  We report the physical properties of Tb2Hf2O7 based on ac magnetic
susceptibility \chi_ac(T), dc magnetic susceptibility \chi(T), isothermal
magnetization M(H), and heat capacity C_p(T) measurements combined with muon
spin relaxation (\muSR) and neutron powder diffraction measurements. No
evidence for long-range magnetic order is found down to 0.1 K. However,
\chi_ac(T) data present a frequency-dependent broad peak (near 0.9 K at 16 Hz)
indicating slow spin dynamics. The slow spin dynamics is further evidenced from
the \muSR data (characterized by a stretched exponential behavior) which show
persistent spin fluctuations down to 0.3 K. The neutron powder diffraction data
collected at 0.1 K show a broad peak of magnetic origin (diffuse scattering)
but no magnetic Bragg peaks. The analysis of the diffuse scattering data
reveals a dominant antiferromagnetic interaction in agreement with the negative
Weiss temperature. The absence of long-range magnetic order and the presence of
slow spin dynamics and persistent spin fluctuations together reflect a
dynamical ground state in Tb2Hf2O7.
