  Correlated-electron systems support a wealth of magnetic excitations, ranging
from conventional spin waves to exotic fractional excitations in
low-dimensional or geometrically-frustrated spin systems. Probing such
excitations on nanometre length scales is essential for unravelling the
underlying physics and developing new spintronic nanodevices. However, no
established technique provides real-space, few-nanometre-scale probing of
correlated-electron magnetic excitations under ambient conditions. Here we
present a solution to this problem using magnetometry based on single
nitrogen-vacancy (NV) centres in diamond. We focus on spin-wave excitations in
a ferromagnetic microdisc, and demonstrate local, quantitative, and
phase-sensitive detection of the spin-wave magnetic field at ~50 nm from the
disc. We map the magnetic-field dependence of spin-wave excitations by
detecting the associated local reduction in the disc's longitudinal
magnetization. In addition, we characterize the spin-noise spectrum by NV-spin
relaxometry, finding excellent agreement with a general analytical description
of the stray fields produced by spin-spin correlations in a 2D magnetic system.
These complementary measurement modalities pave the way towards imaging the
local excitations of systems such as ferromagnets and antiferromagnets,
skyrmions, atomically assembled quantum magnets, and spin ice.
