We report inelastic neutron scattering (INS) measurements on the magnetically frustrated $S=\frac{1}{2}$ sawtooth-chain compound atacamite ${\mathrm{Cu}}_2\mathrm{Cl}{\left(\mathrm{OH}\right)}_3$ 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 the low-energy magnetism of atacamite.

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• Exchange interaction
• First-principles calculations
• Frustrated magnetism
• Magnetic interactions
• Magnetism
• Spin waves
• Density functional theory
• Inelastic neutron scattering
• Neutron techniques
• Spin wave spectroscopy