  We have measured temperature-dependent magnetic Compton profiles (MCPs) from
a single crystal of La$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$. The MCPs, which involved
the scattering of circularly polarized x-rays, are in general related to the
momentum density of all the unpaired spins in the system. Nevertheless, we show
that when the x-ray scattering vector lies along the [110] direction, the
number of magnetic electrons of a specific symmetry, i.e. $d$-electrons of
$x^2-y^2$ symmetry, yield a distinct signature in the MCP, allowing us to
monitor substantial changes in the occupancy of the $d_{x^2-y^2}$ states over
the investigated temperature range of 5-200K. This study indicates that
magnetic Compton scattering can provide a powerful window on the properties of
specific magnetic electrons in complex materials.
