Chemical and valence reconstruction at the surface of ${\mathrm{SmB}}_6$ revealed by means of resonant soft x-ray reflectometry

Samarium hexaboride $\left({\mathrm{SmB}}_6\right)$, a Kondo insulator with mixed valence, has recently attracted much attention as a possible host for correlated topological surface states. Here, we use a combination of x-ray absorption and reflectometry techniques, backed up with a theoretical model for the resonant $M_{4,5}$ absorption edge of Sm and photoemission data, to establish laterally averaged chemical and valence depth profiles at the surface of ${\mathrm{SmB}}_6$. We show that upon cleaving, the highly polar (001) surface of ${\mathrm{SmB}}_6$ undergoes substantial chemical and valence reconstruction, resulting in boron termination and a ${\mathrm{Sm}}^{3+}$ dominated subsurface region. Whereas at room temperature, the reconstruction occurs on a timescale of less than 2 h, it takes about 24 h below 50 K. The boron termination is eventually established, irrespective of the initial termination. Our findings reconcile earlier depth resolved photoemission and scanning tunneling spectroscopy studies performed at different temperatures and are important for better control of surface states in this system.

Figure 1

(a) Experimental geometry. (b) Optical microscopy of the cleaved sample surface. The sample cross section is $1\times 1{\mathrm{mm}}^2$.

Figure 2

(a), (b) TEY (absorption) and reflectivity spectra over the nitrogen $K$ edge and oxygen $K$ edge and samarium $M_{4,5}$ edges. Sm spectra show sharp resonances due to $3d\to 4f$ excitations [54]. (c), (d) Stability of the spectra in TEY and reflectivity modes. The four curves overlap nearly perfectly so that they can hardly be distinguished when overlayed.

Figure 3

SVD decomposition of the TEY data. (a), (b) TEY spectra after subtraction of Shirley-type background [55] and normalization of the peak intensity to one. The false-color plots duplicate the data presented in the line plots and elucidate the trends in the $\theta$-energy parameter space in a more convenient way. Panels (c)–(h) show residuals for one-, two-, and five-component representations. (i) Normalized singular values in decreasing order. (j), (k) The first five most significant components.

Figure 4

(a), (b) CFT calculations for ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$. The spiky spectrum shows the transition energies and their probabilities, as they result from CFT calculation, whereas the continuous curves shows the lifetime-broadened spectra. The corresponding energy-dependent lifetime $\mathrm{\Gamma }\left(E\right)$ is plotted against the right axis. (c) Fit (green line) to the experimental TEY signal (black dots) with the weighted sum of the two Sm components and the smooth background due to the continuum excitations modeled as slope with broadened edges. Only $M_5$ edge is within the plotted region.

Figure 5

Fits to reflectivity data, measured as off-resonant momentum scans (upper row) or on-resonance (lower two rows) energy scans. The red curves correspond to the calculated reflectivity $R^{\text{mod}}(q_z,E)$, while the black symbols show the experimentally measured intensity $R^{\text{expt}}(q_z,E)$. Here, we show representative spectra out of those used in the actual fit so that all energies and momentum transfers are uniformly covered.

Figure 6

(a) Chemical and valence profiles $c_i\left(z\right)$, resulting from reflectivity fits presented in Fig. 5. “$\mathrm{Sm}2+\&\mathrm{Sm}3+$” is the sum of ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$ components, i.e., the total Sm content regardless of the valency. (b), (c) The atomic scattering factors necessary for calculation of the refractive index $n(z,E)$. The factors were taken from Chantler [101], except for the Sm on-resonance region, which derives from the previous Sec. 5 and was further optimized to reflectivity data.

Figure 7

(a) Variation of the photoemission intensity over the cleaved surface, measured at the binding energy of the Sm $4f$ surface peak $(E_{\text{Bind}}\sim 0.5$ eV). Based on this intensity map, one can define regions with initially high (spot 1, black square) and low (spot 2, white square) Sm surface signal. (b) Time evolution of the Sm $4f$ surface peak averaged over the spot 1 and spot 2. The plotted energy range covers the ${}^6\mathrm{F}$ and ${}^6\mathrm{H}{\mathrm{Sm}}^{2+}$ final-state multiplets, while the ${\mathrm{Sm}}^{3+}$ multiplets are found at higher binding energies [31, 114]. (c) Intensity map at the B $1s$ surface peak $(E_{\text{Bind}}\sim 187.3$ eV). (d) Corresponding time evolution for the regions with initially low B $1s$ surface contribution (spot 3) and high contribution (spot 4). The energy position of the respective surface peaks is denoted by the vertical arrows. As time passes on, the inhomogeneity vanishes, both in terms of Sm $4f$ and B $1s$ surface contributions.

Figure 8

Schematic representation of a cleaved surface of ${\mathrm{SmB}}_6$ and the resulting laterally averaged chemical profiles of the aged sample, a state attained upon loss of surface Sm atoms (shown as open circles). (a) The simplest case. (b) An elaboration of the schematic model via inclusion of surface steppiness or roughness. (c) Further elaboration of the qualitative model with separate representation of ${\mathrm{Sm}}^{2+}/{\mathrm{Sm}}^{3+}$ ions and a deeper loss of Sm ions.