Low-temperature specific-heat studies on two square-kagome antiferromagnets

Abstract

We studied the low-temperature specific heats of two antiferromagnets with the two-dimensional square-kagome structure, i.e., ${\mathrm{KCu}}_{6}{\mathrm{AlBiO}}_{4}{({\mathrm{SO}}_{4})}_{5}\mathrm{Cl}$ $({\mathrm{KCu}}_{6})$ and ${\mathrm{Na}}_{6}{\mathrm{Cu}}_{7}{\mathrm{BiO}}_{4}{({\mathrm{PO}}_{4})}_{4}{[\mathrm{Cl},(\mathrm{OH})]}_{3}$ $({\mathrm{NaCu}}_{7})$, with the structural difference that there are interlayer ${\mathrm{Cu}}^{2+}$ ions in ${\mathrm{NaCu}}_{7}$. Both materials show no magnetic ordering down to 50 mK. At zero field, the $C/T$ of ${\mathrm{KCu}}_{6}$ has a finite value when the temperature is close to 0 K. Under the magnetic field, an apparent ${T}^{2}$ dependence appears and its coefficient is progressively suppressed by the field. For ${\mathrm{NaCu}}_{7}$, the specific heat exhibits the ${T}^{2}$ dependence at zero field and under fields. The ratio of the quadratic coefficients of ${\mathrm{KCu}}_{6}$ and ${\mathrm{NaCu}}_{7}$ at high fields is inversely proportional to that of the squared Weiss temperatures, which indicates these two compounds host the same ground state under fields. Our results suggest that the interlayer ${\mathrm{Cu}}^{2+}$ ions in ${\mathrm{NaCu}}_{7}$ play a negligible role in determination of its ground state. We discuss the possible quantum-spin-liquid states in these compounds and further directions to pursue based on our results.