Limits on the Carroll-Field-Jackiw electrodynamics from geomagnetic data

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 $k_{\mathrm{A}\mathrm{F}}$ 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 $k_{\mathrm{A}\mathrm{F}}$-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 $k_{\mathrm{A}\mathrm{F}}$ in the Sun-centered frame read $\mathrm{\mid }(k_{\mathrm{A}\mathrm{F}}{)}_Z\mathrm{\mid }\lesssim 4\times {10}^{-25}\mathrm{G}\mathrm{e}\mathrm{V}$ for $\mathrm{\mid }(k_{\mathrm{A}\mathrm{F}}{)}_X\mathrm{\mid },\mathrm{\mid }(k_{\mathrm{A}\mathrm{F}}{)}_Y\mathrm{\mid }\lesssim {10}^{-24}\mathrm{G}\mathrm{e}\mathrm{V}$ at the two-sigma level. This represents an improvement of about four orders of magnitude over earlier bounds based on other geophysical phenomena.