In-Plane Magnetic Anisotropy of Fe Atoms on ${\mathrm{Bi}}_2{\mathrm{Se}}_3(111)$

The robustness of the gapless topological surface state hosted by a 3D topological insulator against perturbations of magnetic origin has been the focus of recent investigations. We present a comprehensive study of the magnetic properties of Fe impurities on the prototypical 3D topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ using local low-temperature scanning tunneling spectroscopy and integral x-ray magnetic circular dichroism techniques. Single Fe adatoms on the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface, in the coverage range $\approx 1\%$ of a monolayer, are heavily relaxed into the surface and exhibit a magnetic easy axis within the surface plane, contrary to what was assumed in recent investigations on the supposed opening of a gap. Using ab initio approaches, we demonstrate that an in-plane easy axis arises from the combination of the crystal field and dynamic hybridization effects.

Figure 1

(a) STM constant-current image of $1\%$ ML of Fe atoms adsorbed onto a cleaved ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface; $I_{\mathrm{stab}}=500\mathrm{pA}$ and $V_{\mathrm{stab}}=+100\mathrm{mV}$. (b) High-resolution image of two Fe atoms at different binding sites ($A$ and $B$); $I_{\mathrm{stab}}=600\mathrm{pA}$ and $V_{\mathrm{stab}}=-100\mathrm{mV}$. (c) Tunneling spectra taken on two Fe atoms at the indicated binding sites and on a substrate spot [green (gray) line] of the Fe covered surface. For reference, a spectrum on the uncovered ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface is shown (black line), where the thick vertical gray bar refers to the DP, as confirmed by probing the zeroth Landau level in high magnetic fields. Inset: same as (c) after subtracting the substrate spectrum; $I_{\mathrm{stab}}=600\mathrm{pA}$, $V_{\mathrm{stab}}=-100\mathrm{mV}$, $V_{\mathrm{mod}}=3\mathrm{mV}$, and $f_{\mathrm{mod}}=4.1\mathrm{kHz}$.

Figure 2

X-ray study of Fe impurities (coverage $1\%$ ML) on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ at $T=10\mathrm{K}$. (a) Magnetization curves $M(B)$ for directions $\theta =0°,70°$ in red (gray) and blue (black) squares, respectively. The dashed lines represent thermodynamic fits with a moment $m=4{\mu }_B$ and $K=1.9\mathrm{meV}$ (see text). (b) XMCD signals in a field of $B=5\mathrm{T}$ normalized to the XMCD peak intensity at the $L_2$ edge. (c),(d) XAS [red (dark gray) line, upper panel] and XMCD (black line, lower panel) measured in a field of $B=5\mathrm{T}$ for directions (c) $\theta =0°$ and (d) $70°$. Green (light gray) spectra refer to CF calculations with ${ϵ}_0=-0.69\mathrm{eV}$ and ${ϵ}_2=0.32\mathrm{eV}$.

Figure 3

(a),(b) Adsorption geometries of Fe [red (dark gray) spheres] on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ [Bi, big light gray spheres; Se, small yellow (light gray) spheres]. Fe can adsorb at (a) an fcc ($f$ site) or (b) an hcp ($h$ site) hollow site. The corresponding real and imaginary parts of the hybridization functions [$\mathrm{Re}{\Delta }_{ii}(E)+{ϵ}_i$ and $\mathrm{Im}{\Delta }_{ii}(E)$] are given in (c),(d) and (e),(f), respectively, and quantify the interaction of the Fe $3d$ electrons with their environment. ${\Delta }_{ii}(E)$ is shown for all Fe $3d$ orbitals: $E2$ ($d_{xy}$ and $d_{x^2-y^2}$), $E1$ ($d_{xz}$ and $d_{yz}$), and $A1$ ($d_{z^2}$).