Geometrical Frustration in the Ferromagnetic Pyrochlore ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{O}_7$

We report a detailed study of the pyrochlore ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, in which the magnetic ions $\left({\mathrm{Ho}}^{3+}\right)$ are ferromagnetically coupled with $J\sim 1\mathrm{K}$. We show that the presence of local Ising anisotropy leads to a geometrically frustrated ground state, preventing long-range magnetic order down to at least 0.05 K. However, unlike in the case of a frustrated antiferromagnet, this disorder is principally static. In a magnetic field, the ground-state degeneracy is broken and ordered magnetic phases are formed which display an unusual history dependence due to the slow dynamics of the system. These results represent the first experimental evidence for geometrical frustration in a ferromagnetic system.