Engineering entropy: novel phases on the pyrochlore lattice

Frustrated pyrochlores such as Yb$_2$Ti$_2$O$_7$ push our understanding of magnetism to its limits [1, 2]. Here we explore a highly general model for spins on the pyrochlore lattice. We establish a complete phase diagram for the model [3] and are able to identify several previously unstudied limits where classical order breaks down entirely. Here we focus on two limits of special interest: a classical spin liquid and a ``hidden order" spin nematic. These ideas are explored in the context of experiments on the pyrochlore stannates and titanates. [1] J. S. Gardner, M. J. P. Gingras, J. E. Greedan, Rev. Mod. Phys. {\bf 82}, 53, (2010). [2]~K.~A.~Ross, L. Savary, B. D. Gaulin and L. Balents, Phys. Rev. X {\bf 1}, 021002 (2011). [3]~H.~Yan, O.~Benton, L. Jaubert and N.~Shannon, arXiv:1311.3501.