We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound ${\mathrm{Ba}}_2{\mathrm{CuSi}}_2{\mathrm{O}}_6{\mathrm{Cl}}_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance 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 Néel 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 $T_{\text{BKT}}$ 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 ${\mathrm{Ba}}_2{\mathrm{CuSi}}_2{\mathrm{O}}_6{\mathrm{Cl}}_2$ as a model system for exploring BKT dynamics in quantum magnets.

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• BKT transition
• Critical field
• Magnetic phase transitions
• Quantum criticality
• Spin dynamics
• 2-dimensional systems
• Antiferromagnets
• Bose-Einstein condensates
• Magnetic systems
• Nuclear magnetic resonance
• Nuclear magnetic resonance relaxation rate
• Quantum Monte Carlo