Understanding Quantum Critical Magnetism in Han Purple

The ancient purple pigment used to paint the terracotta warriors, BaCuSi₂O₆, is also a quantum magnetic material which consists of stacked Cu²⁺ bilayers hosting spin dimers. Magnetometry and NMR experiments have revealed puzzling critical phenomena at the quantum phase transition (QPT) caused by an applied magnetic field, which suggest that the universal behaviour of the system is not three- but only two-dimensional. By performing high-resolution neutron spectroscopy measurements, we demonstrate that the crystal structure contains three magnetically inequivalent bilayer types, A, B, and C in ratios 3:2:1, and we deduce all of the magnetic interactions, finding them to be effectively ferromagnetic within the bilayers. We show by quantum Monte Carlo simulations that this magnetic structure introduces a regime of anomalous critical behaviour at the QPT that resolves the mystery of the apparent dimensional reduction.