High-field phase diagram of the Haldane-gap antiferromagnet $\mathrm{Ni}{\left({\mathrm{C}}_5{\mathrm{H}}_{14}{\mathrm{N}}_2\right)}_2{\mathrm{N}}_3\left({\mathrm{PF}}_6\right)$

We have determined the magnetic phase diagram of the quasi-one-dimensional $S=1$ Heisenberg antiferromagnet $\mathrm{Ni}{\left({\mathrm{C}}_5{\mathrm{H}}_{14}{\mathrm{N}}_2\right)}_2{\mathrm{N}}_3\left({\mathrm{PF}}_6\right)$ by specific heat measurements to 150 mK in temperature and 32 T in the magnetic field. When the field is applied along the spin-chain direction, a new phase appears at $H_{c2}\approx 14\mathrm{T}$. For the previously known phases of field-induced order, an accurate determination is made of the power-law exponents of the ordering temperature near the zero-temperature critical field $H_c$, owing to the four-fold improvement of the minimum temperature over the previous work. The results are compared with the predictions based on the Bose-Einstein condensation of triplet excitations. Substituting deuterium for hydrogen is found to slightly reduce the interchain exchange.

Figure 1

Specific heat of deuterated NDMAP for a magnetic field parallel to the $c$ axis. (a) Temperature dependence at constant fields. The inset gives an expanded view of the region near the specific heat peak. (b) Magnetic-field dependence at constant temperatures. The lines are guides for the eye.

Figure 2

Specific heat of hydrogenous NDMAP at constant magnetic fields ranging from 20 T to 32 T, applied along the $c$ axis. The lines are guides for the eye.

Figure 3

Magnetic-field dependence of the specific heat of hydrogenous NDMAP in the ordered phases. The field was applied along the $c$ axis. The anomaly at the lowest field of each curve is due to the proximity of the transition to the disordered spin-liquid phase. The uninteresting proton contribution raises the curve at 0.26-0.29 K with respect to those at higher temperatures. The lines are guides for the eye.

Figure 4

Magnetic-field dependence of the specific heat of deuterated NDMAP measured at constant temperatures. The magnetic field was applied along the $a$ axis. The lines are guides for the eye.

Figure 5

Field-temperature phase diagram of NDMAP. The open symbols are for the field applied along the $c$ axis and the closed symbols for the field along the $a$ axis. The circles are for the deuterated samples and the squares and diamonds for the hydrogenous sample. The lines are guides for the eye.

Figure 6

Field-temperature phase diagram of NDMAP below 20 T for the field applied parallel to the $c$ and $a$ axes. The closed symbols are for the deuterated samples of the present work, where the circles are from the temperature-scan data and the diamonds from the field-scan data. The open circles are for hydrogenous samples from Ref. 13. The lines are low-temperature fits of the phase boundaries of the deuterated samples to the expression $T_c\propto {(H-H_c)}^{\alpha }$.