The nuclear spin-lattice relaxation time ${\mathit{T}}_1$ of the proton in the s=1 Haldane-gap system Ni(${\mathrm{C}}_2$${\mathrm{H}}_8$${\mathrm{N}}_2$${)}_2$${\mathrm{NO}}_2$${\mathrm{ClO}}_4$ (NENP) has been measured at low temperatures in high magnetic fields (4 T<H<8 T) below the critical field. From the experimental results below 4 K, the field dependence of the energy gap for the lowest-energy mode of the three excitation modes, which has been predicted theoretically in NENP, are obtained. The results of ${\mathit{T}}_1$ below 4 K are well explained by treating the magnetic excitations as free fermions rather than free bosons.

• Received 26 September 1991

DOI:https://doi.org/10.1103/PhysRevB.45.7837