  Enhanced magnetism has recently been reported for the
topological-insulator/ferromagnet interface Bi$_2$Se$_3$/EuS with Curie
temperatures claimed to be raised above room temperature from the bulk EuS
value of 16 K. Here we investigate the analogous interface Bi$_2$Se$_3$/EuSe.
EuSe is a low-temperature layered ferrimagnet that is particularly sensitive to
external perturbations. We find that superconducting quantum interference
device (SQUID) magnetometry of Bi$_2$Se$_3$/EuSe heterostructures reveals
precisely the magnetic phase diagram known from EuSe, including the
ferrimagnetic phase below 5 K, without any apparent changes from the bulk
behavior. Choosing a temperature of 10 K to search for magnetic enhancement, we
determine an upper limit for a possible magnetic coercive field of 3 mT. Using
interface sensitive x-ray absorption spectroscopy we verify the magnetic
divalent configuration of the Eu at the interface without contamination by
Eu3+, and by x-ray magnetic circular dichroism (XMCD) we confirm at the
interface the magnetic hysteresis obtained by SQUID. XMCD data obtained at 10 K
in a magnetic field of 6 T indicate a magnetic spin moment of mz,spin = 7
$\mu$B/Eu$^{2+}$, in good agreement with the SQUID data and the expected
theoretical moment of Eu2+. Subsequent XMCD measurements in zero field show,
however, that sizable remanent magnetization is absent at the interface for
temperatures down to about 10 K.
