Condensed Matter Seminars

Frustration arises in magnetic materials when pairwise interactions between the magnetic moments cannot be satisfied simultaneously, leading to exotic properties such as spin liquid and spin ice at low temperatures. Some cases, however, exhibit spin glass behaviors, and it has been a theoretical and experimental challenge to understand whether or not the spin glass state is an intrinsic ground state for the materials. Here we have studied a quasi-two dimensional triangular lattice of bi-pyramids with dominant antiferromagnetic nearest neighbor interactions. We show that the magnetic problem can be mapped into a problem of two independent degrees of freedom, tri-color and binary sign: the color represents the director of the collinear spins of each bi-pyramid, while the binary sign represents spins within each bi-pyramid that are either parallel or antiparallel to the director. At the mean-field level, the tri-color orders long range in a 3 × 3 structure, while the binary sign has numerous degenerate ground states. When combined, the two degrees of freedom yield the collinear bi-pyramid spin ground states for the hybrid lattice. Infinite number of coplanar bi-pyramid spin states can be systematically generated by collective rotations of spins from the collinear states. For long range ordered collinear and coplanar states, we identify ‘partial but extensive’ spin zero-energy modes of excitations that are qualitatively different from the ‘local’ zero-energy excitations found in the spin liquid states of the pure two-dimensional kagome and pure three-dimensional pyrochlore lattices. We argue that due to the infinite ground state degeneracy and the unique characteristics of the zero-energy excitations the ground state of the quasi-two-dimensional hybrid antiferromagnet becomes a spin glass.