Soft magnetic excitations and quantum critically in Sr$_3$Ru$_2$O$_7$

The application of a magnetic field of approximately $B_c=8~T$ induces quantum critical behavior in Sr$_3$Ru$_2$O$_7$. Near $B_c$, the resistivity shows an anomalous power law temperature dependence and the linear specific heat becomes large. In addition, new ordered phases with strong nematic tendencies appear below $1~K$ near $ B_c$. These phases have recently been identified as spin density wave order. Here we report an inelastic neutron scattering study of the low-energy magnetic excitations. We find a dramatic field-induced softening of the collective magnetic excitations in the region surrounding $B_c$. This suggests that the quantum critically observed in Sr$_3$Ru$_2$O$_7$ is magnetic in origin. The presence of additional magnetic excitations can also explain the increase in entropy and specific heat present near $B_c$.