  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.
