Incipient antiferromagnetism in the Eu-doped topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$

Rare-earth ions typically exhibit larger magnetic moments than transition-metal ions and thus promise the opening of a wider exchange gap in the Dirac surface states of topological insulators. Yet in a recent photoemission study of Eu-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ films, the spectra remained gapless down to $T=20$ K. Here we scrutinize whether the conditions for a substantial gap formation in this system are present by combining spectroscopic and bulk characterization methods with theoretical calculations. For all studied Eu doping concentrations, our atomic multiplet analysis of the $M_{4,5}$ x-ray absorption and magnetic circular dichroism spectra reveals a ${\mathrm{Eu}}^{2+}$ valence and confirms a large magnetic moment, consistent with a $4f^7{}^{8}S_{7/2}$ ground state. At temperatures below 10 K, bulk magnetometry indicates the onset of antiferromagnetic (AFM) ordering. This is in good agreement with density functional theory, which predicts AFM interactions between the Eu impurities. Our results support the notion that antiferromagnetism can coexist with topological surface states in rare-earth-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and call for spectroscopic studies in the Kelvin range to look for novel quantum phenomena such as the quantum anomalous Hall effect.

Figure 1

Experimental Eu $M_{4,5}$ edges XAS (top) and normalized XMCD (bottom) intensities of (a) 2%, (b) 4%, and (c) 9% Eu-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ thin films measured at $T=10$ K in an external magnetic field of 9 T with left-circular ($I_{\text{left}}$) and right-circular ($I_{\text{right}}$) x-ray polarization. The inset in (a) schematically illustrates the experimental geometry. The inset in (b) highlights the additional small spectral weight at the $M_5$ edge of the 4% Eu-doped sample, which is absent for the other two samples.

Figure 2

(a) Magnetic field dependence of the $M_5$ edge XMCD TEY signal for 2% Eu-doped (squares), 4% Eu-doped (triangles), and 9% Eu-doped (circles) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ measured at $T=10$ K, at normal incidence of the x rays. The inset exemplarily illustrates the 2% Eu-doped sample fitted with a Brillouin function (brown line). (b) Normalized XMCD measured at 10 K in an external magnetic field of 12 T for normal incidence of the x rays, as well as for ${70}^{\circ }$ off-normal, i.e., nearly grazing incidence, showing no noticeable anisotropy.

Figure 3

Sum-rule analysis for the 9% Eu-doped sample. (a) Left- and right-circularly polarized XAS spectra of the Eu $M_{4,5}$ edges, obtained after the background corrections described in Sec. 2 ($I_{\text{left}}$, solid, light blue line, and $I_{\text{right}}$, solid dark red line), along with the corresponding XMCD data (solid green line, lower panel). The dashed lines show the total integrated XAS and XMCD spectral weight, respectively. The arrows mark the values of $r, p$, and $q$ used in Eqs. (1) and (2). $E_0$ and $E_1$ denote the onset and the end energy of the entire $M_{4,5}$ edges, and $E_{\text{cutoff}}$ denotes the energy separating the $M_4$ and $M_5$ contributions. (b, c) Distribution of $m_{\text{orb}}$ and $m_{\text{spin}}$, respectively, obtained after application of the sum rules 8192 times, for different sets of fitting parameters, as described in the main text.

Figure 4

Top panel: Experimental Eu $M_{4,5}$ XAS averaged over the two polarizations and XMCD spectra of (a) 2% and (b) 4% Eu-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ measured at $T=10$ K in an external magnetic field of 9 T. Bottom panel: Calculated average XAS and XMCD spectra for ${\mathrm{Eu}}^{2+}$ and ${\mathrm{Eu}}^{3+}$ obtained by atomic multiplet theory. The dashed vertical lines are drawn as a guide to the eye, highlighting the position of particular features in the spectra.

Figure 5

Magnetic field dependence of the CFT-calculated spin magnetic moment $m_z^{\text{spin}}$ (solid line) and of the experimental $M_5$ edge XMCD TEY signal for the 2% Eu-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ thin film (full circles) measured at $T=10$ K at normal incidence of the x rays. The shaded area indicates the error, as estimated in the main text.

Figure 6

Normalized (a) Bi $N_{4,5}$ and (b) Te $M_{4,5}$ XAS (top panel) and XMCD (bottom panel) intensities of the 2% Eu-doped sample measured at 5 K in an external magnetic field of 2 T.

Figure 7

Field-cooled magnetic susceptibility $\chi$ for 2% Eu-doped (solid black), 4% Eu-doped (solid red), and 9% Eu-doped (solid blue) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ in a 2–100 K temperature range. The arrows indicate the Néel temperature estimated from the cusp in the $\chi \left(T\right)$ curves. In the inset, a comparison of the inverse magnetic susceptibility for the corresponding samples is shown at low temperatures from 2 to 35 K. The black solid lines represent linear Curie-Weiss fits to the experimental data.

Figure 8

(a–d) ARPES spectra of Eu-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ thin films with doping ranging from 0% to 9%, measured near the $\overline{\mathrm{\Gamma }}$ point at 20 K using a photon energy $h\nu =21.2$ eV. (e–h) Corresponding second derivative plots. (i) Wide-energy-range spectrum near the $\overline{\mathrm{\Gamma }}$ point for the 2% Eu-doped sample.

Figure 9

(a) Energy momentum cut along the $\overline{\mathrm{\Gamma }}\overline{\text{M}}$ direction for the 2% sample. (b)–(f) Constant energy maps for binding energies ranging from 0 to 2.8 eV. The hexagonal shapes are the boundaries of the two-dimensional Brillouin zones. (g) ResPES data for the 4% sample showing the Bi $5d$ and Eu $4f$ core levels. (h) Distance dependence of the exchange interaction $J_{ij}$ between pairs of Eu impurities placed in the same ($•$) or neighboring ($\blacksquare$) Bi layers within one quintuple layer. The inset shows $4f$ dominated total DOS of the Eu dimer (black) and total DOS of the host material (gray) together with the energy dependence of the exchange coupling strength $J_{01}$ (blue). (i) LDA band structure and ARPES data for the 2% sample. The LDA bands are shown in $\overline{\mathrm{\Gamma }}\overline{\text{M}}$ and $\overline{\mathrm{\Gamma }}\overline{\text{K}}$ directions with symbols whose size and opaqueness is proportional to the spectral weight. The red dotted line shows the position of the theoretical Fermi level, which differs from the experimental one by 150 meV due to the intrinsic $n$ doping in the measured sample.