  When the transition temperature of a continuous phase transition is tuned to
absolute zero, new ordered phases and physical behaviour emerge in the vicinity
of the resulting quantum critical point. Sr3Ru2O7 can be tuned through quantum
criticality with magnetic field at low temperature. Near its critical field Bc
it displays the hallmark T-linear resistivity and a T log(1/T) electronic heat
capacity behaviour of strange metals. However, these behaviours have not been
related to any critical fluctuations. Here we use inelastic neutron scattering
to reveal the presence of collective spin fluctuations whose relaxation time
and strength show a nearly singular variation with magnetic field as Bc is
approached. The large increase in the electronic heat capacity and entropy near
Bc can be understood quantitatively in terms of the scattering of conduction
electrons by these spin-fluctuations. On entering the spin density wave (SDW)
phase present near Bc, the fluctuations become stronger suggesting that the SDW
order is stabilised through an "order-by-disorder" mechanism.
