Ground States of the Classical Antiferromagnet on the Pyrochlore Lattice

We study the classical ground states of the exchange-coupled Heisenberg antiferromagnet on the Pyrochlore lattice, a non-Bravais lattice made of corner-sharing tetrahedra. In particular, we map out the entire phase diagram for the case of first and second nearest neighbor interactions. In this phase diagram we find {\it four} complex non-coplanar ground states based on different ordering modes. These are the Cuboctahedral Stack state, a $<111>$ stacking of Cuboctahedral states, and three families of commensurate spiral: the Kawamura states, constructed from three different combinations of $\{\tfrac{3}{4}\tfrac{3}{4}0\}$ modes, the Double-Twist state, also constructed from $\{\tfrac{3}{4}\tfrac{3}{4}0\}$ modes, and the Multiply-Modulated Commensurate Spiral state, constructed from $\{\tfrac{3}{4}\tfrac{1}{4}\tfrac{1}{2}\}$ modes. We also briefly look at states involving the two kinds of third nearest neighbor interactions on the Pyrochlore lattice. In this region of parameter space we again find the Cuboctahedral Stack state, and we also find another non-coplanar state in the form of a new kind of Alternating Conic Spiral.