Finite-size effects and magnetic order in the spin-$\frac{1}{2}$ honeycomb-lattice compound ${\text{InCu}}_{2/3}{\text{V}}_{1/3}{\text{O}}_3$

High-field electron spin resonance, nuclear magnetic resonance, and magnetization studies addressing the ground state of the quasi-two-dimensional spin-$\frac{1}{2}$ honeycomb lattice compound ${\text{InCu}}_{2/3}{\text{V}}_{1/3}{\text{O}}_3$ are reported. Uncorrelated finite-size structural domains occurring in the honeycomb planes are expected to inhibit long-range magnetic order. Surprisingly, ESR data reveal the development of two collinear antiferromagnetic (AFM) sublattices below $\sim 20\text{K}$, whereas NMR results show the presence of the staggered internal field. Magnetization data evidence a spin reorientation transition at $\sim 5.7\text{T}$. Quantum Monte Carlo calculations show that switching on the coupling between the honeycomb spin planes in a finite-size cluster yields a Néel-like AFM spin structure with a substantial staggered magnetization at finite temperatures. This may explain the occurrence of a robust AFM state in ${\text{InCu}}_{2/3}{\text{V}}_{1/3}{\text{O}}_3$ despite an unfavorable effect of structural disorder.

Figure 1

(Color online) Frequency $\nu$ dependence of the ESR signals at $T=8\text{K}$: (a) selected spectra at different $\nu$. Open circles, solid circles, triangles and squares indicate the resonance field $B_{\text{res}}$ of the lines $L_1-L_4$; (b) the $\nu$ vs $B$ diagram of the resonance modes. The symbols correspond to respective $L_{\text{i}}$ in panel (a), solid lines are model curves (see the text).

Figure 2

(Color online) ${}^{114}\text{I}\text{n}$ NMR line at 35 and 10 K at fields (a) smaller and (b) larger than $B_{\text{c}}\sim 6\text{T}$; (c) $T_1^{-1}$ relaxation rate of ${}^{51}\text{V}$ nuclei as a function of $B$ at $T=4.2\text{K}$. Lines are guides for the eye. Inset: ${}^{51}\text{V}$ NMR spectra at fields smaller (left) and larger (right) than $B_{\text{c}}$ at 55 and 5 K.

Figure 3

(Color online) Field dependence of the magnetization $M\left(B\right)$ at different temperatures for $B\parallel$ $o$-axis after a subtraction of a small $T$-independent spurious ferromagneticlike signal persisting up to room temperature. Inset: (a) field derivative of $M\left(B\right)$; (b) $T$ dependence of the reorientation field. Error bars correspond to the width of the transition.

Figure 4

$T$ dependence of the staggered magnetization $m_{\text{st}}$ of the honeycomb lattice with interplane couplings $J_z=0.1$, 0.2, 0.3 and $0.4J_{\text{afm}}$ for the system size $14\times 28\times 14$. Inset: $m_{\text{st}}$ vs $T/J_{\text{afm}}$ for $J_z=0.2J_{\text{afm}}$ for different system sizes.