Coupled dimerized alternating-bond quantum spin chains in the distorted honeycomb-lattice magnet Cu$_5$SbO$_6$

TL;DR

This work investigates Cu$_5$SbO$_6$ as a distorted honeycomb magnet and identifies a magnetic network of interacting FM-AFM dimerized spin chains described by the $J_1$-$J_2$-$J_4$ model. Using powder INS and magnetometry, complemented by first-order dimer expansion and quantum Monte Carlo simulations, the authors extract exchange parameters and verify them against thermodynamic and spectroscopic data. Structure refinements via XRD/XAFS/TEM reveal stacking faults and Cu oxidation states, which are integrated into the magnetic analysis. The findings show that interlayer coupling via $J_4$ is significant, and the model reproduces the triplet excitation spectrum, highlighting Cu$_5$SbO$_6$ as a platform for exploring emergent quantum phenomena in quasi-1D dimerized magnets.

Abstract

We analyze powder-averaged inelastic neutron scattering and magnetization data for the distorted honeycomb compound Cu$_5$SbO$_6$ using a first-order dimer expansion calculation and quantum Monte Carlo simulations. We show that, in contrast to the previously proposed honeycomb lattice model, Cu$_5$SbO$_6$ accommodates interacting dimerized spin chains with alternating ferromagnetic-antiferromagnetic couplings along the chain. Moreover, unlike the typical couplings observed in other Cu$^{2+}$-based distorted honeycomb magnets, the spin chains in Cu$_5$SbO$_6$ primarily couple through an antiferromagnetic coupling $J_4$ that arises between the honeycomb layers, rather than the expected interchain $J_3$ coupling in the layers. This finding reveals a different magnetic coupling scheme, $J_1$-$J_2$-$J_4$, for Cu$_5$SbO$_6$. In addition, utilizing x-ray spectroscopy and transmission electron microscopy, we also refine the crystal structure and stacking-fault model of the compound.

Figures (7)

• Figure 1: (a) A monoclinic unit cell of Cu$_5$SbO$_6$ is displayed in which spin chains consisted of SbO$_6$ octahedra (in silver) and edge-sharing Cu$_2$O$_6$ double plaquettes (in green) are aligned along the $a$-axis. The unit cell boundary is indicated by the dashed lines. (b) A chain segment with alternating $J_1$ and $J_2$ couplings is shown. The dashed purple and solid yellow lines represent intra-dimer $J_1$ and inter-dimer $J_2$ couplings, respectively. (c) The $ab$-plane projection of a single Cu$_2$SbO$_6$ layer is displayed. $B_{1}$ = 2.314 Å is the Cu-O bond perpendicular to the plaquette whereas $B_{2}$ = 1.994 Å and $B_{3}$ = 2.043 Å are the Cu-O bonds within the plaquette. The dot-dash turquoise lines represent inter-chain $J_3$ couplings. (d) A single layer projected on to the $ac$-plane is shown, where the dotted orange lines represent inter-chain $J_4$ couplings perpendicular to the honeycomb planes. The super-exchange path responsible for the $J_4$ coupling in Cu$_5$SbO$_6$ is displayed in (e) along with the corresponding path in Na$_2$Cu$_2$TeO$_6$. The crystal structure illustrations are generated by VESTAMomma2011.
• Figure 2:
• Figure 3: (a) A projection of the crystal structure onto the $bc^*$ plane showing the ideal stacking sequence of Cu$_5$SbO$_6$. (b) Two equivalent representatives of in-plane translations of a honeycomb layer that contain one stacking fault depicted by the purple arrows. The grey arrows represent the ideal translation vector. '1', '2', and '3' are sub-lattice labels of the honeycomb layer. The atom representations are the same as in Fig. \ref{['ucell']}(a). (c) A TEM image in the $ac$ plane of the sample synthesized at 1000 $^\circ$C. (d), (e) SAED patterns in the $(H, 0, L)$ planes of samples synthesized at 1000 $^\circ$C and 1150 $^\circ$C, respectively. (f) A simulated SAED pattern computed with $p_1 = p_2 = 1/2$. The crystal structure illustrations are generated by VESTAMomma2011.
• Figure 4: (a) Magnetic susceptibility as a function of temperature, $\chi(T)$, measured with an applied magnetic field $H = 100$ Oe. The solid curves are the best fits. (b), (c) Magnetization of dimerized spins $M_\mathrm{dim}$ as a function of applied magnetic field normalized with the saturated magnetization $M_\mathrm{sat} = g\mu_\mathrm{B}S$ measured at $T = 120$ K. The solid lines are model calculations described in text. The data are collected with $\boldsymbol{H}$ parallel to the $ab$ plane (circle symbols) and to the $c^*$ axis (square symbols).
• Figure 5: Powder averaged TOF INS intensity maps as a function of energy transfer and wavevector at (a) $T = 4$ K and (b) $T = 200$ K. Yellow dashed lines in (a) mark $\hbar\omega =$ 11 meV and 21 meV indicating the band of magnetic scattering. Solid symbols in (a) are excitation energies extracted from BT-7 spectrometer taken at 2.8 K. Error bars in (a) represent five standard deviations. Density of states (DOS) of (c) the $J_1$-$J_2$-$J_3$ model, and of (d) the $J_1$-$J_2$-$J_4$ model.