Critical BKT dynamics in the archetypal 2D spin system Ba$_2$CuSi$_2$O$_6$Cl$_2$

TL;DR

This study combines NMR experiments and quantum Monte Carlo simulations to reveal Berezinskii-Kosterlitz-Thouless (BKT) critical fluctuations in a quasi-2D spin-1/2 dimer compound, establishing it as a model for BKT physics in quantum magnets.

Contribution

It provides the first detailed experimental and theoretical evidence of BKT-type fluctuations in Ba$_2$CuSi$_2$O$_6$Cl$_2$, linking 2D critical behavior with BEC of triplons.

Findings

Observation of a broad peak in relaxation rate indicating 2D BKT fluctuations.

Quantitative agreement between experimental phase boundaries and an effective XXZ model.

Identification of a nearly field-independent BKT transition temperature ratio.

Abstract

We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance (NMR) spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the N\'eel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets.