  We report on the results of 23Na NMR in the honeycomb lattice magnet
Na2Co2TeO6 which has been nominated as a Kitaev material. Measurements of
magnetic shift and width of the NMR line as functions of temperature and
magnetic field show that a spin-disordered phase does not appear up to a field
of 9 T. In the antiferromagnetic phase just below the Neel temperature TN, we
find a temperature region extending down to ~TN/2 where the nuclear
spin-lattice relaxation rate 1/T1 remains enhanced and is further increased by
a magnetic field. This region crosses over to a low temperature region
characterized by the rapidly decreasing 1/T1 which is less field-sensitive.
These observations suggest incoherent spin excitations with a large spectral
weight at low energies in the intermediate temperature region transforming to
more conventional spin-wave excitations at low temperatures. The drastic change
of the low-energy spin dynamics is likely caused by strong damping of spin
waves activated only in the intermediate temperature region, which may be
realized for triple-q magnetic order possessing partially-disordered moments as
scattering centers of spin waves. In the paramagnetic phase near TN, dramatic
field suppression of 1/T1 is observed. From analysis of the temperature
dependence of 1/T1 based on the renormalized-classical description of a
two-dimensional quantum antiferromagnet, we find the field-dependent spin
stiffness constant that scales with TN as a function of magnetic field. This
implies field suppression of the energy scale characterizing both
two-dimensional spin correlations and three-dimensional long-range order, which
may be associated with an increasing effect of frustration in magnetic fields.
