  The singlet ground state magnetism in pyrochlore osmates Y$_2$Os$_2$O$_7$ and
Ho$_2$Os$_2$O$_7$ is studied by DC and AC susceptibility, specific heat, and
neutron powder diffraction measurements. Despite the expected non-magnetic
singlet in the strong spin-orbit coupling (SOC) limit for Os$^{4+}$ ($5d^4$),
Y$_2$Os$_2$O$_7$ exhibits a spin-glass (SG) ground state below 4 K with weak
magnetism, suggesting possible proximity to a quantum phase transition between
the non-magnetic state in the strong SOC limit and the magnetic state in the
strong superexchange limit. Ho$_2$Os$_2$O$_7$ has the same structural
distortion as occurs in Y$_2$Os$_2$O$_7$. However, the Os sublattice in
Ho$_2$Os$_2$O$_7$ shows long-range magnetic ordering below 36\,K. The sharp
difference of the magnetic ground state between Y$_2$Os$_2$O$_7$ and
Ho$_2$Os$_2$O$_7$ signals the singlet ground state magnetism in
$R_2$Os$_2$O$_7$ is fragile and can be disturbed by the weak $4f-5d$
interactions.
