Determining AC magnetic susceptibility of kilogram-level test masses for TianQin

The effect from interaction of alternating current (AC) magnetic field with kilogram-level test mass (TM) limits the detectivity of the TianQin space-based gravitational wave (GW) detection. The quantified effect requires the determination of AC magnetic susceptibility χ(f) of 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 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.