Ferromagnetic fragmented ground state in the pyrochlore Ho$_2$Ru$_2$O$_7$

The consecutive magnetic ordering of the Ho and Ru ions in the pyrochlore Ho2Ru2O7 and their interplay are investigated by neutron scattering, magnetic and specific heat measurements. The Ru magnetic moments order at 95 K into an easy-plane antiferromagnetic state, while the Ho moments order at 1.55 K into an unsaturated ferromagnetic state that retains an extensive ground state entropy and present complex spin dynamics throughout the low temperature phase. These unexpected features are analyzed in terms of a fragmented ferromagnetic state equivalent to the pyrochlore kagome ice. Selection of this unusual state relies on a subtle compromise between long-range ferromagnetic interactions between holmium moments and a repulsive cubic field, both mediated by the ruthenium lattice.