Irreversible proliferation of magnetic moments at cleaved surfaces of the topological Kondo insulator SmB6

TL;DR

This study reveals that the magnetic moments on the surface of the topological Kondo insulator SmB6 irreversibly increase over time after cleaving, indicating persistent surface magnetic evolution linked to its topological properties.

Contribution

It provides the first evidence of irreversible surface magnetic moment growth in SmB6 using XAS and RIXS, highlighting surface magnetic dynamics in topological Kondo insulators.

Findings

Surface magnetic moments grow irreversibly over time.

Surface-sensitive spectra show increased large-moment atomic states.

Surface magnetic evolution exceeds changes in 4f orbital occupation.

Abstract

The compound SmB$_6$ is the best established realization of a topological Kondo insulator, in which a topological insulator state is obtained through Kondo coherence. Recent studies have found evidence that the surface of SmB$_6$ hosts ferromagnetic domains, creating an intrinsic platform for unidirectional ballistic transport at the domain boundaries. Here, surface-sensitive X-ray absorption (XAS) and bulk-sensitive resonant inelastic X-ray scattering (RIXS) spectra are measured at the Sm N$_{4,5}$-edge, and used to evaluate electronic symmetries, excitations and temperature dependence near the surface of cleaved samples. The XAS data show that the density of large-moment atomic multiplet states on a cleaved surface grows irreversibly over time, to a degree that likely exceeds a related change that has recently been observed in the surface 4f orbital occupation.

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The topological Kondo insulator (TKI) state is a variant of the topological insulator state pred1 ; ColemanReview ; FuOriginal ; ZahidMooreReview , in which a topologically ordered insulating electronic band structure is obtained from Kondo physics. The realization of a TKI state in mixed-valent SmB6 was strongly indicated by early theoretical investigations pred1 ; pred2 , and has now been established through direct measurement of the topological surface states via angle resolved photoemission MadhabARPES ; FengARPES ; ShiSpinTexture ; Kondo110K ; ReinertChargeFluctuations ; JonathanSmB6PEreview and transport studies TKItransport ; TKIsurfaceFM . Strong evidence has recently been found suggesting that the surface of polished SmB6 samples can also host ferromagnetic domains TKIsurfaceFM , a property that is theoretically associated with exotic axion electrodynamics, an inverse spin-galvanic effect, and ballistic one dimensional transport channels at domain boundaries magTI1 ; MagTI2 ; MagTI3 ; ZahidMooreReview . Moreover, surface sensitive X-ray photoemission (XPS) measurements have shown that the surface 4f occupation evolves irreversibly towards 4f5 as a function of time following cleavage in ultra high vacuum (UHV) surfaceValencePhMag . Here, multiplet-dominated X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) measurements in the vacuum ultraviolet (VUV) regime are used as a symmetry-sensitive probe to map the Sm N4,5-edge excitations and show that a similarly large change in the density of large-moment samarium sites accompanies this time evolution. This evolution is consistent with expectations for the transition from a Kondo insulating state to magnetism, and represents a means for incrementally tuning the strength of the surface magnetic instability.

Measurements were performed at the beamline 4.0.3 (MERLIN) RIXS endstation (MERIXS) YiDeDetector ; YiDeSRN at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory. Large single crystals of SmB6 were grown by the Al flux method as in Ref. surfaceValencePhMag , cleaved at low temperature, and maintained at a UHV pressure of approximately 3$\times$10*-10* Torr. The photon beam had a grazing 30o or angle of incidence to the cleaved [001] sample face, and scattered photons were measured at 90o to the incident beam trajectory. XAS was measured using the total electron yield (TEY) method, and the expected penetration depth of measurements is roughly d$\lesssim$2 nm for XAS universalCurve and d$\sim$10-30 nm for RIXS XrayPath . To minimize sensitivity to surface inhomogeneity, the beam profile on the sample was configured as a very broad strip with dimensions of roughly $10\times 600\mu m^{2}$ (similar results from additional cleaves are shown in the online Supplimental Material (SM) SM ).

Atomic multipet simulations were performed with typical renormalization values for the multipolar Slater-Condon interaction parameters SM . Similar multiplet models that focus on Sm f-electrons, disregarding the itinerant 5d electron gas, have been remarkably successful in reproducing XAS and XPS features of SmB6 multipletSmB6_PES2015 ; JonathanSmB6PEreview . The multiplet ground states have f-electron angular momentum quantum numbers of (4f5) J=5/2 and (4f6) J=0, representing the presence or absence of a hole in the J=5/2 4f bands. The atomic multiplet picture is expected to be most accurate as a description of the resonance states, which are dominated by extremely strong angular momentum coupling between the 4d core hole and 5d electrons on the scattering site (a $\sim$20eV combined energy scale). Multiplet state energetics in the VUV are defined in terms of coherent local moment symmetries. In contrast to the previous study of 4f charge density at the SmB6 surface surfaceValencePhMag , atomic multiplet measurements in the VUV are sensitive to the coherent multi-particle symmetry of electrons in hybridized electronic orbits involving both the scattering site and neighboring atoms WrayFrontiers ; EdwinProc . This multiplet symmetry can be thought of as the ‘nominal valence’ state defining local moment degrees of freedom, and can deviate significantly from the atomically resolved charge density.

The samarium N4,5-edge XAS spectrum of a pristine SmB6 surface that has been recently cleaved and maintained at T$<$100K within UHV is shown in Fig. 1(a) (blue curve). To facilitate comparison of features, the non-resonant background has been aligned beneath the resonance at $h\nu$=123 eV, and the curves have been set to have the same integrated area. The spectrum contains a large number of features, and the higher energy features have broader line shapes, as is the typical trend for core hole lifetimes at a multiplet-split resonance HaverkortAutoIon ; KotaniIdea ; KotaniIdea2 ; WrayNiO ; WrayFrontiers ; WrayRIXSinterference ; EdwinProc . Relatively sharp line shapes are observed in the incident energy range from 126-133, suggesting that there may be a charge transfer threshold at h\nu$$\sim133 eV HaverkortAutoIon ; EdwinProc .

The spectrum changes pronouncedly as the sample is aged. Difference spectra in Fig. 1(b) show that as time progresses, spectral intensity shifts into higher energy features at $h\nu>136$ eV, and the sharper 126-133 eV features shift into a new spectral pattern that bears little resemblance to that seen initially. Even though the time interval between each pair of successive curves is approximately the same (45 to 60 min), the magnitude of the change is significantly larger for the interval from 4.5 to 5.5 hr, in which the sample was heated to room temperature. Cycling back to low temperature (black curve) resulted in only small quantitative changes. Later scans did not reveal continued changes, however the aging trend can be taken further still by exposing the sample surface to air (see red curve), suggesting that aging the surface is promoting changes in the f-electron count that resemble oxidation. The fractional change in feature intensities after thermal cycling is dramatic, and ranges from 10-50$\%$ throughout most of the spectrum.

To identify the physical significance of the surface evolution, a multiplet simulation in Fig. 1(c) shows the features expected in Sm N4,5-edge XAS from J=0 and J=5/2 sites. Dashed drop-lines highlight an excellent qualitative match between the regions that lose intensity during the aging process and the J=0 features, while the J=5/2 features correlate with a gain (or reduced loss) of intensity. Only one feature is clearly anomalous in this analysis. The lowest energy XAS peak at h\nu$$=126.6 eV is not reproduced by either the J=0 or the J=5/2 multiplet calculation, and has temperature dependence consistent with a J=5/2 symmetry attribution.

Similar XAS measurements have also been performed as a function of time on an electron doped sample with the composition Sm0.98La0.02B6 (see Fig. 2). In this case, the sample was maintained at T$<$100K for a much longer 46 hr period, and the measurements confirm earlier observations that the aging process at low temperature proceeds on a time scale longer than 1 day surfaceValencePhMag . Heating to T=250K produced small changes that were fully reversed upon cycling back to T$<$100K. This is in contrast to the more rapid measurement on undoped SmB6, and suggests that the physical end-point of low temperature aging is the same as the rapidly achieved end-point of room temperature aging.

Lanthanum is expected to act as a net electron donor, entering an ionization state much closer to 3+ as compared to Sm. Doping into the Sm 4f orbitals of roughly 0.3e-/La atom is attributed from susceptibility studies tempAndValence . The initial Sm0.98La0.02B6 XAS spectrum is nearly identical to the slightly aged t=4.5 hr spectrum of undoped SmB6, and the final aged (cycled) curve is qualitatively identical to XAS from the fully aged undoped SmB6 sample. The fact that J=5/2 features in the base (t$\sim 3$ hr) spectrum of Sm0.98La0.02B6 are more prominent than in the low temperature spectrum of SmB6 is at odds with the identification of La as an electron donor, and suggests some variability in the nature of the cleaved surface (this is confirmed in Fig. S3 of the SM SM ).

Measuring resonant inelastic scattering at the photon energies used for XAS reveals a wide range of excitations, some of which are quite sharp in energy, as seen in Fig. 3(a). Prominent features at E=0.9, 2.5, 3.7 and 5.2 eV appear to be Raman-like (non-dispersive), however the upper bound of intensity on the energy loss axis disperses with a slope similar to 1 as a function of incident energy, starting from $\sim$3 eV at an incident energy of h$\nu$=126.6 eV, as expected for scattering scenarios that involve interplay with degrees of freedom that have similar energetics with or without a core hole present. This suggests that a truly accurate model of the RIXS excitations must incorporate significant non-local physics, going beyond the degrees of freedom on a single scattering site. The RIXS spectrum and optical conductivity allenOptical1977 ; RussianOC ; newOC both picks up intensity from roughly 1.5eV, suggesting the onset of a large density of itinerant continuum states, however the optical data contain no candidates for any of the energetically sharp features seen by RIXS.

In spite of not fulfilling this requirement, the atomic multiplet model is still expected to be accurate for certain relatively localized excitations, and to yield accurate matrix elements of the ‘direct RIXS’ scattering process AmentRIXSReview ; WrayRIXSinterference . One can attribute a tentative correspondence between energy loss regions with large intensity in the J=5/2 simulation and the intensity seen by RIXS (see highlighted regions in Fig. 3(a-b)). The feature at E$\sim$0.9 eV gives a particularly close correspondence, and has no competing interpretation within the J=0 simulation (Fig. 3(c)). This E$\sim$0.9 eV mode is actually a collection of closely spaced features, with additional peaks visible in the $h\nu=$127.8 and 130.8 eV curves. Lower energy excitations visible in the simulations are not resolved from the elastic line, which is strong due to the broad off-angle tail of specular reflection in the VUV WrayFrontiers . The lack of easily identifiable J=0 derived features may indicate that single-atom excitations on 4f6 sites are shorter lived (i.e. broader), possibly because they can easily delocalize into 4f5X states, where ‘X’ indicates an electron that has entered a more delocalized band symmetry. The anomalous $h\nu=126.6$ eV resonance, which does not occur in our multiplet simulations, resonates primarily with the 0.9 eV feature, corroborating identification of the $h\nu=126.6$ eV resonance with scattering from a J=5/2 site.

A sufficiently large increase in the density of J=5/2 sites in the mixed-valent samarium lattice is expected to destabilize the Kondo insulating state and induce magnetism, as has been seen in high pressure studies pressureNf ; pressure2 ; pressureNickButch . The amplitude of the surface change can be evaluated from the XAS data in Fig. 1, if we adopt the approximation that the spectra can be broken down into linear combinations of pure J=5/2 and J=0 curves (see derivations in the SM SM ). The accuracy of this approximation is supported in the present case by the observation of a fairly stable isospectral (constant intensity) point at 136.7-137eV for all warming curves.

Monovalent J=5/2 and J=0 XAS spectra algebraically obtained from comparing SmB6 XAS measurements at the pristine (t=3 hr) and aged (cycled) surface are plotted in Fig. 4(b). Shaded regions represent error margins as described in the caption, and are associated with different extrapolated changes in the population of J=5/2 and J=0 sites over the aging period. The outer shaded boundaries represent extreme scenarios that lead to clear anomalies in the extrapolated monovalent curves, such as duplicated features and negative XAS intensity SM . The best fit J=0 XAS curve is obtained with the assumption that the J=5/2 population grows by a remarkable 60-80$\%$. Growth estimates beneath 40$\%$ lead to multiple significant artifacts in the extrapolated XAS spectrum. Based on the extrapolated XAS curves, we can assess that a single-atom multiplet calculation provides many matrix elements of the N4,5-edge resonance process, but is of marginal use for understanding the RIXS excitations, and omits XAS features that appear to be associated with coupling to itinerant states.

High pressure studies have found that a new magnetic ground state pressureNf ; pressure2 ; pressureNickButch is realized in bulk SmB6 beyond a crossover point thought to occur when the fractional density of 4f5 sites reaches roughly $n_{5/2}\sim 0.65$ pressureNf ; pressureNickButch . Combined examination of the extrapolated J=5/2 and J=0 curves enables an algebraic derivation of the t=3 hr J=5/2 site density as $n_{5/2}$=0.39$\pm$0.05 SM , with a surface evolution plotted in Fig. 4(a). In distinguishing $n_{5/2}$ from the nominal bulk 4f occupancy, which is thought to be $n_{f}\lesssim 5.5$ pressureNf ; pressureNickButch ; JonathanSmB6PEreview ; XASvalenceTdep ; JonathanARPES_DMFT , this picture suggests that the transition is one from a singlet-dominated low temperature regime, with fewer observed large-moment sites than the 4f occupancy alone would suggest, to an aged surface in which local moments are less screened. This scenario matches the attributed behavior as the crystal is driven into a magnetic state under pressure pressureNf ; pressureNickButch . We note that the nature of the magnetic order achieved under pressure is not definitively understood, however a proximate ferromagnetic state can be achieved from 1$\%$ Fe doping at ambient pressure Fe1pctMag . The air-exposed end point of $n_{5/2}\sim 0.9$ is consistent with the proposed interpretation of an earlier soft X-ray M-edge XAS measurement CdopingAndXAS .

A comprehensive interpretation of the mechanism behind the observed irreversible surface changes is beyond the scope of the present study. Such a theory may need to address multiple factors including the correlated electronic structure, the intrinsically polar and anisotropic nature of cleaved surfaces, and the presence of multiple known surface reconstructions JonathanSmB6PEreview ; STM1 ; flashed . The bulk of the sample also evolves towards a lower 4f occupancy with increasing temperature pressureNf ; JonathanSmB6PEreview ; XASvalenceTdep ; JonathanARPES_DMFT ; Kondo110K . However, the bulk-sensitive RIXS spectrum undergoes no easily visible changes as a function of temperature SM , suggesting that surface aging is a far more dramatic effect. The La doped sample is thought to have roughly identical bulk temperature dependence tempAndValence .

These resonant X-ray absorption results show that the density of large-moment Sm sites in the top $\lesssim$2 nm of cleaved SmB6 more than doubles as the surface ages in UHV. The increase can be accelerated by heating to room temperature, and is taken further through exposure to air. Lower energy excitations of SmB6 are mapped with RIXS, providing a window into dynamics and energetics of the valence electrons, which will serve as a reference for future theoretical and spectroscopic investigations. The large surface changes seen by electron yield XAS are distinct from the lack of extraordinary temperature dependence at depths of 10-30 nm, as evaluated from RIXS spectra. The increased density of large-moment sites on aged samples provides a plausible explanation for the recent observation of ferromagnetic domains at a polished SmB6 surface TKIsurfaceFM . More generally, the apparent sensitivity of the surface evolution to temperature and the gas environment provides mechanisms for control of the surface properties, to achieve a desired interplay between surface magnetic moments and the topologically ordered bulk electronic structure.

Acknowledgements: The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. C.H.M. was supported by the DFG (through SFB 1170 “ToCoTronics”, projects C06). We are grateful for productive discussions with H. Dehghani and J. Hoffman.