Specific Heat Study of an $S=1/2$ Alternating Heisenberg Chain System: ${\mathrm{F}}_5\mathrm{P}\mathrm{N}\mathrm{N}$ in a Magnetic Field

We have measured the specific heat of an $S=1/2$ antiferromagnetic alternating Heisenberg chain pentafulorophenyl nitronyl nitroxide in magnetic fields up to $H>H_{\mathrm{C}2}$. This compound has a field-induced magnetic ordered (FIMO) phase between $H_{\mathrm{C}1}$ and $H_{\mathrm{C}2}$. Characteristic behaviors are observed depending on the magnetic field up to above $H_{\mathrm{C}2}$ outside of the $H\mathrm{\text{−}}T$ boundary for the FIMO. The temperature and field dependence of the specific heat are qualitatively in good agreement with the theoretical calculation on an $S=1/2$ two-leg ladder [Wang et al., Phys. Rev. Lett. 84, 5399 (2000)]. This agreement suggests that the observed behaviors are related with the low-energy excitation in the Tomonaga-Luttinger liquid.

Figure 1

Magnetic field versus temperature phase diagram for ${\mathrm{F}}_5\mathrm{P}\mathrm{N}\mathrm{N}$ based on data from the previous [10] and present specific heat measurements.

Figure 2

Some representative data for temperature dependence of $C$ of ${\mathrm{F}}_5\mathrm{P}\mathrm{N}\mathrm{N}$ in magnetic fields up to 8 T. A broken line shows the lattice contribution.

Figure 3

Temperature dependence of $C_{\mathrm{m}}$ in magnetic fields. (a) $0\mathrm{T}\le H\le 2.5\mathrm{T}$ (spin-gapped phase), (b)–(c) $3\mathrm{T}\le H\le 6.5\mathrm{T}$ (gapless phase), and (d) $7\mathrm{T}\le H\le 8\mathrm{T}$ (spin-polarized phase). A solid line in (b) shows linear-$T$ dependence of $C_{\mathrm{m}}$. Down arrows in (b)–(c) indicate a hump in $C_{\mathrm{m}}$. Up arrows in (b)–(c) and down arrows in (d) indicate a shoulder $C_{\mathrm{m}}$. Insets show theoretical calculations of the strongly coupled two-leg ladder system [12].

Figure 4

The maximum magnetic specific heat $C_{\mathrm{m}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and the corresponding temperature $T_{\mathrm{m}\mathrm{a}\mathrm{x}}$ versus magnetic field $H$. Errors at around $H_{\mathrm{C}2}$ are due to the broader maximum of $C_{\mathrm{m}}$.