Common Glass-Forming Spin-Liquid State in the Pyrochlore Magnets Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$

Despite a well-ordered pyrochlore crystal structure and strong magnetic interactions between the Dy$^{3+}$ or Ho$^{3+}$ ions, no long range magnetic order has been detected in the pyrochlore titanates Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$. To explore the actual magnetic phase formed by cooling these materials, we measure their magnetization dynamics using toroidal, boundary-free magnetization transport techniques. We find that the dynamical magnetic susceptibility of both compounds has the same distinctive phenomenology, that is indistinguishable in form from that of the dielectric permittivity of dipolar glass-forming liquids. Moreover, Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$ both exhibit microscopic magnetic relaxation times that increase along the super-Arrhenius trajectories analogous to those observed in glass-forming dipolar liquids. Thus, upon cooling below about 2K, Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ both appear to enter the same magnetic state exhibiting the characteristics of a glass-forming spin-liquid.