  Fourfold anisotropic magnetoresistance (AMR) have been widely observed in
quantum materials, but the underlying mechanisms remain poorly understood. Here
we find, in a variety of three-dimensional Dirac materials that can be
unifiedly described by the massive Dirac equation, the intrinsic orbital
magnetic moment of electrons vary synchronously with the magnetic field and
give rise to a {\pi} periodic correction to its velocity, further leading to
unusual fourfold AMR, dubbed intrinsic orbital fourfold AMR. Our theory not
only explains the observation of fourfold AMR in bismuth but also uncovers the
nature of the dominant fourfold AMR in thin films of antiferromagnetic
topological insulator MnBi2Te4, which arises from the near cancellation of the
twofold AMR from the surface states and bulk states due to distinct
spin-momentum lockings. Our work provides a new mechanism for creation and
manipulation of intrinsic fourfold AMR in both conventional conductors and
various topological insulators.
