Figure 1

(a),(b) Incommensurate propagation vector ${\tilde{k}}_{\mathrm{IC}}$ in units of $2\pi /d_{\mathrm{NN}}$ as a function of applied field for $\mathbf{H}\Vert \mathbf{c}$ (left) and $\mathbf{H}\Vert \mathbf{a}$ (right) compared to the theoretical prediction for the quadrupolar-nematic phase [3, 4, 5, 6, 11], using the experimental magnetization $m_{a,c}$ of Ref. 14, normalized to $1/2$ at the saturation field. (c),(d) Specific heat for $\mathbf{H}\Vert \mathbf{c}$ (left) and $\mathbf{H}\Vert \mathbf{a}$ (right). The distinct anomaly evidences a phase transition at all fields and the change in shape near $H_{\mathrm{Q}}\sim 8\mathrm{T}$ suggests a change of the universality class.Reuse & Permissions

Figure 2

(a)–(c) Scans of the dipolar correlations at $T=0.1\mathrm{K}$ for the three reciprocal space directions are resolution limited at zero field and broadened at high fields above $H_{\mathrm{Q}}\sim 8\mathrm{T}$. (d)–(f) Magnetic field dependence of the inverse dipolar correlation length $\kappa ={\xi }^{-1}$. The onset of short-range order at $H_{\mathrm{Q}}$ is clearly seen for all three reciprocal space directions.Reuse & Permissions

Figure 3

Polarized cross sections measured at $T=70\mathrm{mK}$ for the magnetic reflections $\mathbf{Q}=(1,k_{\mathrm{IC}},0)$ with $\mathbf{H}\Vert \mathbf{c}$ [left panels, (a)–(c)] and $\mathbf{Q}=(0,-k_{\mathrm{IC}},1)$ with $\mathbf{H}\Vert \mathbf{a}$ [right panels, (d)–(f)].Reuse & Permissions

Figure 4

(a) FFH chain at $H=0$ seen as two intercalated Heisenberg AF chains (closed and open arrows), vertically displaced to illustrate the direction of the NN-bond vector-chirality [(green) crosses and (red) dots]. Néel solitons [(red) solid arcs] propagate freely on a Heisenberg AF chain and are bound to $S=1$ states by $J_1$ in the FFH chain, resulting in vector-chiral LR order. (b),(c) FFH chain for $H>H_{\mathrm{Q}}$. (b) Two-magnon (four-soliton) states provide $\Delta S^z=2$ magnetization steps. (c) Propagating individual solitons costs no extra $J_1$ energy, as long as one soliton in the even subchain is followed by one in the odd subchain. This nonlocal order is reflected in the AF sequence of the bond pseudospin ${\sigma }_n^z$ (numbers). (d),(e) Two FFH chains coupled by a FM diagonal interchain interaction $J_5$. (d) $H=0$: $J_5$ binds two two-solitons into a four-soliton bound state and thus stabilizes dipolar LR order. (e) $H>H_{\mathrm{Q}}$: Propagation of individual solitons costs no extra $J_5$ energy, as long as the nonlocal AF order of the bond pseudospin is kept.Reuse & Permissions