Two-Step Magnetic Ordering in Quasi-One-Dimensional Helimagnets: Possible Experimental Validation of Villain’s Conjecture about a Chiral Spin Liquid Phase

Low-temperature specific heat, magnetic susceptibility, and zero-field muon spin resonance ($\mu \mathrm{SR}$) measurements have been performed in the quasi-one-dimensional molecular helimagnetic compound $\mathrm{Gd}(hfac{)}_3\mathrm{NITEt}$. The specific heat presents two anomalies at $T_0=2.19\pm 0.02\mathrm{K}$ and $T_N=1.88\pm 0.02\mathrm{K}$, which both disappear upon the application of a weak magnetic field. Conversely, magnetic susceptibility and $\mu \mathrm{SR}$ data show the divergence of two-spin correlation functions only at $T_N=1.88\pm 0.02\mathrm{K}$. These results suggest an experimental validation of Villain’s conjecture of a two-step magnetic ordering in quasi-one-dimensional $XY$ helimagnets; i.e., the paramagnetic phase and the helical spin solid phase are separated by a chiral spin liquid phase, where translational invariance is broken without violation of rotational invariance.

Figure 1

Schematic representation of Villain’s conjecture. In the chiral spin liquid phase, corkscrews all turning clockwise (or all anticlockwise) with in general ${\phi }_i\ne {\phi }_j$. In the helical spin solid phase, same angle value ${\phi }_0$ for all spins.

Figure 2

Temperature dependence of the specific heat of $\mathrm{Gd}(hfac{)}_3\mathrm{NITEt}$ measured in zero field (●) and in external field $H$ of 1000 Oe (□) and 5000 Oe (○). Inset (a) specific heat $C$, divided by the gas constant $R=8.314\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$ and by the temperature, of $\mathrm{Gd}(hfac{)}_3\mathrm{NITEt}$ molecular chains plotted as $C/(RT)$ vs $T^2$. Inset (b) excess of specific heat, estimated by subtracting the $C/R=0.297T+0.00295T^3$ contribution from the total $C/R$ value.

Figure 3

(a) Magnetic susceptibility vs temperature of $\mathrm{Gd}(hfac{)}_3\mathrm{NITEt}$ collected in both ZFC and FC modes with external field $H=5.5\mathrm{Oe}$, from 300 K to 1.75 K. In the inset the anomaly at $T\sim 1.9\mathrm{K}$ in the effective magnetic moment is shown. (b) Fast (${\lambda }_{1\mu }$) and slow (${\lambda }_{2\mu }$) relaxation rates of a $\mathrm{Gd}(hfac{)}_3\mathrm{NITiEt}$ powder sample, corresponding to two different components of the muon asymmetry, reported as a function of temperature in zero field.