Spin-disordered states in the antiferromagnetic Heisenberg model on the triangular lattice

To gain a starting point for an explanation of a recent experiment by Takeda et al. on ${\mathrm{NaTiO}}_2$, the triangular-lattice antiferromagnetic Heisenberg model with S=1/2 is investigated by a fermion mean-field theory. We find two self-consistent solutions that describe a spin disordered state with a finite excitation gap. Both phases are consistent with the experiment and thereby should be regarded as promising candidates for the physical state realized in ${\mathrm{NaTiO}}_2$.