Atomic-Scale Magnetism of Cr-Doped Bi₂Se₃ Thin Film Topological Insulators

Magnetic doping is the most common method for breaking time-reversal-symmetry surface states of topological insulators (TIs) to realize novel physical phenomena and to create beneficial technological applications. Here we present a study of the magnetic coupling of a prototype magnetic TI, that is, Cr-doped Bi₂Se₃, in its ultrathin limit which is expected to give rise to quantum anomalous Hall (QAH) effect. The high quality Bi_2–<i>x</i>Cr_<i>x</i>Se₃ epitaxial thin film was prepared using molecular beam epitaxy (MBE), characterized with scanning transimission electron microscopy (STEM), electrical magnetotransport, and X-ray magnetic circularly dichroism (XMCD) techniques, and the results were simulated using density functional theory (DFT) with spin–orbit coupling (SOC). We observed a sizable spin moment <i>m</i>_spin = (2.05 ± 0.20) μ_B/Cr and a small and negative orbital moment <i>m</i>_orb = (−0.05 ± 0.02) μ_B/Cr of the Bi_1.94Cr_0.06Se₃ thin film at 2.5 K. A remarkable fraction of the (Cr_Bi–Cr_I)³⁺ antiferromagnetic dimer in the Bi_2–<i>x</i>Cr_<i>x</i>Se₃ for 0.02 < <i>x</i> < 0.40 was obtained using <i>first-principles</i> simulations, which was neglected in previous studies. The spontaneous coexistence of ferro- and antiferromagnetic Cr defects in Bi_2–<i>x</i>Cr_<i>x</i>Se₃ explains our experimental observations and those based on conventional magnetometry which universally report magnetic moments significantly lower than 3 μ_B/Cr predicted by Hund’s rule