Ordering Phenomena in Transition Metal Oxides

Dimensional reduction in frustrated quantum critical magnets   

We discuss ordering transitions in layered magnets. Upon approaching quantum criticality, one expects a crossover from two-dimensional (2d) to three-dimensional (3d) behavior at an energy scale set by the inter-layer coupling. Experimentally, the relevant crossover scale is often surprisingly small or even unobservable. Using the Mott-insulating magnet BaCuSi₂O₆ as an example, we illustrate two distinct mechanisms which can drastically suppress the dimensional crossover scale, namely (i) inter-layer frustration and (ii) inhomogeneous condensates due to inequivalent layers. We also discuss thermal transitions and related scenarios for metallic systems.