We present temperature-dependent x-ray diffraction and temperature- and field-dependent Raman scattering studies of single crystal Mn3O4, which reveal the novel magnetostructural phases that evolve in the spinels due to the interplay between strong s
pin-orbital coupling, geometric frustration, and applied magnetic field. We observe a structural transition from tetragonal to monoclinic structures at the commensurate magnetic transition at T2=33K, show that the onset and nature of this structural transition can be controlled with an applied magnetic field, and find evidence for a field-tuned quantum phase transition to a tetragonal incommensurate or spin glass phase.
A number of spectacular experimental anomaliescite{li-2007,fujita-2005} have recently been discovered in certain cuprates, notably {LBCO} and {LNSCO}, which exhibit unidirectional spin and charge order (known as ``stripe order). We have recently prop
osed to interpret these observations as evidence for a novel ``striped superconducting state, in which the superconducting order parameter is modulated in space, such that its average is precisely zero. Here, we show that thermal melting of the striped superconducting state can lead to a number of unusual phases, of which the most novel is a charge $4e$ superconducting state, with a corresponding fractional flux quantum $hc/4e$. These are never-before observed states of matter, and ones, moreover, that cannot arise from the conventional Bardeen-Cooper-Schrieffer (BCS) mechanism. Thus, direct confirmation of their existence, even in a small subset of the cuprates, could have much broader implications for our understanding of high temperature superconductivity. We propose experiments to observe fractional flux quantization, which thereby could confirm the existence of these states.
We discuss how quantum dimer models may be used to provide proofs of principle for the existence of exotic magnetic phases in quantum spin systems.
