Critical Low-Energy Spin Dynamics in the BEC-Type Antiferromagnets

The NMR nuclear spin-lattice relaxation rate (1/T₁) data in quantum spin systems provide privileged access to low-energy spin fluctuations and are directly comparable to theoretical predictions for the corresponding spin-spin correlation functions. In particular, gapless quasi-1D systems are addressed by the Tomonaga-Luttinger Liquid (TLL) theory, a purely 1D, effective, low-energy description, providing a 1D-critical, power-law prediction for the temperature (T) dependence of 1/T₁. We showed that in real compounds an RPA-based correction factor has to be applied to this power-law, in order to account for the enhancement of the 1/T₁ rate induced by the 3D-critical fluctuations related to the low-T BEC ordering. Using this TLL+RPA description, we successfully fitted the 1/T₁(T) data in a spin-ladder compound (C₇H₁₀N)₂CuBr₄ (DIMPY) and in an Ising spin chain BaCo₂V₂O₈, providing thereby the first direct determination of the TLL interaction parameter K that confirms the theoretical predictions [1].

We now focus on describing spin fluctuations in quasi-2D systems, where our results in Ba₂CuSi₂O₆Cl₂ suggest that the 1/T₁ data could provide a clear signature for the system’s effective dimensionality. However, we find only a partial agreement with the Quantum Monte Carlo (QMC) simulations, leaving the subject open to further investigation.

Finally, from the 1/T₁ data recorded precisely at the saturation field in the SrZnVO(PO₄)₂ compound we learn that the theoretically predicted quantum critical T^3/4 dependence cannot be experimentally accessed in any compound, because the convergence into this low-T limit is too slow and the theoretical prediction is no longer valid when the BEC transition is too close. Nevertheless, the complete description provides correct semi-quantitative account of the data [2].