A bstract Lorentz-symmetry violation may be described via the CPT-odd, dimension-3, Carroll-Field-Jackiw term, which couples the electromagnetic fields to a constant 4-vector k AF selecting a preferred direction in spacetime. We solve the field equations using the Green’s method for a static point-like magnetic dipole and find the k AF -dependent corrections to the standard dipolar magnetic field that strongly dominates the near-Earth magnetic field. Given the very good agreement between current models and ground- and satellite-based geomagnetic data, our strongest constraints on the components of k AF in the Sun-centered frame read |( k AF ) Z | ≲ 4 × 10 −25 GeV for |( k AF ) X |, |( k AF ) Y | ≲ 10 −24 GeV at the two-sigma level. This represents an improvement of about four orders of magnitude over earlier bounds based on other geophysical phenomena.
Carvalho et al. (2026) studied this question.