Figure 1

(a) Schematic diagram of the zigzag triangular ladder and of its equivalent chain with first- ($J_1$) and second-nearest-neighbor ($J_2$) exchange interactions. (b) Projection along [001] of the crystal structure of $\beta$-CaCr${}_2$O${}_4$. Cycloids running along c rotate either clockwise or anticlockwise, as shown by the circular arrows. The thick lines illustrate the connection between neighboring clockwise (or anticlockwise) cycloids. The cycloids running along $c$ and rotating clockwise [anticlockwise] are in green (dark gray) [orange (medium gray)]. Thick green (dark gray) [orange (medium gray)] lines connect clockwise [anticlockwise] cycloids. (c) Temperature evolution of the susceptibility in 0.3 T. Inset: ac susceptibility below 30 K. (d) Topology of the connection between anticlockwise cycloids (not drawn to scale).Reuse & Permissions

Figure 2

(a) Inelastic neutron-scattering powder spectra recorded at 1.5 K ($k_f=2.662$ Å${}^{-1}$). (b) $Q$ scans ($k_f=1.550$ Å${}^{-1}$) at constant energy transfer $\omega =0.5$ and 1 meV. (c) Calculation of the magnon dispersion along $[1\hspace{0.5em}0\hspace{0.5em}L]$ performed according to Eq. (1) for $J_2=5$ meV, $J_1=1.5$ meV, $J^{\text{'}}=-0.05$ meV, and $D=0.2$ meV. (d) Calculation of the corresponding powder-averaged excitation spectrum.Reuse & Permissions

Figure 3

Inelastic neutron-scattering powder spectra recorded at 30 K ($k_f=2.662$ Å${}^{-1}$) (top), and $Q$ scans at $E=0.5$ meV at 4, 18, and 25 K (bottom). Inset: Inelastic neutron-scattering powder spectra recorded at 25 K at $k_f=1.550$ Å${}^{-1}$.Reuse & Permissions

Figure 4

(a) Temperature evolution between 12 and 30 K of $\omega$ scans at constant momentum transfer $Q=1.15$ Å${}^{-1}$ ($k_f=1.550$ Å${}^{-1}$). (b) Same as (a) in the 12–190 K range. Corresponding intensity profiles of selected $\omega$ scans below $T_N$ (c) and above $T_N$ (d). Data have been corrected for background intensity (based on a linear fit to the $Q=1.15$ Å${}^{-1}$ $\omega$ scan at 190 K) and the Bose factor.Reuse & Permissions