Investigation of the structural and magnetic properties of MBE-grown Cr-doped Bi$_2$Se$_3$ thin films

We report a study of the structural and magnetic properties of Cr-doped Bi$_2$Se$_3$ thin films grown by MBE. We will present a thorough exposition of the electronic character of the magnetic ground state of this material as determined by x-ray magnetic circular dichroism (XMCD) as well as complementary measurements by polarised neutron reflectometry, X-ray diffraction and SQUID magnetometry. We observe the formation of a ferromagnetic ground state (via SQUID), below a measured $T_c \sim 8.5$~K with a saturation magnetization of $2.1$~$\mu_{\mathrm{B}}$/Cr. By XRD we observe a reduction in $c$-axis lattice parameter with increasing Cr concentration up to 12~at.\% of dopant. XMCD and EXAFS studies indicate that, contrary to expectations, the Cr dopes into the system as Cr$^{2+}$ due to covalency between the Cr-$d$ and Se-$p$ orbitals. We will demonstrate that no evidence is found of surface enhancement of the magnetic order and present recent work on the effect of ferromagnetic proximity coupling.