Gapping of the soft mode in a temporally-quenched random field Ising ferromagnet

Gapless collective modes underlie quantum criticality, yet how quenched disorder reshapes their softening remains unsettled. In the Ising magnet LiHoF₄, the lowest electronuclear mode corresponds to the gapless collective mode and was reported to behave gapless. In this work, we use microwave spectroscopy to track the evolution of the lowest electronuclear mode in LiHo_x​Y_1−xF₄, a dipolar transverse-field Ising magnet that realizes a random-field Ising model. For light dilution (x=0.99), the mode softens continuously toward zero frequency on approach to the quantum critical point, consistent with the critical soft mode previously seen for x=1. By contrast, strong dilution (x=0.65) cuts off the softening: a finite gap of 1.43±0.10 GHz opens, and the electronuclear absorption disappears on the ferromagnetic side of the transition. This gapping cannot be explained by vacancy scattering alone. Instead, the data support a unified mechanism in which off-diagonal dipolar couplings generate random longitudinal fields whose temporal character controls the fate of the soft mode: in the paramagnet, fast spin dynamics average these fields to zero on GHz timescales, preserving coherence, whereas in the disordered ferromagnet, frozen dynamics render them effectively quenched, dephasing the excitation and opening a gap. Random-field-induced quenching thus provides a framework for disorder-driven departures from universality in quantum Ising magnets.