We have developed a much sensitve technique to conduct magnetometry under ultrahigh pressures up to 6.3~GPa, which can detect a weak volume susceptibilities as small as $sim 10^{-4}$. An opposed-anvil-type high-pressure cell is designed by numerical analysis to give nearly zero magnetic response, in a commercial SQUID magnetometer. We introduced procedures for subtracting background contributions from a high-pressure cell by taking displacements of the cell parts into account, and found a way of resolving tiny magnetism of a sample from given magnetometer response curves. A non-magnetic material, binderless tungsten carbide ceramic, is employed. To increase sample-signal-to-background ratio further, a conical shaped gasket and cupped anvils are introduced, yielding nearly ten times better space efficiency. The new set-up and analysis are applied to measure the paramagnetic susceptibilities of spin orbit entangled moment under pressures.
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