distorted stacked 3D Shastry-Sutherland spin-lattice geometry is calculated and found to be in disagreement with experimental observations, indicating the presence of another source of anisotropy.