Magnetic ordering induced by interladder coupling in the spin-$\frac{1}{2}$ Heisenberg two-leg ladder antiferromagnet ${\mathrm{C}}_9$${\mathrm{H}}_{18}$${\mathrm{N}}_2$${\mathrm{CuBr}}_4$

We present specific-heat and neutron-scattering results for the $S=\mathrm{1/2}$ quantum antiferromagnet (dimethylammonium)(3,5-dimethylpyridinium)${\mathrm{CuBr}}_4$. The material orders magnetically at ${\mathit{T}}_N=1.99\left(2\right)$ K, and magnetic excitations are accompanied by an energy gap of 0.30(2) meV due to spin anisotropy. The system is best described as coupled two-leg spin-1/2 ladders with the leg exchange $J_{\mathrm{leg}}=0.60\left(2\right)$ meV, rung exchange $J_{\mathrm{rung}}=0.64\left(9\right)$ meV, interladder exchange $J_{\mathrm{int}}=0.19\left(2\right)$ meV, and an interaction-anisotropy parameter $\lambda =0.93\left(2\right)$, according to inelastic neutron-scattering measurements. In contrast to most spin ladders reported to date, the material is a rare example in which the interladder coupling is very near the critical value required to drive the system to a Néel-ordered phase without the assistance of a magnetic field.

Figure 1

(a) Crystal structure of DLCB, in which the ladder chain extends along the $b$ axis. Outlined is a nuclear unit cell. (b) Projection of CuBr${}_4^{-2}$ tetrahedra onto a plane perpendicular to the $b$ axis, showing proposed interladder couplings. Different lines stand for the different bonds. Red and yellow lines indicate the intraladder coupling $J_{\mathrm{rung}}$ and interladder coupling $J_{\mathrm{int}}$, respectively. Black arrows indicate the directions of the spins. The parallelogram is a projection of a magnetic unit cell.

Figure 2

(a) Specific heat of DLCB. Inset: Semilog plot of the magnetic component of specific heat, after subtraction of a phonon contribution, against $1/T$. The solid line is a fit showing exponential, activated behavior at low temperatures. (b) Background-subtracted neutron-peak intensity at $\mathit{q}=(0.5,0.5,-0.5)$ as a function of temperature. Error bars represent one standard deviation. The solid line is a fit to a power law as described in the text. Inset: Rocking-curve scans through $\mathit{q}=(0.5,0.5,-0.5)$, made at $T=$ 0.3 and 2.5 K. The solid line is a guide to the eye.

Figure 3

(a) Background-subtracted constant-$\mathit{q}$ scan in DLCB at the magnetic zone center (0.5,0.5,$-$0.5), measured at CTAX at $T=$ 1.5 K. The solid line is a fit to a Gaussian profile convolved with the instrumental resolution function. Error bars represent one standard deviation. (b–e) Background-subtracted constant-energy slices measured at MACS at $T=$ 1.7 K for excitation energies of 0.2–0.4, 0.4–0.6, 0.7–0.9, and 1.2–1.4 meV.

Figure 4

False-color map of the spin-wave spectra at $T=$ 1.5 K (a) along the ladders [010] and (b) perpendicular to the ladders along [10$\overline{1}$] measured at DCS and (c) perpendicular to the ladders along [100] measured at MACS. Red and yellow lines are calculations for the acoustic and optical branches of one-magnon dispersion, respectively. Data shown as circles were obtained at CTAX.