Field-tunable Berezinskii-Kosterlitz-Thouless correlations in a Heisenberg magnet

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material Cu(pz)${}_2$(2-HOpy)${}_2$${}_2$. Due to the moderate intralayer exchange coupling of $J\mathrm{/}{k}_{\mathrm{B}}=6.8$ K, the application of laboratory magnetic fields induces a substantial $XY$ anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange $J^{\mathrm{\prime }}\mathrm{/}{k}_{\mathrm{B}}\approx 1$ mK only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance and ${\mu }^{+}$SR measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum Monte Carlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of Cu(pz)${}_2$(2-HOpy)${}_2$${}_2$ is determined by the field-tuned $XY$ anisotropy and the concomitant BKT physics.