Dimensional reduction at the BEC quantum critical point in BaCuSi$_{2}$O$_{6}$.

We present results on the magnetic spin dimer system BaCuSi$_{2}$O$_{6}$, which can be tuned across a Bose-Einstein condensation (BEC) quantum critical point (QCP) to an ordered BEC of spins by applying an external magnetic field. Experimental results reveal a continuous crossover in critical scaling behaviour near the QCP from 3d to 2d BEC universality, indicating that dimensionality itself is an emergent property at the QCP of this particle density-tuneable BEC. Geometrical frustration leading to inter-layer decoupling is identified as the mechanism responsible for this unique manifestation of a lower dimensional QCP in the 3d BaCuSi$_{2}$O$_{6}$ spin system. While the theoretical concept of dimensional reduction has been extensively discussed in many different contexts as a route to low dimensionality in bulk materials, this is the first experimental realisation of dimensionally reduced criticality.