The Magnetic Ground State of Atacamite Cu$_2$Cl(OH)$_3$: The Crucial Role of Frustrated Zigzag Chains Revealed by Inelastic Neutron Scattering

Abstract

We report inelastic neutron scattering (INS) measurements on the magnetically frustrated $S=\frac12$ sawtooth-chain compound atacamite Cu$_2$Cl(OH)$_3$ featuring inequivalent Cu(1) and Cu(2) sites. Transverse to the sawtooth chains, INS reveals two dispersive spin-wave modes and a gap of at least 0.75 meV. This behavior is rationalized within a zigzag-chain model of Cu(2) spins in an effective magnetic field of Cu(1) spins. The model is compatible with first-principles calculations and accounts for INS dispersions within linear spin-wave theory calculations. Our results reveal a unique case of an effective separation of energy scales between two differently oriented one-dimensional chains, with the zigzag-chain model being essential to fully characterize atacamite's low-energy magnetism.

Figures (5)

• Figure 1: (Left) Magnetic structure derived from single-crystal neutron diffraction dataHeinze_2021, with exchange pathways from the 5 strongest exchange values according to the first-principles analysis in Heinze_2021. (Right) Expanded in-plane perspectives of the sawtooth-chain and zigzag-chain components in atacamite. The angles between the nearest-neighbor Cu(2) spins in the expanded zigzag chain have been greatly exaggerated for clarity.
• Figure 2: (a) Experimental INS data of (co-aligned) single-crystalline atacamite measured on Pelican at ANSTO at 1.5 K and at zero external field. Strong dispersion can be observed in the (H,0,0) direction with two separate nested modes. (b) LSWT calculations of the low-energy spin-wave modes in atacamite along (H,0,0) for a zigzag-chain model with an effective mean field $h$ = 0.26 meV as defined in Eq. (\ref{['eq:atacamite_hamiltonian']}), using Sunny Sunny. Note that normalized moment values have been used in this calculation, hence ignoring the effect of suppressed moments.
• Figure 3: A constant-$Q$ INS spectrum at (0.5,0,0). An integration width of Q = 0.04 r.l.u. has been used for the experimental data. A width of Q = 0.15 r.l.u. has been used for the LSWT-calculated data to mimic experimental broadening. The red line is a double Gaussian fit to the INS data and the dashed blue line is the Sunny LSWT calculation, equivalent to that in Fig. \ref{['fig:aniso_zigzag']}. For the lower-energy INS mode, peak energy = (1.30$\,\pm\,$0.03) meV and FWHM = (0.4$\,\pm\,$0.1) meV. For the higher-energy INS mode, peak energy = (1.76$\,\pm\,$0.03) meV and FWHM = (0.4$\,\pm\,$0.1) meV.
• Figure 4: Constant-$Q$ INS spectra at (0.50,0,0) and at (0.75,0,0), both with an integration width of $Q$ = 0.04 r.l.u.. Neutron counts are within error of each other from below 0.75 meV, indicating that this is the minimum of the gap. The inset shows a subtraction of the constant-$Q$ spectrum at (0.75,0,0) from the spectrum at (0.50,0,0). A fiducial line is drawn along zero counts to guide the eye.
• Figure 5: Atacamite's magnetic structure Heinze_2021 and isotropic exchange interactions for the zigzag-chain model. To the right is the model shown for four Cu(2) atoms with exaggerated angles for clarity. Additionally, the staggered mean field components at each spin site for one spin chain are represented by transparent blue arrows pointing in the $b$ direction, used to effectively model the residual coupling of the full 3D exchange network.