  Polarized and unpolarized neutron scattering was used to measure the wave
vector- and frequency-dependent magnetic fluctuations in the normal state (from
the superconducting transition temperature, T_c=35, up to 350 K) of single
crystals of La_{1.86}Sr_{0.14}CuO_4. The peaks which dominate the fluctuations
have amplitudes that decrease as T^{-2} and widths that increase in proportion
to the thermal energy, k_B T (where k_B is Boltzmann's constant), and energy
transfer added in quadrature. The nearly singular fluctuations are consistent
with a nearby quantum critical point.
