AbstractWhen 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 B_c it displays the hallmark T-linear resistivity and a $T\,{{{{{{\mathrm{log}}}}}}}\,(1/T)$ 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 B_c is approached. The large increase in the electronic heat capacity and entropy near B_c can be understood quantitatively in terms of the scattering of conduction electrons by these spin-fluctuations. On entering the spin-density-wave ordered phase present near B_c, the fluctuations become stronger suggesting that the order is stabilised through an “order-by-disorder” mechanism.