  We report a positive muon spin relaxation and rotation (\muSR) study of the
quantum spin ice materials Yb2Ti2O7 and Yb2Sn2O7 focusing on the low field
response. In agreement with earlier reports, data recorded in small
longitudinal fields evidence anomalously slow spin dynamics in the microsecond
range below the temperature T_c at which the specific heat displays an intense
peak, namely T_c = 0.24 K and 0.15 K, respectively, for the two systems. We
found that slow dynamics extends above T_c up to at least 0.7 K for both
compounds. The conventional dynamical Gaussian Kubo-Toyabe model describes the
\muSR spectra recorded above T_c. At lower temperatures a published analytical
extension of the Gaussian Kubo-Toyabe model provides a good description,
consistent with the existence of short-range magnetic correlations. While the
physical response of the two systems is qualitatively the same, Yb2Ti2O7
exhibits a much larger local magnetic susceptibility than Yb2Sn2O7 below T_c.
Considering previously reported ac susceptibility, neutron scattering and \muSR
results, we suggest the existence of anomalously slow spin dynamics to be a
common physical property of pyrochlore magnetic materials. The possibility of
molecular spin substructures to be associated to the slow dynamics and
therefore the short-range correlations is mentioned. The slow spin dynamics
observed under field does not exclude the presence of much faster dynamics
detected in extremely low or zero field.
