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We report a combined $^{115}$In NQR, $^{51}$V NMR and $\mu$SR spectroscopicstudy of the low-temperature magnetic properties of InCu$_{2/3}$V$_{1/3}$O$_3$,a quasi-two dimensional (2D) compound comprising in the spin sector a honeycomblattice of antiferromagnetically coupled spins $S=1/2$ associated withCu$^{2+}$ ions. Despite substantial experimental and theoretical efforts, theground state of this material was has not been ultimately identified. Inparticular, two characteristic temperatures of about $\sim 40$ K and $\sim 20$K manifesting themselves as anomalies in different magnetic measurements arediscussed controversially. A combined analysis of the experimental datacomplemented with theoretical calculations of exchange constants enabled us toidentify below 39 K an ``intermediate'' quasi-2D static spin state. This spinstate is characterized by a staggered magnetization with a temperatureevolution that agrees with the predictions for the 2D XY model. We observe thatthis state gradually transforms at 15 K into a fully developed 3Dantiferromagnetic N\'eel state. We ascribe such an extended quasi-2D staticregime to an effective magnetic decoupling of the honeycomb planes due to astrong frustration of the interlayer exchange interactions which inhibitslong-range spin-spin correlations across the planes. Interestingly, we findindications of the topological Berezinsky-Kosterlitz-Thouless transition in thequasi-2D static state of the honeycomb spin-1/2 planes ofInCu$_{2/3}$V$_{1/3}$O$_3$.

Ground state and low-temperature magnetism of the quasi-two-dimensional honeycomb compound InCu$_{2/3}$V$_{1/3}$O$_3$