The subtle interplay between low-dimensionality and spin correlations can lead to exotic ground states with unconventional excitations in two-dimensional honeycomb-lattice-based quantum magnets. Herein, we present the structural, magnetic, and heat capacity measurements; density functional theory $+$ Hubbard $U$ ($\mathrm{DFT}+U$) based electronic structure calculations; and quantum Monte Carlo simulations for $\mathrm{NaCuIn}{\left({\mathrm{PO}}_4\right)}_2$. The structure of $\mathrm{NaCuIn}{\left({\mathrm{PO}}_4\right)}_2$ consists of a well-separated, $\mathit{S}=\frac{1}{2}$ distorted ${\mathit{J}}_1\text{−}{\mathit{J}}_2$ honeycomb layer which is a combination of the magnetic couplings ${\mathit{J}}_1$ (forming spin dimers) and ${\mathit{J}}_2$ (constituting spin chains). At high temperatures, the magnetic susceptibility $\chi \left(T\right)$ follows paramagnetic behavior with a Curie-Weiss temperature ${\theta }_{\mathrm{CW}}\approx -16$ K, implying the presence of antiferromagnetic interactions. A broad maximum is observed at about $13\mathrm{K}$ in $\chi \left(T\right)$, indicating the presence of short-range spin correlations. The quantum Monte Carlo simulations using the $\mathit{S}=\frac{1}{2}{\mathit{J}}_1\text{−}{\mathit{J}}_2$ Heisenberg model on a distorted honeycomb lattice are in good agreement with the measured magnetic susceptibility data. The obtained ratio of the exchange couplings ($\frac{{\mathit{J}}_2}{{\mathit{J}}_1}$) is 2.63, which is consistent with the value obtained from our $\mathrm{DFT}+U$ calculations. The title material undergoes a magnetic long-range order at 0.4 K in the heat capacity, which is suppressed with an applied magnetic field of 10 kOe. The magnetic heat capacity data follow a linear temperature-dependent behavior well above the transition temperature, suggesting the presence of gapless excitations. The observed behavior can be attributed to the presence of low connectivity and weak magnetic frustration in this two-dimensional distorted honeycomb lattice.

• Received 16 January 2023
• Revised 13 April 2023
• Accepted 7 June 2023

DOI:https://doi.org/10.1103/PhysRevB.107.214430