Magnetic-Order Crossover in Coupled Spin Ladders

We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-$1/2$ Heisenberg antiferromagnetic ladder compound ${(\mathrm{C}}_7{\mathrm{H}}_{10}\mathrm{N}{)}_2{\mathrm{CuBr}}_4$. The staggered order was previously evidenced from a continuous and symmetric splitting of ${}^{14}\mathrm{N}$ NMR spectral lines on lowering the temperature below $T_c\simeq 330\mathrm{mK}$, with a saturation towards $\simeq 150\mathrm{mK}$. Unexpectedly, the split lines begin to further separate away below $T^{*}\sim 100\mathrm{mK}$, while the linewidth and the line shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxation rate $T_1^{-1}$ measurements. A very strong suppression reflecting the ordering, $T_1^{-1}\sim T^{5.5}$, observed above $T^{*}$, is replaced by $T_1^{-1}\sim T$ below $T^{*}$. These original NMR features are indicative of the unconventional nature of the crossover, which may arise from a unique arrangement of the ladders into a spatially anisotropic and frustrated coupling network.

Figure 1

Crystal structure of DIMPY, where orange balls in green tetrahedra represent spin-$1/2$ Cu ions of ${\text{CuBr}}_4$ units and solid lines represent predominant exchange pathways forming a ladderlike network. Broken lines represent much weaker couplings between the ladders. (a) View presenting the ladders side by side. (b) View along the ladder direction showing the coupling of the ladders along the $b$ and $c$ axes.

Figure 2

(a) ${}^{14}\mathrm{N}$ NMR spectra as a function of the temperature in an applied field of 9.0 T and (b) in 15.0 T. Dashed vertical lines correspond to the first saturation of the line splittings at around 150 mK on cooling. (c) The line splitting as a function of the temperature, where three different regimes are identified and presented using different background colors and separated by the vertical dash-dotted lines. (d) Normalized linewidth as a function of the temperature.

Figure 3

(a) ${}^{14}\mathrm{N}$ NMR relaxation rate $T_1^{-1}$ as a function of the temperature in 9.0 and 15.0 T. (b) Temperature evolution of the stretch exponent $\alpha$ in the relaxation function. (c) Nuclear magnetization recovery curves for 15 T at 545, 197, and 82.5 mK, from upper to lower panels. Solid lines are fits using the theoretical relaxation function with varying $\alpha$, while dotted lines are with $\alpha =1$ for comparison.