Determining AC Magnetic Susceptibility of Kilogram-Level Test Masses for TianQin

The effect from the interaction of the alternating current (AC) magnetic field with kilogram-level test mass (TM) limits the detectivity of the TianQin space-based gravitational wave detection. The quantified effect requires the determination of the AC magnetic susceptibility Χ(f) of the TM. A torque method is proposed to measure the Χ(f) of kg-level samples at the mHz band with a precision of 1×10^-7. Combined with our previous work Phys. Rev. Appl. 18 044010 (2022), the general frequency-dependent susceptibility of the alloy cube with side length 𝐿 and electrical conductivity 𝜎 is determined as Χ(f) = Χ₀ + (0.24 ±0.01)σμ₀L²f from 0.1 mHz to 1 Hz. The determination is helpful for the preliminary estimation of the in-band eddy current effect in the TianQin noise budget. The technique can be adopted to accurately measure Χ(f) of the actual TM in other precision experiments, where the magnetic noise is a significant detection limit.