Signatures of in-plane and out-of-plane magnetization generated by synchrotron radiation in magnetically doped and pristine topological insulators

Possibility of in-plane and out-of-plane magnetization generated by synchrotron radiation (SR) in magnetically doped and pristine topological insulators (TIs) is demonstrated and studied by angle-resolved photoemission spectroscopy. We show experimentally and by ab initio calculations how nonequal depopulation of the Dirac cone (DC) states with opposite momenta in V-doped and pristine TIs generated by linearly polarized SR leads to the hole-generated uncompensated spin accumulation followed by the SR-induced magnetization via spin-torque effect. Moreover, the photoexcitation of the DC is asymmetric, and it varies with the photon energy. We find a relation between the photoexcitation asymmetry, the generated spin accumulation, and the induced in-plane and out-of-plane magnetic field. Experimentally the SR-generated in-plane and out-of-plane magnetization is confirmed by the $k_{\parallel }$ shift of the DC position and by the gap opening at the Dirac point even above the Curie temperature. Theoretical predictions and estimations of the measurable physical quantities substantiate the experimental results.

Figure 1

Lines (a),(b),(c): series of ARPES intensity maps of the TSSs measured along the SR incidence plane ($\overline{\mathrm{\Gamma }K}$) (Geometry 1) for pristine TIs with stoichiometry ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.8}{\mathrm{Se}}_{1.2}$ (a) and ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ (b) and for V-doped TIs with stoichiometry ${\mathrm{Bi}}_{1.37}{\mathrm{V}}_{0.03}{\mathrm{Sb}}_{0.6}{\mathrm{Te}}_2\mathrm{Se}$ (c) at temperature 17–20 K by using linear $p$-polarized SR at different photon energy. The profiles of comparable intensities of the TSSs with opposite momenta (MDC) cut at the energy corresponding to enhanced intensity (marked by horizontal white lines) are presented at the bottom of each inset.

Figure 2

TSS intensity asymmetry ($A$) trend vs photon energy estimated from the ARPES intensity maps presented in Figs. 1–1 and Figs. 1S, 2S in the Supplemental Material [41] measured along $\overline{\mathrm{\Gamma }K}$ and $\overline{\mathrm{\Gamma }M}$ directions of the surface Brillouin zone.

Figure 3

(a)–(f) Calculated energy-momentum distribution of the photoemission intensity from the DC surface states along $\overline{\mathrm{\Gamma }}\overline{K}$ (Geometry 1) (a)–(c) and along $\overline{\mathrm{\Gamma }}\overline{M}$ (Geometry 2) (d)–(f) for the three photon energies: $h\omega =16$ (a),(d), 21 (b),(e), and 28 eV (c),(f). In all cases a $p$-polarized light is incident along $\overline{\mathrm{\Gamma }}\overline{K}$ at an angle of $\theta ={73}^{\circ }$. (g),(h) Photon energy dependence of the total intensity from the upper Dirac cone integrated over negative $k_{\parallel }$ ($I_{\mathrm{left}}$, full circles) and positive $k_{\parallel }$ ($I_{\mathrm{right}}$, open circles) along $\overline{\mathrm{\Gamma }}\overline{K}$ (g) and along $\overline{\mathrm{\Gamma }}\overline{M}$ (h). (i),(j) Normalized difference between the integrated intensities in the opposite directions, $[I_{\mathrm{left}}\left(h\nu \right)-I_{\mathrm{right}}\left(h\nu \right)]/[I_{\mathrm{left}}\left(h\nu \right)+I_{\mathrm{right}}\left(h\nu \right)]$, for two angles of incidence, $\theta ={50}^{\circ }$ and ${73}^{\circ }$. In graph (i) the light incidence plane is parallel to ${\mathbf{k}}_{\parallel }$ (both for $\overline{\mathrm{\Gamma }}\overline{K}$ and for $\overline{\mathrm{\Gamma }}\overline{M}$), and in graph (j) it is perpendicular to ${\mathbf{k}}_{\parallel }$ ($\overline{\mathrm{\Gamma }}\overline{M}$), i.e., Geometry 1 and 2, respectively.

Figure 4

(a) Calculated dependence of the in-plane component of a total SR-induced magnetization vs the asymmetry in the hole generation with opposite spins (A) for different temperatures between 1 and 300 K. (b) Modification of the DC state dispersions obtained by the plane crossing along $k_x$ (at $k_y=0)$ which indicate the influence of the out-of-plane and in-plane components of induced magnetization, i.e., opening the gap at the DP and the $k_x$ shift of the DC states, respectively. The solid lines represent the modified upper DC state dispersion, while the dotted ones show the $k_{\left|\right|}$ shift of the DC without the gap opening. (c),(d) Calculated temperature dependences of the energy gap at the DP due to the out-of-plane component of the induced magnetization for magnetically doped and pristine TIs and corresponding $k_{\parallel }$ shift of the DP relative to $k_{\parallel }=0$ in the direction orthogonal to the magnetization as a function of temperature.

Figure 5

(a) ($k_x,k_y$) projections of the DC state maps cut at the energy near the Fermi level measured at 55 K for ${\mathrm{Bi}}_{1.37}{\mathrm{V}}_{0.03}{\mathrm{Sb}}_{0.6}{\mathrm{Te}}_2\mathrm{Se}$ with opposite circular polarization of SR showing an opposite TSS intensity asymmetry. (b) The ($k_x,k_y$) shift of the DP position generated by the SR-induced in-plane magnetization using linearly $p$-polarized SR (marked by green crosses in all insets) and circularly polarized SR of opposite chirality (marked by blue crosses). The position $k_{\parallel }=0$ corresponds to the position of maximum of intensity of the MDC profile measured using linearly polarized SR. (c) Comparison between the $k_{\parallel }$ position of the intensity maximum in the MDC profiles measured at the DC states near the Fermi level and at the DP using different polarization of SR.

Figure 6

Experimentally observed MDC profiles of the DC states and their $k_{\parallel }$ shift measured under photoexcitation by circularly polarized SR of opposite chirality at the DP (bottom; insets show the ARPES maps) and at different cutting energies (middle and top) relative to the Fermi level above the DP for ${\mathrm{Bi}}_{1.37}{\mathrm{V}}_{0.03}{\mathrm{Sb}}_{0.6}{\mathrm{Te}}_2\mathrm{Se}$.

Figure 7

(a) Experimental ARPES dispersion maps for ${\mathrm{Bi}}_{1.97}{\mathrm{V}}_{0.03}{\mathrm{Te}}_{2.4}{\mathrm{Se}}_{0.6}$ measured at temperature 17 K in the $\overline{\mathrm{\Gamma }M}$ direction at photon energies of 20 and 28 eV. The reversing of the asymmetry in the intensity of the DC states with opposite momentum at these photon energies is observed. Below each ARPES dispersion map the corresponding MDC profile of intensity of DC and bottom CB states measured at the cutting energies marked by the horizontal blue and red lines are presented. The cutting energies were chosen for showing the CB states close to the CB edge (blue lines) and well-defined intensity asymmetry for the DC states (red line). (b) Schematic presentation of the $k_{\parallel }$ shift of the DC states relative to the non-spin-polarized CB states at different orientation of in-plane magnetic fields ($M_y$).

Figure 8

(a) Experimental ARPES dispersion map for ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ measured at temperature 17 K in the $\overline{\mathrm{\Gamma }K}$ direction at photon energy of 19 eV showing the $k_{\parallel }$ shift of the DC states relative to the bottom CB states connected with the asymmetry in the intensity of the DC states with opposite momentum. Here, approximations of the DC and CB states' positions obtained as a result of fitting procedure are shown by black and red lines, respectively, in comparison with MDC profiles in the region of the CB states. (b) Statistically estimated $k_{\parallel }$-shift variation measured along the DC branches at different cutting energies (with simultaneous fitting of both DC peaks in the MDC profiles). (c) Fitting of the MDC profiles for the CB states cut at different energies relative to the Fermi level with decomposition into spectral components. Here, the profiles of the DC states and their $k_{\parallel }$ positions are presented, for comparison.

Figure 9

(a) Calculated photon-energy dependence of the $k_{\parallel }$-distribution $S(k_{\parallel },h\nu )$ of the net out-of-plane spin in photoelectrons excited by a $p$-polarized SR along the SR incidence plane ($\overline{\mathrm{\Gamma }K}$) from the upper DC of ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ for $h\nu$ from 5 to 31 eV. (b) Photon energy dependence of the net out-of-plane spin integrated over $k_{\parallel }$ from $-0.12$ to $0.12{\AA }^{-1}$ along $\overline{\mathrm{\Gamma }K}$ .

Figure 10

(a) ARPES intensity maps measured for V-doped TIs with stoichiometry ${\mathrm{Bi}}_{1.09}{\mathrm{V}}_{0.06}{\mathrm{Sb}}_{0.85}{\mathrm{Te}}_3$ under photoexcitation by SR with different polarizations at temperature of 55 K. The corresponding dispersions in the $d^{2}N/d{E}^2$ form are shown in the middle line (b) for better visualization of the DC states splitting at the DP. Line (c): corresponding EDCs measured at the DP ($k_{\parallel }=0$) and the result of the fitting procedure with decomposition into spectral components. (d) The $k_x,k_y$ mapping at the DP ($E=0.043$ eV) and (e) the $k_{\parallel }$ shift of the DC states at the DP developed under photoexcitation by SR of opposite chirality.

Figure 11

METHODS section. Schematic presentation of the ARPES measurement geometries with the analyzer slit oriented along (Geometry 1) and perpendicular to (Geometry 2) the SR incidence plane.