Absence of quantum criticality and bulk 3D magnetism in green dioptase

Green dioptase is a naturally occurring antiferromagnetic mineral that in recent years has been suggested as a candidate to exhibit quantum fluctuations at both above and below T N. Our work uses muon spectroscopy to study the dynamic and static properties of the magnetism in zero applied field. We observe the antiferromagnetic transition through tracking out the evolution of the muon spin precession frequency as a function of temperature. T N is calculated to be 15 K and the critical exponent of the transition matches with that of a 3D Heisenberg system. We also note that no evidence for any quantum magnetic fluctuations is observed either above or below T N.