Very-low-temperature specific heat of quinolinium(TCNQ)2, a random-exchange Heisenberg antiferromagnetic chain

Measurements of the specific heat of quinolinium${\mathrm{}\left(\mathrm{TCNQ}\right)\mathrm{}}_2$ (quinolinium di-tetracyanoquinodimethanide) are reported for the temperature range $0.07<T<\mathrm{}5\mathrm{}$ K and magnetic field range $0<H<\mathrm{}20\mathrm{}$ kOe. The results do not fit a model in which the magnetic contribution to the specific heat $C_H$ is that of a regular antiferromagnetic chain, a quarter-filled band, or isolated magnetic impurities. A good fit to the data is obtained using the Bulaevskii model for a random-exchange Heisenberg chain with a density of states having the form $\rho \left(\epsilon \right)=A{k}^{\alpha -1\mathrm{}}{\left|\epsilon \right|}^{-\alpha }$, where $\epsilon$ is the quasiparticle energy and $A$ and $\alpha$ are parameters chosen to fit the data. For the sample used, a good fit is obtained using $A=(1.03\mathrm{}\pm 0.11)\times {10}^{-3\mathrm{}} {\mathrm{K}}^{\alpha -1\mathrm{}}$ and $\alpha =0.82\mathrm{}\pm 0.01$.