  For hole systems with an effective spin j=3/2, we present an invariant
decomposition of the spin density matrix that can be interpreted as a multipole
expansion. The charge density corresponds to the monopole moment and the spin
polarization due to a magnetic field corresponds to a dipole moment while heavy
hole-light hole splitting can be interpreted as a quadrupole moment. For quasi
two-dimensional hole systems in the presence of an in-plane magnetic field B
the spin polarization is a higher-order effect that is typically much smaller
than one even if the minority spin subband is completely depopulated. On the
other hand, the field B can induce a substantial octupole moment which is a
unique feature of j=3/2 hole systems.
