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.
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