  Conventional crystalline magnets are characterized by symmetry breaking and
normal modes of excitation called magnons with quantized angular momentum
$\hbar$. Neutron scattering correspondingly features extra magnetic Bragg
diffraction at low temperatures and dispersive inelastic scattering associated
with single magnon creation and annihilation. Exceptions are anticipated in
so-called quantum spin liquids as exemplified by the one-dimensional spin-1/2
chain which has no magnetic order and where magnons accordingly fractionalize
into spinons with angular momentum $\hbar/2$. This is spectacularly revealed by
a continuum of inelastic neutron scattering associated with two-spinon
processes and the absence of magnetic Bragg diffraction. Here, we report
evidence for these same key features of a quantum spin liquid in the
three-dimensional Heisenberg antiferromagnet NaCaNi$_2$F$_7$. Through specific
heat and neutron scattering measurements, Monte Carlo simulations, and analytic
approximations to the equal time correlations, we show that NaCaNi$_2$F$_7$ is
an almost ideal realization of the spin-1 antiferromagnetic Heisenberg model on
a pyrochlore lattice with weak connectivity and frustrated interactions.
Magnetic Bragg diffraction is absent and 90\% of the spectral weight forms a
continuum of magnetic scattering not dissimilar to that of the spin-1/2 chain
but with low energy pinch points indicating NaCaNi$_2$F$_7$ is in a Coulomb
phase. The residual entropy and diffuse elastic scattering points to an exotic
state of matter driven by frustration, quantum fluctuations and weak exchange
disorder.
