Ordering in weakly coupled random singlet spin chains

The influence of bond randomness on long-range magnetic ordering in the weakly coupled $S=1/2$ antiferromagnetic spin chain materials Cu(py)${}_2$(Cl${}_{1-x}$Br${}_x$)${}_2$ is studied by muon spin rotation and bulk measurements. Disorder is found to have a strong effect on the ordering temperature $T_{\mathrm{N}}$, and an even stronger one on the saturation magnetization $m_0$, but considerably more so in the effectively lower-dimensional Br-rich materials. The observed behavior is attributed to random singlet ground states of individual spin chains, but remains in contradiction with chain mean-field theory [Joshi and Yang, Phys. Rev. B 67, 174403 (2003)] predictions. In this context, we discuss the possibility of a universal distribution of ordered moments in the weakly coupled random singlet chains model.

Figure 1

Bulk properties of Cu(py)${}_2$(Cl${}_{1-x}$Br${}_x$)${}_2$ samples. (a) Measured temperature dependence of magnetic susceptibility for a field applied along the chain axis (symbols), and fit of the theoretical curve for the uniform quantum $S=1/2$ HAF chain (Refs. 19 and 20) (solid line). From the bottom up, the data are offset along the $y$ axis by 0, 1, 2, 3, 4.2, and 5.8 × 10${}^{-3}$ emu/mol, respectively. (b) Measured temperature dependence of specific heat (symbols). The vertical offsets are 0, 0.16, 0.27, 0.55, 0.75, and 1 J/mol K, respectively.

Figure 2

Composition dependence of the in-chain exchange constant $J$ [from fits to $\chi \left(T\right)$], the ordering temperature $T_{\mathrm{N}}$ (from calorimetry), and the low-temperature ordered moment $m_0$ (chain-MF estimates and $\mu$-SR measurements).

Figure 3

Muon spin asymmetry measured vs time in several Cu(py)${}_2$(Cl${}_{1-x}$Br${}_x$)${}_2$ and Cu(py)${}_2$(Br${}_{1-y}$Cl${}_y$)${}_2$ samples at $T\sim 20$ mK (solid symbols) and just above $T_{\mathrm{N}}$ (open symbols). The plots for $y=0$, $0.05$, and $0.1$ and $x=0.05$,0 are offset along the $y$ axis by 0, 0.1, 0.2, 0.3, and 0.43, respectively. The solid lines are fits to the data as described in the text.

Figure 4

Characteristic field at the principal muon stopping site, assumed to be proportional to the magnetic order parameter, plotted against temperature in units of the average in-chain exchange constant $J$ in Cu(py)${}_2$(Cl${}_{1-x}$Br${}_x$)${}_2$ and Cu(py)${}_2$(Br${}_{1-y}$Cl${}_y$)${}_2$ (symbols). Within each family of materials, the relative magnitudes of the precession field can be directly compared. Lines are guides to the eye.