Realization of the Nersesyan-Tsvelik model in $\left(\text{NO}\right)\left[\text{Cu}{\left({\text{NO}}_3\right)}_3\right]$

The topology of the magnetic interactions of the copper spins in the nitrosonium nitratocuprate $\left(\text{NO}\right)\left[\text{Cu}{\left({\text{NO}}_3\right)}_3\right]$ suggests that it could be a realization of the Nersesyan-Tsvelik model [A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003)], whose ground state was argued to be either a resonating valence-bond state or a valence-bond crystal. The measurement of thermodynamic and magnetic resonance properties reveals a behavior inherent to low-dimensional spin $S=\frac{1}{2}$ systems and provides indeed no evidence for the formation of long-range magnetic order down to 1.8 K.

Figure 1

(Color online) (a) Schematic representation of the anisotropic confederate flag model; (b) schematic representation of the crystal structure of $\left(\text{NO}\right)\left[\text{Cu}{\left({\text{NO}}_3\right)}_3\right]$. Green spheres denote the ${\text{Cu}}^{2+}$ ions. The dumbbells represent the ${\text{NO}}^{+}$ cation groups. The ${\text{NO}}_3^{-}$ anion groups are represented by tilted and flat triangles. Note, that $J^{\prime }=2J_2$.

Figure 2

(Color online) Temperature dependences of the specific heat $C$ measured at ${\mu }_{0}H=0\text{T}$ (○) and ${\mu }_{0}H=1.5\text{T}$ (◻) in $\left(\text{NO}\right)\left[\text{Cu}{\left({\text{NO}}_3\right)}_3\right]$, respectively. The fitting curves are shown by solid lines.

Figure 3

(Color online) Temperature dependence of the intensity of the ESR spectra $I_{\text{ESR}}$ normalized to the room temperature value for a magnetic field parallel $(\parallel )$ and perpendicular $(\perp )$ to the plane of ${\text{CuO}}_4$ plaquettes. Inset: the temperature dependence of the values of the $g$-factor tensor $g_{\parallel }$ and $g_{\perp }$.

Figure 4

(Color online) Temperature dependences of the magnetic susceptibility taken at ${\mu }_{0}H=0.1\text{T}$ (○) and of the normalized magnetic susceptibility from the ESR data (◻) of $\left(\text{NO}\right)\left[\text{Cu}{\left({\text{NO}}_3\right)}_3\right]$. The lines represent fits to the data.

Figure 5

(Color online) Right panel: magnetic susceptibility derived from exact diagonalizations ($\alpha =J^{\prime }/J$ characterizes the interchain coupling). $N$ is the system size and various geometries have been used $\left[4\times 4,8\times 2,6\times 4\right]$. Left panel: ${\chi }_{\text{max}}{T}_{\text{max}}/\left(N_{\text{A}}{g}^2{\mu }_B^2/k_B\right)$ as a function of $\alpha$. The exact result for decoupled chains $\left(\alpha =0\right)$ is shown by a square.

Figure 6

(Color online) Temperature dependence of the ESR linewidth $\Delta H_{\text{pp}}$ for a magnetic field parallel and perpendicular to the plane of ${\text{CuO}}_4$ plaquettes, respectively (symbols). The dashed line shows the scaled product ${\chi }_{\text{spin}}\left(T\right)\cdot T$.