Coexisting order and disorder hidden in a quasi-two-dimensional frustrated magnet

Frustrated magnetic interactions in a quasi-two-dimensional [111] slab of pyrochlore lattice were studied. For uniform nearest neighbor (NN) interactions, we show that the complex magnetic problem can be mapped onto a model with two independent degrees of freedom, tri-color and binary sign. This provides a systematic way to construct the complex classical spin ground states with collinear and coplanar bi-pyramid spins. We also identify `partial but extended zero-energy excitations amongst the ground states. For nonuniform NN interactions, the coplanar ground state can be obtained from the collinear bi-pyramid spin state by collectively rotating two spins of each tetrahedron with an angle, $alpha$, in an opposite direction. The latter model with $alpha sim 30^circ$ fits the experimental neutron data from SCGO well.