Thermodynamic Properties in the Approach to the Quantum Critical Point of the Spin-Ladder Material ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$

Magnetic susceptibility and heat capacity measurements as a function of temperature on a single-crystal sample of a spin-ladder material, ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$, are reported. Principal susceptibilities, parallel and perpendicular to the ladder direction, respectively, show broad maxima around 22 and 17 K. Both susceptibilities decay exponentially down to about 5 K and thereafter they are essentially independent of temperature. These findings amount to a signature of a quantum phase transition from a spin-liquid to Néel ordered state previously predicted theoretically. No anomaly is found in the heat capacity around the transition temperature.

Figure 1

(a) The crystal structure of ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$. Hydrogen atoms are omitted for clarity. (b) The arrangement of the ladders in the $bc$ plane normal to the ladder direction. Thick lines show the rungs of the ladders and dotted lines are drawn to show the exchange interaction path between the nearest neighboring Co atoms.

Figure 2

The temperature dependence of the magnetic susceptibility parallel ($\parallel$) and perpendicular ($\perp$) to the ladder direction of a single-crystal sample of ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$. ZFC means the measurement performed with warming after the sample had been cooled in zero field to 1.8 K and a magnetic field of 100 Oe had been applied there. While FC susceptibility was measured with cooling from 300 K in the same magnetic field.

Figure 3

The low temperature part of the magnetic susceptibility of a single-crystal sample of ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$ parallel ($\parallel$) and perpendicular ($\perp$) to the ladder direction. The dotted lines are theoretical ones discussed in the text.

Figure 4

The temperature dependence of the magnetic susceptibility of a single-crystal sample of ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$ measured in magnetic fields applied to the ladder direction.

Figure 5

The temperature dependence of the heat capacity, including the contribution of lattice, of a single-crystal sample of ${\mathrm{Na}}_2{\mathrm{Co}}_2({\mathrm{C}}_2{\mathrm{O}}_4{)}_3({\mathrm{H}}_2\mathrm{O}{)}_2$ measured in zero field plotted in a logarithmic scale. Inset shows the temperature dependence of the heat capacity plotted in a linear scale for a wider temperature range.