  The Coulomb interaction among massless Dirac fermions in graphene is
unscreened around the isotropic Dirac points, causing a logarithmic velocity
renormalization and a cone reshaping. In less symmetric Dirac materials
possessing anisotropic cones with tilted axes, the Coulomb interaction can
provide still more exotic phenomena which have not been experimentally unveiled
yet. Here, using site-selective nuclear magnetic resonance, we find a
non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent
ferrimagnetism in tilted Dirac cones that appear on the verge of charge
ordering in an organic compound. Our theoretical analyses based on the
renormalization-group approach and the Hubbard model show that these
observations are the direct consequences of the long-range and short-range
parts of the Coulomb interaction, respectively. The cone reshaping and the
bandwidth renormalization, as well as the novel magnetism revealed here, can be
ubiquitous and vital for many Dirac materials.
