  Interacting quantum systems are attracting increasing interest for developing
precise metrology. In particular, the realisation that quantum-correlated
states and the dynamics of interacting systems can lead to entirely new and
unexpected phenomena have initiated an intense research effort to explore
interaction-based metrology both theoretically and experimentally. However, the
current framework of interaction-based metrology mainly focuses on
single-parameter estimations, a demonstration of multiparameter metrology using
interactions as a resource was heretofore lacking. Here we demonstrate an
interaction-based multiparameter metrology with strongly interacting nuclear
spins. We show that the interacting spins become intrinsically sensitive to all
components of a multidimensional field when their interactions are
significantly larger than their Larmor frequencies. Using liquid-state
molecules containing strongly interacting nuclear spins, we demonstrate the
proof-of-principle estimation of all three components of an unknown magnetic
field and inertial rotation. In contrast to existing approaches, the present
interaction-based multiparameter sensing does not require external reference
fields and opens a path to develop an entirely new class of multiparameter
quantum sensors.
