Frustrated random-singlet state with ice-type structural fluctuation in spinel titanates

In ice, it is well known that the orientation of H 2 O molecules is disordered by geometrical frustration. Ice-analogous materials having a pyrochlore lattice display interesting phenomena such as the spin-ice state and the magnetic monopole. In the spinel titanate MgTi 2 O 4 , the Ti ions have a quantum spin in the pyrochlore lattice. The Ti ions are displaced, accompanied by the spin-singlet formation. Since this displacement pattern follows the ice rule, the title compound is a material analogous to ice. When a small quantity of Ti ions are replaced with Mg ions, the ice-type structural fluctuation exists. In this structural ice-type state, the spins are also fluctuating at a nanosecond scale down to 0.3 K. We ascribed this phenomenon to the gapless frustrated random-singlet state, in which the spin-singlet pairs are resonating, and the orphan spins are hopping.