Measurement of the remanent magnetic quadrupole moment of a macroscopic mass using a torsion balance for gravitational experiment

Magnetic effects significantly contribute to errors in gravitational experiments. Typically, remanent magnetism is characterized by magnetic dipole interactions. However, this approach neglects higher-order magnetic terms, particularly the remanent magnetic quadrupole moment (RMQM) interaction, which may compromise experimental accuracy. This paper focuses on measuring the RMQM of a macroscopic mass to evaluate its impact. Measurements were performed using a rotating torsion pendulum equipped with custom-designed magnetic coils. The investigation examines two predominantly non-magnetic samples, one of which is an optimized pendulum specifically designed to test the equivalence principle. The results indicate that the RMQM components of interest for the pendulum have a magnitude of $3.7(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{m}}^{3}$. Given a reported magnetic field gradient of $0.1\text{ }\text{ }\mathrm{nT}/\mathrm{cm}$, the RMQM interaction can introduce a non-negligible correction at the ${10}^{\ensuremath{-}14}$ precision level in the equivalence principle test. For the second sample, the RMQM components of interest are measured to be $43.8(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{m}}^{3}$. The uncertainty is mainly due to statistical error and the coil installation error. This RMQM measurement could be similarly applied to other gravitational experiments if needed.