Theory of Two-Step Magnetic Ordering Phenomena in a Geometrically Frustrated Heisenberg Pyrochlore Antiferromagnet with Long Range Dipolar Interactions

A model for a Heisenberg antiferromagnet on a pyrochlore lattice with exchange and dipole-dipole interactions is studied via mean-field theory. In treating the dipoles by use of the Ewald method, a soft (critical) mode with a unique ordering wave vector is selected for all strengths of the dipole-dipole coupling. For weak dipoles a partially ordered, three sublattice spin structure (P state), with q_{ord}= (1/2 1/2 1/2), is selected. A fully ordered, four sublattice spin structure (F state), with q = (000), competes with the P state and becomes the stable structure as the temperature is reduced. Our results are compared against other theoretical calculations and connections to recent experimental results for Gd2Ti2O7 are discussed.