We report inelastic neutron scattering experiments in ${\mathrm{Ca}}_2{\mathrm{Y}}_2{\mathrm{Cu}}_5{\mathrm{O}}_{10}$ and map out the full one-magnon dispersion which extends up to a record value of 53 meV for frustrated ferromagnetic (FM) edge-sharing ${\mathrm{CuO}}_2$ chain (FFESC) cuprates. A homogeneous spin-1/2 chain model with a FM nearest-neighbor (NN), an antiferromagnetic (AFM) next-nearest-neighbor (NNN) inchain, and two diagonal AFM interchain couplings (ICs) analyzed within linear spin-wave theory (LSWT) reproduces well the observed strong dispersion along the chains and a weak one perpendicularly. The ratio $\alpha =|J_{a2}/J_{a1}|$ of the FM NN and the AFM NNN couplings is found as $\sim 0.23$, close to the critical point ${\alpha }_c=1/4$ which separates ferromagnetically and antiferromagnetically correlated spiral magnetic ground states in single chains, whereas ${\alpha }_c>0.25$ for coupled chains is considerably upshifted even for relatively weak IC. Although the measured dispersion can be described by homogeneous LSWT, the scattering intensity appears to be considerably reduced at $\sim 11.5$ and $\sim 28\mathrm{meV}$. The gaplike feature at 11.5 meV is attributed to magnon-phonon coupling whereas based on density matrix renormalization group simulations of the dynamical structure factor the gap at 28 meV is considered to stem partly from quantum effects due to the AFM IC. Another contribution to that gap is ascribed to the intrinsic superstructure from the distorting incommensurate pattern of CaY cationic chains adjacent to the ${\mathrm{CuO}}_2$ ones. It gives rise to nonequivalent ${\mathrm{CuO}}_4$ units and Cu-O-Cu bond angles $\mathrm{\Phi }$ and a resulting distribution of all exchange integrals. The $J$'s fitted by homogeneous LSWT are regarded as average values. The record value of the FM NN integral $J_1=24\mathrm{meV}$ among FFESC cuprates can be explained by a nonuniversal $\mathrm{\Phi }(\ne {90}^{\circ })$ and Cu-O bond length dependent anisotropic mean direct FM Cu-O exchange ${\overline{K}}_{pd}\sim 120\mathrm{meV}$, similar to a value of 105 meV for ${\mathrm{Li}}_2{\mathrm{CuO}}_2$, in accord with larger values for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{CuGeO}}_3$ $(\sim 110\mathrm{meV})$ reported by Braden et al. [Phys. Rev. B 54, 1105 (1996)] phenomenologically. Enhanced $K_{pd}$ values are also needed to compensate a significant AFM $J_{dd}\ge$ 6 meV from the $dd$ channel, generic for FFESC cuprates but ignored so far.

• Received 11 June 2018
• Revised 13 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.104415