Bose glass behavior in $({\mathrm{Yb}}_{1-x}{\mathrm{Lu}}_x{)}_4{\mathrm{As}}_3$ representing randomly diluted quantum spin-$\frac{1}{2}$ chains

The site-diluted compound ${\left({\mathrm{Yb}}_{1-x}{\mathrm{Lu}}_x\right)}_4{\mathrm{As}}_3$ is a scarce realization of the linear Heisenberg antiferromagnet partitioned into finite-size segments and is an ideal model compound for studying field-dependent effects of quenched disorder in the one-dimensional antiferromagnets. It differentiates from the systems studied so far in two aspects—the type of randomness and the nature of the energy gap in the pure sample. We have measured the specific heat of single-crystal ${\left({\mathrm{Yb}}_{1-x}{\mathrm{Lu}}_x\right)}_4{\mathrm{As}}_3$ in magnetic fields up to 19.5 T. The contribution $C_{\perp }$ arising from the magnetic subsystem in an applied magnetic field perpendicular to the chains is determined. Compared to pure ${\mathrm{Yb}}_4{\mathrm{As}}_3$, for which $C_{\perp }$ indicates a gap opening, for diluted systems a nonexponential decay is found at low temperatures which is consistent with the thermodynamic scaling of the specific heat established for a Bose-glass phase.

Figure 1

(a) Molar zero-field magnetic specific heat of the pure and doped samples plotted in semilogorithmic scale as a function of $1/T$. (b) The exponential dependence of $C_{\perp }$ as a function of $1/T$ in the low-temperature region. The corresponding Pearson correlation coefficients $r$ are provided.

Figure 2

Comparison between experiment and theory for the diluted samples subject to an applied field. In panels (a) and (b), the field applied is $B=12\mathrm{T}$ and 18 T, respectively. In panels (c) and (d), the nonmagnetic impurity concentration amounts to $x=1\%$ and $x=3\%$, respectively. The symbols are explained in the legend.

Figure 3

The behavior of the contribution $C_{\perp }$ to the specific heat for the diluted ${\left({\mathrm{Yb}}_{1-x}{\mathrm{Lu}}_x\right)}_4{\mathrm{As}}_3$. In the region of low temperatures, panels (a) and (b) as well as their insets illustrate nonexponential decay of the $C_{\perp }\left(T\right)$ vs $1/T$. Panels (c) and (d) display the realization of the corresponding BG scaling law of $C_{\perp }\left(T\right){(k_{B}T/J)}^{5/4}$ for ${(J/k_{B}T)}^{1/2}\ge 2.4$. The open and full symbols represent the experimental data and the QTM estimates, respectively, and the values $r$ denote the corresponding Pearson correlation coefficients.

Figure 4

The deviations of the measured $C_{\perp }$ data from those fitted by the exponential and the stretched exponential dependence plotted by full circles and squares, respectively. In panels (a) and (b) some representative weak and intermediate applied fields are selected. Error bars attain at most the size of the symbols and are omitted.