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Article

Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB6

by
Monica Ciomaga Hatnean
*,
Talha Ahmad
,
Marc Walker
,
Martin R. Lees
and
Geetha Balakrishnan
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
*
Author to whom correspondence should be addressed.
Crystals 2020, 10(9), 827; https://doi.org/10.3390/cryst10090827
Submission received: 19 August 2020 / Revised: 11 September 2020 / Accepted: 14 September 2020 / Published: 17 September 2020
(This article belongs to the Special Issue Advances in Topological Materials)
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Abstract

:
SmB 6 is a mixed valence topological Kondo insulator. To investigate the effect of substituting Sm with magnetic Ce ions on the physical properties of samarium hexaboride, Ce-substituted SmB 6 crystals were grown by the floating zone method for the first time as large, good quality single crystal boules. The crystal growth conditions are reported. Structural, magnetic and transport properties of single crystals of Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) were investigated using X-ray diffraction techniques, electrical resistivity and magnetisation measurements. Phase composition analysis of the powder X-ray diffraction data collected on the as-grown boules revealed that the main phase was that of the parent compound, SmB 6 . Substitution of Sm ions with magnetic Ce ions does not lead to long-range magnetic ordering in the Sm 1 − x Ce x B 6 crystals. The substitution with 5% Ce and above suppresses the cross-over from bulk conductivity at high temperatures to surface-only conductivity at low temperatures.

1. Introduction

Extensive investigations of the physical properties and excitations in the rare earth (RE) hexaboride compounds, REB 6 , have been carried out over the past decades. These strongly correlated electron systems display an array of interesting magnetic and electrical properties, such as superconductivity (YB 6 [1,2,3]), intricate antiferromagnetic ordered phases owing to the displacement of rare earth ions within the rigid framework formed by the boron ions (GdB 6 [4,5,6]), complex antiferromagnetic phases with Kondo-like characteristics (CeB 6 [7,8,9,10]), semimetallic behaviour correlated with the transition to an unusual ferromagnetic state (EuB 6 [11,12,13]), typical metallic behaviour (LaB 6 [14,15,16]) or an exotic Kondo-like topological insulating state (SmB 6 [17,18,19]). Amongst the rare earth hexaboride compounds, cerium and samarium hexaborides have puzzled experimentalists and theoreticians alike, for a long time, in view of their intriguing physical properties. SmB 6 and CeB 6 are isostructural, crystallising in the same cubic CsCl-type structure ( P m 3 ¯ m space group) [20,21,22]. Sm and Ce ions replace the Cs ion, whilst the B 6 cubo-octohedral clusters take the place of the Cl ions at the corners of the cube. Nevertheless, the similarities between samarium and cerium hexaborides stop at the structural level, as they display very unusual, but different physical properties.
SmB 6 has long been known to be a Kondo insulator [23,24]; in recent times, new theoretical and experimental studies demonstrated that samarium hexaboride is a topological Kondo insulator (TKI) exhibiting topological surface properties [18,25,26,27,28,29,30,31], although this remains open to further investigation [32]. SmB 6 is one of the most investigated Kondo insulators, mainly due to its exciting low temperature transport behaviour. As the temperatures decreases, an energy gap arises due to the interaction of the strongly correlated f-electrons and the conducting d-electrons, leading to an exponential increase in the electrical resistance of SmB 6 [33,34,35]. Unexpectedly, upon further cooling, the resistance of SmB 6 does not continue rising, as would be the case for a conventional insulator, but instead the resistance saturates at a finite value, below 5 K. This plateau in the resistivity has been attributed to a transition from a bulk conductivity characteristic of the high temperature region to a surface-dominated conductivity with bulk insulation at low temperature [36]. SmB 6 is a mixed valence system that does not order magnetically, despite exhibiting antiferromagnetic correlations [33,37,38,39,40]. The Sm 3 + :Sm 2 + ratio was determined to be independent of the temperature, and equal to approximately 0.6∼0.7:0.4∼0.3 [37,41]. Nevertheless, recent studies have shown that, upon the application of an external pressure, the Sm 3 + configuration can be stabilised for sufficient time to allow long-range magnetic ordering of the samarium ions [42,43].
CeB 6 is known to have a typical dense Kondo compound behaviour and a complex magnetic phase diagram [44,45,46,47]. Cerium hexaboride exhibits Kondo-like behaviour and has a Kondo temperature of T K = 19 K. Upon cooling, CeB 6 undergoes two magnetic ordering transitions: the first to a state in which antiferroquadrupolar and field-induced octupolar order coexist, below T Q = 3.2 K, and then to an antiferromagnetic ordering of the Ce dipoles, below T N = 2.3 K. Moreover, a subsequent study reported a new transition, of unknown origin, at T 2 = 1.6 K [45].
Recent progress, e.g., the discovery of the coexistence of an unusual metallic surface state and an insulating bulk state in SmB 6 [19,48] and the observation of the long-range-ordered multipolar phases in CeB 6 [47], has generated new interest in these materials. One route towards the investigation of the exotic metallic surface state arising in SmB 6 and understanding of its topological nature, is through chemical substitution in this TKI with other rare earth ions. Recently, studies have been carried out on Eu, Gd, La, Y and Yb-substituted SmB 6 [18,21,49,50,51,52,53,54]. High levels of substitution of non-magnetic ions (above 30%), and substitutions with small amounts of magnetic ions, were found to destroy the saturation seen in the low temperature resistivity of pure SmB 6 . It would therefore be interesting to investigate the effect that the substitution with a magnetic rare earth, such as Ce, in samarium hexaboride has on the robustness of the topological surface state of this TKI. Such an investigation is of course best carried out on high quality single crystals. In the present work, we investigated single crystals of Sm 1 − x Ce x B 6 , with a focus on studying the effects that the substitution of the magnetic Ce ion have on the structural and physical properties of SmB 6 . The physical properties of Ce-substituted SmB 6 samples have previously been investigated; however, this has only been done on polycrystalline samples and flux grown crystals [21,49,54]. Crystals of pure cerium and samarium hexaboride have previously been grown using the floating zone (FZ) technique [55,56,57]; however, Ce-substituted SmB 6 compounds have only been grown in crystal form using the flux method [54]. SmB 6 crystals grown using Al flux could suffer from contamination by the flux affecting some of the physical properties of the crystals, thereby making it difficult to study the intrinsic properties of pure samarium hexaboride [58]. We have successfully grown, for the first time, crystal boules of Sm 1 − x Ce x B 6 by the FZ method, which yields large, good quality crystals, free from flux or crucible contamination. The crystals obtained are especially suitable for the investigation of how the substitution with magnetic ions affects the surface and bulk behaviour of this interesting TKI.

2. Materials and Methods

Crystal boules of Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) were grown by the floating zone technique [57] using a CSI FZ-T-12000-X_VI-VP four-mirror xenon arc lamp (3 kW) optical image furnace (Crystal Systems Incorporated, Yamanashi, Japan). The crystal quality was checked using a backscattering X-ray Photonic-Science Laue camera system (Photonic-Science, St Leonards-on-Sea, UK). Single crystal samples were aligned for selected experiments, and rectangular prism-shaped samples with [001], [1-10] and [110] directions perpendicular to the faces of the prism were cut from the Sm 1 − x Ce x B 6 crystal boules.
Phase composition analysis was carried out using a Panalytical X-Pert Pro MPD diffractometer (Malvern Panalytical Ltd, Malvern, UK) with Cu K α 1 radiation ( λ K α 1 = 1.5406 Å). The diffraction patterns were collected at room temperature over an angular range of 10 to 110 ∘ in 2 θ with a step size in the scattering angle 2 θ of 0.013 ∘ and at various scanning times. The analysis of the X-ray patterns was performed using the Fullprof software suite [59].
Chemical composition of the crystal boules was investigated by energy dispersive X-ray spectroscopy (EDX) using a Zeiss SUPRA 55-VP scanning electron microscope (Carl Zeiss GmbH, Jena, Germany). LaB 6 was used as a standard for the EDX measurements. X-ray photoelectron spectroscopy (XPS) analysis was also carried out in order to determine the elemental composition and the valence of the Sm ions. The samples were attached to electrically-conductive carbon tape, mounted on to a sample bar and loaded into a Kratos Axis Ultra DLD (Kratos Analytical Ltd, Manchester, UK) spectrometer (base vacuum of ∼2 × 10 − 10 mbar). The measurements were performed using a monochromated Al K α X-ray source, at room temperature and at a take-off angle of 90 ∘ with respect to the surface parallel. The data were analysed in the CasaXPS package (Casa Software Ltd, Teignmouth, UK), using Shirley backgrounds and mixed Gaussian-Lorentzian (Voigt) line-shapes and asymmetry parameters, where appropriate.
Magnetic susceptibility measurements were performed with a Quantum Design Magnetic Property Measurement System (Quantum Design Incorporated, San Diego, USA) on rectangular-prism-shaped Sm 1 − x Ce x B 6 samples with an applied field parallel to the [100] (tetragonal), [110] (rhombic) and [111] (trigonal) crystallographic directions. The samples were cooled to 1.8 K in zero field and then the susceptibility as a function of temperature up to 300 K was measured on warming and then cooling with an applied field of H = 500 Oe.
Alternating current ( a c ) resistivity measurements were performed using a Quantum Design Physical Property Measurement System on bar shaped samples of the Sm 1 − x Ce x B 6 single crystals using the standard four-probe technique. Silver wire contacts were attached with silver paint, in a linear configuration, to the surfaces of the samples. The resistivity measurements were made from 2 to 300 K on both cooling and warming in zero applied field with an ac current of 1 mA at a frequency of 113 Hz.

3. Results and Discussion

3.1. Crystal Growth

Stoichiometric ratios of high purity SmB 6 (99.9%, American Elements UK, Manchester, UK) and CeB 6 (99.5%, Cerac Incorporated, Milwaukee, USA) powders were mixed together by ball milling for over 15 h, to prepare 5%, 10% and 20% Ce-substituted SmB 6 polycrystalline samples. The resulting materials were then isostatically pressed into rods (typically 5–7 mm diameter and 40–50 mm long) and sintered in an alumina boat, at 1450 ∘ C in a flow of argon gas for 12 h. Before the sintering process, the furnace was evacuated to give a vacuum of ∼ 10 − 5 mbar. The resulting polycrystalline feed rods were used for the crystal growth. A binder (polyvinyl alcohol or polyvinyl butyral) was mixed with the powders in some cases to facilitate the formation of the rods.
Crystals of Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) were successfully grown by the floating zone method. The growths were carried out in an argon atmosphere at a pressure of ∼3 bar, using a growth rate of 18 mm/h. The feed and the seed rods were counter-rotated at ∼15–25 rpm. Initially, a crystal boule of SmB 6 was used as a seed. Once good quality crystals were obtained, Sm 1 − x Ce x B 6 crystal seeds were used for subsequent growths. A dark grey coloured deposition on the quartz tube surrounding the feed and seed rods was observed for all the growths, indicating the evaporation of boron during the growth process.
The Sm 1 − x Ce x B 6 boules were typically 4–5 mm in diameter and measured approximately 45–50 mm in length. All the crystals obtained developed facets as they grew and two very strong facets were present on almost the entire lengths of most of the grown crystals. Figure 1a–c show photographs of Sm 1 − x Ce x B 6 crystals grown in argon atmosphere at a growth speed of 18 mm/h. The quality of the grown boules was investigated by X-ray Laue diffraction, and Laue photographs were taken along the length of the boule, on the faceted sides (see Figure 1). The Laue patterns were identical along the whole length of the crystal boules.

3.2. Structural and Composition Analysis

Structural and phase purity analysis was carried out using powder X-ray diffraction measurements on small pieces of the Sm 1 − x Ce x B 6 crystals selected from close to the end of each crystal boule. Figure 2a–c show the patterns for x = 0.05 , 0.10 and 0.20, and profile matching (goodness of fit, GOF = 1.35, 1.51 and 1.92, respectively) to the cubic P m 3 ¯ m space group [20] indicates that in each case the main phase is Sm 1 − x Ce x B 6 , with no significant impurity phases present. One peak that does not belong to the P m 3 ¯ m cubic structure can be observed at ∼26.6 ∘ in the powder X-ray profiles of each of the Sm 1 − x Ce x B 6 crystals grown. The impurity was identified to be a hexagonal ( P 6 3 / m m c ) SmBO 3 phase [60]. Lattice parameters calculated from the profile matching were determined to be 4.1351(2) Å, 4.1384(2) Å and 4.1393(2) Å, respectively, for Sm 0.95 Ce 0.05 B 6 , Sm 0.90 Ce 0.10 B 6 and Sm 0.80 Ce 0.20 B 6 (see Table 1). The values are in agreement with those reported in previous studies on Sm 1 − x Ce x B 6 polycrystalline samples [21].
Figure 2d shows the dependence of the lattice constant on the concentration of Ce for the Sm 1 − x Ce x B 6 samples. The composition dependence of the cubic parameter, a, does not obey Vegard’s law [61], for the Sm 1 − x Ce x B 6 series. The anomalously large positive deviation observed in Figure 2d can be attributed to the mixed valence of samarium ions [37,38,62]. As the concentration of the Ce-substituent changes from x = 0 to 1, the Ce 3 + ions replace the Sm 3 + ions preferentially, whereas the concentration of Sm 2 + ions remains constant [21,38,50]. The effective ionic radius [63,64] of Ce 3 + (1.01 Å) is larger than the ionic radius of Sm 3 + (0.958 Å); thus, the substitution of samarium with cerium ions results initially in a lattice expansion (up to x ∼ 0.6 ). Further substitution of samarium with cerium is followed by a subtle lattice contraction, which is attributed to the replacement of the larger Sm 2 + ions (1.15 Å) with Ce 3 + . A similar effect on the lattice constant has been observed in the case of Gd and La-substituted SmB 6 [38,50,65].
Composition analysis of the crystals of Sm 1 − x Ce x B 6 was carried out by EDX to determine the concentrations of Ce in each crystal. The results, given in Table 2, show that the ratios for Sm:Ce are similar to the expected chemical compositions for the crystals, relative to the starting compositions of the polycrystalline materials (5%, 10% and 20% Ce-substituted SmB 6 samples).
Core level XPS spectra were recorded using a pass energy of 20 eV (resolution ∼0.4 eV) on an area of 300 μ m × 700 μ m of the Sm 1 − x Ce x B 6 crystals and used to study the electronic states of Sm 4d, Ce 3 d 3 / 2 and Ce 3 d 5 / 2 levels, shown in Figure 3. The Sm 4d XPS spectrum (see Figure 3a) is composed of one singlet, at 123.5 eV, and one multiplet, at 134.1 eV, separated by approximately 10.6 eV. The Sm 2 + (4 f 6 ground-state) feature appears near 129 eV (Sm 4d photoelectron line position), which is in agreement with previously published XPS studies on pure SmB 6 [66,67]. The Sm 3 + (4 f 5 ) multiplet appears at a higher binding energy, well separated from the 2+ peak. The contributions of the two features to the XPS spectra were used to determine the valence of the Sm ions. The results, given in Table 2, reveal that Sm 1 − x Ce x B 6 are mixed valence systems, similar to the parent compound SmB 6 [37,38]. The average Sm valence values of the Sm 1 − x Ce x B 6 boules are slightly larger than the values determined previously for pure SmB 6 [67,68,69,70], due to surface oxidation effects (an increased concentration of Sm 3 + to the detriment of the Sm 2 + ions). Previous XPS results reported an increased average Sm valence and a B/Sm ratio lower than the nominal stoichiometric value of 6:1 when the SmB 6 crystals were exposed to ambient conditions [67]. To confirm this hypothesis, XPS spectra were collected on two SmB 6 crystal samples, an as-grown and a cleaved crystal fragment. The average samarium valence is ∼2.8 for the as-grown crystal fragment of SmB 6 . In the case of SmB 6 cleaved in-situ from the as-grown crystal, the Sm valence is 2.7, corresponding to a Sm 3 + :Sm 2 + ratio of approximately ∼0.7:∼0.3, which is in agreement with previous results [37,41].
The Ce 3d spectrum, shown in Figure 3b, is comprised of two multiplets, at 885.8 eV and 904.8 eV, corresponding to the spin-orbit split 3 d 5 / 2 and 3 d 3 / 2 core levels. The spin-orbit splitting is approximately 19 eV, with the complex electronic structure of different Ce oxidation states yielding useful spectral features which can be used to distinguish Ce 3 + and Ce 4 + . In our data, each component of the Ce 3d XPS spectrum is dominated by two features. The absence of a third component at 916 eV, characteristic of the Ce 4 + (4 f 0 ) [71,72], indicates that the Ce ion is in the 3+ state in the Sm 1 − x Ce x B 6 samples. The analysis of the XPS results, given in Table 2, allowed us to estimate the amount of Ce-substituent in the Sm 1 − x Ce x B 6 crystal boules. A comparison of the Ce concentrations determined from the XPS spectra and those estimated from the EDX compositional analysis is provided in Table 2.

3.3. Magnetisation

Zero-field-cooled warming (ZFCW) and field-cooled cooling (FCC) magnetisation versus temperature curves were collected on pieces of the Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) single crystals with an applied field of 500 Oe along three different crystallographic directions ([001], [110] and [111]). The temperature dependence of the d c magnetic susceptibility, χ T , is shown in Figure 4a. The magnetic susceptibility measured along the different crystallographic directions for all three Sm 1 − x Ce x B 6 crystals decreased on warming from 1.8 K to room temperature. In addition, for each Sm 1 − x Ce x B 6 composition, the magnetic susceptibilities collected with field applied along the three different high-symmetry directions all overlap to within experimental error across the whole temperature range.
The temperature dependent magnetic susceptibility of the Sm 1 − x Ce x B 6 crystals was compared with data collected on a pure SmB 6 crystal grown by the floating zone method [57]. In the temperature range 300 to 60 K, the magnetic susceptibility of Ce-substituted and pure SmB 6 crystals show a similar behaviour, i.e., a gradual increase of χ T with decreasing temperature. Below 60 K, the Sm 1 − x Ce x B 6 crystals exhibit a more rapid increase in susceptibility, down to 1.8 K. In contrast, the susceptibility data of pure SmB 6 crystals contain a broad maximum centred around 50–60 K, characteristic of a Kondo insulator, before a more gradual upturn at lower temperatures. Moreover, in the temperature range 1.8–60 K, the magnetic susceptibility of Sm 1 − x Ce x B 6 crystals increases sharply with increasing Ce content. The change in the magnetic response of both Ce-substituted and pure SmB 6 crystals below 60 K coincides with the increase observed in the resistivity (see Figure 5).
Attempts to fit the temperature-dependent reciprocal magnetic susceptibilities, χ − 1 T (see Figure 4b), in the temperature range 100–300 K reveal that pure SmB 6 and the Sm 1 − x Ce x B 6 materials all appear to follow a Curie–Weiss law. The effective moment, μ eff , per formula unit at 300 K varies from 2.4 ( 1 ) μ B for x = 0.00 to 2.5 ( 1 ) μ B for x = 0.20 . The form of χ T for the Sm 1 − x Ce x B 6 crystals is qualitatively similar than data reported for aluminium flux grown Ce-substituted SmB 6 single crystals, although the effective moments in our samples are substantially lower, especially for lower Ce concentrations [54]. The χ T data are consistent with magnetic response expected for a mixture of 4 f 1 Ce 3 + ions 2.54 μ B / Ce 3 + and divalent and trivalent Sm ions in a variety of magnetic and nonmagnetic electronic configurations, 4 f 6 , 4 f 5 d 1 , and 4 f 5 [68,73,74].
A previous study reported that substituting Sm with another magnetic rare earth ion, such as Gd 3 + , in large concentrations (≥40%), leads to antiferromagnetic ordering at low temperature due to coupling between the Gd sites [18]. This is predicted by the existence of a saturation plateau in the normalised magnetic susceptibility data of 40% Gd-substituted SmB 6 . In contrast, the magnetisation curves for our Sm 1 − x Ce x B 6 crystals exhibit a rapid increase at low temperatures, but with no evidence for the onset of long-range magnetic order down to 2 K, as shown in the inset of Figure 4b. For the Ce 3 + concentrations used in our work, the magnetic data suggest that the Ce ions are distributed randomly in the lattice.

3.4. Resistivity

Alternating current resistivity versus temperature, ρ T , measurements were made on bar shaped samples cut from the Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) single crystals. The ac resistivity data are shown in Figure 5 for temperatures between 1.8 and 300 K. These resistivity data are compared with data for a pure SmB 6 crystal grown by the FZ method and reported in our previous work [57]. At 300 K, the Sm 1 − x Ce x B 6 samples all have resistivity values similar to SmB 6 and ρ 300 K increases with x. Below 300 K, SmB 6 exhibits a continuous increase in the bulk electrical resistivity. In contrast, the ρ T data for the Ce-substituted samples exhibit a broad maximum centred around 150 K, followed by an increasingly prominent minimum at ∼50 K. On further cooling below 50 K, the resistivity of SmB 6 increases by four orders of magnitude, whereas the resistivity of the Ce-substituted samples increases by only a single order of magnitude or less. Nevertheless, the Sm 1 − x Ce x B 6 samples still have resistivities larger than pure CeB 6 , over the entire temperature range studied. The resistivity of CeB 6 is approximately 10 − 5   Ω -cm from 2 to 300 K [75], whereas for the Sm 1 − x Ce x B 6 samples it is 10 − 3   Ω -cm or higher over the same temperature range, for the x = 0.20 sample.
In contrast to the saturation plateau seen in the resistivity of SmB 6 at lowest temperatures, ρ T for the Sm 1 − x Ce x B 6 samples increases monotonically with decreasing temperature below 10 K. These results are in agreement with the transport measurements performed on aluminium flux grown Ce-substituted SmB 6 single crystals [54]. There is an evolution from the TKI behaviour of pure SmB 6 to a dense Kondo system with low temperature spin ordering of CeB 6 [7,8,75]. The data suggest that it is bulk conductivity, modified by crystalline electric field and Kondo effects alongside phonon scattering, that determines the form of the ρ T curves for these Sm 1 − x Ce x B 6 samples over the entire temperature range studied. A more quantitative description of the transport properties of the Sm 1 − x Ce x B 6 crystals, including extensive measurements in a magnetic field, will be presented elsewhere [76].

4. Conclusions

Crystal boules of Sm 1 − x Ce x B 6 (x = 0.05, 0.10, and 0.20) compounds were grown, for the first time, by the FZ technique. Investigation of the crystals using X-ray diffraction techniques revealed that the Ce-substituent is successfully incorporated in the SmB 6 structure and that the structural distortions due to the substitution of Sm with Ce follow a similar trend to the one reported for polycrystalline samples of Ce-substituted SmB 6 . EDX and XPS results confirm that the Ce concentration is close to the nominal stoichiometric values of x = 0.05 , 0.10 and 0.20. Analysis of the average Sm valence data determined by XPS on Sm 1 − x Ce x B 6 and pure SmB 6 samples showed that the results are extremely dependent on the quality of the surface studied; i.e., an increase in the Sm valence is observed when the surface is exposed to ambient conditions. Magnetic property measurements show that our Sm 1 − x Ce x B 6 crystals exhibit no sign of long-range magnetic ordering, at substitution concentrations below 20%. Temperature dependent resistivity measurements revealed that a 5% (and above) substitution with Ce suppresses the crossover from bulk to surface conductivity seen in pure SmB 6 as the temperature is reduced. Detailed low temperature magneto-transport measurements are now being carried out to investigate the bulk and surface properties of the Sm 1 − x Ce x B 6 crystals.

Author Contributions

M.C.H. and T.A. performed the crystal growths; characterisation measurements were carried out by M.C.H. and T.A. with M.W. and M.R.L.; M.C.H., T.A., M.W., M.R.L. and G.B. analysed the data; M.C.H. and T.A. drafted the paper; M.R.L. and G.B. reviewed the manuscript; G.B. secured the funding and managed the project. All authors have read and agreed to the published version of the manuscript.

Funding

Financial support was provided by EPSRC, UK, through grant EP/T005963/1.

Acknowledgments

The authors thank S. York for the EDX compositional analysis, and A. Julian and T. E. Orton for valuable technical support.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:
RERare earth
TKITopological Kondo insulator
FZFloating zone
EDXEnergy dispersive X-ray spectroscopy
XPSX-ray photoelectron spectroscopy
acAlternating current
ZFCWZero-field-cooled warming
FCCField-cooled cooling

References

  1. Matthias, B.T.; Geballe, T.H.; Andres, K.; Corenzwit, E.; Hull, G.W.; Maita, J.P. Superconductivity and Antiferromagnetism in Boron-Rich Lattices. Science 1968, 159, 530. [Google Scholar] [CrossRef]
  2. Lortz, R.; Wang, Y.; Tutsch, U.; Abe, S.; Meingast, C.; Popovich, P.; Knafo, W.; Shitsevalova, N.; Paderno, Y.B.; Junod, A. Superconductivity mediated by a soft phonon mode: Specific heat, resistivity, thermal expansion, and magnetization of YB6. Phys. Rev. B 2006, 73, 024512. [Google Scholar] [CrossRef] [Green Version]
  3. Flachbart, K.; Gabáni, S.; Kačmarčik, J.; Mori, T.; Otani, S.; Pavlík, V. Low Temperature Properties and Superconductivity of YB6 and YB4. AIP Conf. Proc. 2006, 850, 635. [Google Scholar]
  4. Coles, B.R.; Griffiths, D. Antiferromagnetic behaviour of GdB6. Proc. Phys. Soc. (1958–1967) 1961, 77, 213–215. [Google Scholar] [CrossRef]
  5. Nozaki, H.; Tanaka, T.; Ishizawa, Y. Magnetic behaviour and structure change of GdB6 single crystals at low temperatures. J. Phys. C Solid State Phys. 1980, 13, 2751. [Google Scholar] [CrossRef]
  6. Semeno, A.V.; Gil’manov, M.I.; Sluchanko, N.E.; Shitsevalova, N.Y.; Filipov, V.B.; Demishev, S.V. Antiferromagnetic Resonance in GdB6. JETP Lett. 2018, 108, 237–242. [Google Scholar] [CrossRef]
  7. Fujita, T.; Suzuki, M.; Komatsubara, T.; Kunii, S.; Kasuya, T.; Ohtsuka, T. Anomalous specific heat of CeB6. Solid State Commun. 1980, 35, 569–572. [Google Scholar] [CrossRef]
  8. Takase, A.; Kojima, K.; Komatsubara, T.; Kasuya, T. Electrical resistivity and magnetoresistance of CeB6 single crystal. Solid State Commun. 1980, 36, 461–464. [Google Scholar] [CrossRef]
  9. Friemel, G.; Li, Y.; Dukhnenko, A.; Shitsevalova, N.Y.; Sluchanko, N.E.; Ivanov, A.; Filipov, V.B.; Keimer, B.; Inosov, D.S. Resonant magnetic exciton mode in the heavy-fermion antiferromagnet CeB6. Nat. Commun. 2012, 3, 830. [Google Scholar] [CrossRef] [Green Version]
  10. Koitzsch, A.; Heming, N.; Knupfer, M.; Büchner, B.; Portnichenko, P.Y.; Dukhnenko, A.V.; Shitsevalova, N.Y.; Filipov, V.B.; Lev, L.L.; Strocov, V.N.; et al. Nesting-driven multipolar order in CeB6 from photoemission tomography. Nat. Commun. 2016, 7, 10876. [Google Scholar] [CrossRef]
  11. Guy, C.N.; von Molnar, S.; Etourneau, J.; Fisk, Z. Charge transport and pressure dependence of Tc of single crystal, ferromagnetic EuB6. Solid State Commun. 1980, 33, 1055–1058. [Google Scholar] [CrossRef] [Green Version]
  12. Goodrich, R.G.; Harrison, N.; Vuillemin, J.J.; Teklu, A.; Hall, D.W.; Fisk, Z.; Young, D.; Sarrao, J. Fermi surface of ferromagnetic EuB6. Phys. Rev. B 1998, 58, 14896–14902. [Google Scholar] [CrossRef] [Green Version]
  13. Nie, S.; Sun, Y.; Prinz, F.B.; Wang, Z.; Weng, H.; Fang, Z.; Dai, X. Magnetic semimetals and quantized anomalous Hall effect in EuB6. Phys. Rev. Lett. 2020, 124, 076403. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  14. Arko, A.J.; Crabtree, G.; Karim, D.; Mueller, F.M.; Windmiller, L.R.; Ketterson, J.B.; Fisk, Z. de Haas-van Alphen effect and the Fermi surface of LaB6. Phys. Rev. B 1977, 13, 5240–5247. [Google Scholar] [CrossRef] [Green Version]
  15. Bai, L.; Ma, N.; Liu, F. Structure and chemical bond characteristics of LaB6. Phys. B Condens. Matter 2009, 404, 4086–4089. [Google Scholar] [CrossRef]
  16. Kasai, H.; Nishibori, E. Spatial distribution of electrons near the Fermi level in the metallic LaB6 through accurate X-ray charge density study. Sci. Rep. 2017, 7, 41375. [Google Scholar] [CrossRef] [PubMed]
  17. Wolgast, S.; Kurdak, Ç.; Sun, K.; Allen, J.W.; Kim, D.J.; Fisk, Z. Low-temperature surface conduction in the Kondo insulator SmB6. Phys. Rev. B 2013, 88, 180405(R). [Google Scholar] [CrossRef] [Green Version]
  18. Kim, D.J.; Xia, J.; Fisk, Z. Topological surface state in the Kondo insulator samarium hexaboride. Nat. Mater. 2014, 13, 466–470. [Google Scholar] [CrossRef]
  19. Tan, B.S.; Hsu, Y.T.; Zeng, B.; Ciomaga Hatnean, M.; Harrison, N.; Zhu, Z.; Hartstein, M.; Kiourlappou, M.; Srivastava, A.; Johannes, M.D.; et al. Unconventional Fermi surface in an insulating state. Science 2015, 349, 287–290. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  20. Stackelberg, M.; Neumann, F. Die kristallstruktur der boride der zusammensetzung MeB6. Zeitschrift für Physikalische Chemie 1932, B19, 314. [Google Scholar]
  21. Aivazov, M.I.; Aleksandrovich, S.V.; Mkrtchyan, V.S. Magnetic susceptibility of CexLa1−xB6, CexEu1−xB6, SmxLa1−xB6, and SmxCe1−xB6 solid solutions. Phys. Status Solidi 1980, 62, 109–114. [Google Scholar] [CrossRef]
  22. Funahashi, S.; Tanaka, K.; Iga, F. X-ray atomic orbital analysis of 4f and 5d electron configuration of SmB6 at 100, 165, 230 and 298 K. Acta Crystallogr. Sect. B Struct. Sci. 2010, 66, 292–306. [Google Scholar] [CrossRef] [PubMed]
  23. Aeppli, G.; Fisk, Z. Kondo insulators. Comments Condens. Matter Phys. 1992, 16, 155–165. [Google Scholar]
  24. Riseborough, P.S. Heavy fermion semiconductors. Adv. Phys. 2000, 49, 257–320. [Google Scholar] [CrossRef]
  25. Fu, L.; Kane, C.L.; Mele, E.J. Topological insulators in three dimensions. Phys. Rev. Lett. 2007, 98, 106803. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  26. Moore, J.E.; Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 2007, 75, 121306(R). [Google Scholar] [CrossRef] [Green Version]
  27. Roy, R. Topological phases and the quantum spin Hall effect in three dimensions. Phys. Rev. B 2009, 79, 195322. [Google Scholar] [CrossRef] [Green Version]
  28. Dzero, M.; Sun, K.; Galitski, V.; Coleman, P. Topological Kondo insulators. Phys. Rev. Lett. 2010, 104, 106408. [Google Scholar] [CrossRef] [Green Version]
  29. Takimoto, T. SmB6: A promising candidate for a topological insulator. J. Phys. Soc. Jpn. 2011, 80, 123710. [Google Scholar] [CrossRef]
  30. Dzero, M.; Sun, K.; Coleman, P.; Galitski, V. Theory of topological Kondo insulators. Phys. Rev. B 2012, 85, 045130. [Google Scholar] [CrossRef] [Green Version]
  31. Neupane, M.; Alidoust, N.; Xu, S.Y.; Kondo, T.; Ishida, Y.; Kim, D.J.; Liu, C.; Belopolski, I.; Jo, Y.J.; Chang, T.R.; et al. Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6. Nat. Commun. 2013, 4, 2991. [Google Scholar] [CrossRef] [PubMed]
  32. Hlawenka, P.; Siemensmeyer, K.; Weschke, E.; Varykhalov, A.; Sánchez-Barriga, J.; Shitsevalova, N.Y.; Dukhnenko, A.V.; Filipov, V.B.; Gabáni, S.; Flachbart, K.; et al. Samarium hexaboride is a trivial surface conductor. Nat. Commun. 2018, 9, 517. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  33. Menth, A.; Buehler, E.; Geballe, T.H. Magnetic and semiconducting properties of SmB6. Phys. Rev. Lett. 1969, 22, 295–297. [Google Scholar] [CrossRef]
  34. Allen, J.W.; Batlogg, B.; Wachter, P. Large low-temperature Hall effect and resistivity in mixed-valent SmB6. Phys. Rev. B 1979, 20, 4807–4813. [Google Scholar] [CrossRef]
  35. Cooley, J.C.; Aronson, M.C.; Fisk, Z.; Canfield, P.C. SmB6: Kondo insulator or exotic metal? Phys. Rev. Lett. 1995, 74, 1629–1632. [Google Scholar] [CrossRef] [PubMed]
  36. Phelan, W.; Koohpayeh, S.; Cottingham, P.; Freeland, J.; Leiner, J.; Broholm, C.; McQueen, T. Correlation between bulk thermodynamic measurements and the low-temperature-resistance plateau in SmB6. Phys. Rev. X 2014, 4, 031012. [Google Scholar]
  37. Kasuya, T.; Takegahara, K.; Fujita, T.; Tanaka, T.; Bannai, E. Valence fluctuating state in SmB6. J. Phys. Colloq. 1979, 40, 308–313. [Google Scholar] [CrossRef] [Green Version]
  38. Kasuya, T. Mixed-salence state in SmB6. Europhys. Lett. (EPL) 1994, 26, 283–287. [Google Scholar] [CrossRef]
  39. Flachbart, K.; Gabáni, S.; Herrmannsdörfer, T.; Konovalova, E.; Paderno, Y.; Pavlík, V. Low-temperature magnetic properties of SmB6. Phys. B Condens. Matter 2000, 284–288, 1353–1354. [Google Scholar] [CrossRef]
  40. Gheidi, S.; Akintola, K.; Akella, K.S.; Côté, A.M.; Dunsiger, S.R.; Broholm, C.; Fuhrman, W.T.; Saha, S.R.; Paglione, J.; Sonier, J.E. Intrinsic Low-Temperature Magnetism in SmB6. Phys. Rev. Lett. 2019, 123, 197203. [Google Scholar] [CrossRef] [Green Version]
  41. Chazalviel, J.N.; Campagna, M.; Wertheim, G.K.; Schmidt, P.H.; Longinotti, L.D. Electronic structure of SmB6 and related rare-earth borides by x-ray photoelectron spectroscopy. Physica B+C 1977, 86–88, 237–238. [Google Scholar] [CrossRef]
  42. Barla, A.; Derr, J.; Sanchez, J.P.; Salce, B.; Lapertot, G.; Doyle, B.P.; Rüffer, R.; Lengsdorf, R.; Abd-Elmeguid, M.M.; Flouquet, J. High-Pressure Ground State of SmB6: Electronic Conduction and Long Range Magnetic Order. Phys. Rev. Lett. 2005, 94, 166401. [Google Scholar] [CrossRef] [PubMed]
  43. Miyazaki, H.; Hajiri, T.; Ito, T.; Kunii, S.; Kimura, S.I. Momentum-dependent hybridization gap and dispersive in-gap state of the Kondo semiconductor SmB6. Phys. Rev. B 2012, 86, 075105. [Google Scholar] [CrossRef] [Green Version]
  44. Hall, D.; Fisk, Z.; Goodrich, R.G. Magnetic-field dependence of the paramagnetic to the high-temperature magnetically ordered phase transition in CeB6. Phys. Rev. B 2000, 62, 84–86. [Google Scholar] [CrossRef] [Green Version]
  45. Goodrich, R.G.; Young, D.P.; Hall, D.; Balicas, L.; Fisk, Z.; Harrison, N.; Betts, J.; Migliori, A.; Woodward, F.M.; Lynn, J.W. Extension of the temperature-magnetic field phase diagram of CeB6. Phys. Rev. B 2004, 69, 054415. [Google Scholar] [CrossRef] [Green Version]
  46. Terzioglu, C.; Ozturk, O.; Kilic, A.; Goodrich, R.; Fisk, Z. Magnetic and electronic measurements in CeB6. J. Magn. Magn. Mater. 2006, 298, 33–37. [Google Scholar] [CrossRef]
  47. Portnichenko, P.; Akbari, A.; Nikitin, S.; Cameron, A.; Dukhnenko, A.; Filipov, V.; Shitsevalova, N.; Čermák, P.; Radelytskyi, I.; Schneidewind, A.; et al. Field-Angle-Resolved Magnetic Excitations as a Probe of Hidden-Order Symmetry in CeB6. Phys. Rev. X 2020, 10, 021010. [Google Scholar] [CrossRef] [Green Version]
  48. Hartstein, M.; Toews, W.H.; Hsu, Y.T.; Zeng, B.; Chen, X.; Ciomaga Hatnean, M.; Zhang, Q.R.; Nakamura, S.; Padgett, A.S.; Rodway-Gant, G.; et al. Fermi surface in the absence of a Fermi liquid in the Kondo insulator SmB6. Nat. Phys. 2018, 14, 166–172. [Google Scholar] [CrossRef]
  49. Aivazov, M.I.; Aleksandrovich, S.V.; Evseev, B. Physical properties of solid solutions SmxCe1−xB6. Inorg. Mater. 1980, 16, 300–303. [Google Scholar]
  50. Kasaya, M.; Tarascon, J.M.; Etourneau, J. Study of the valence transition in La- and Yb-substituted SmB6. Solid State Commun. 1980, 33, 1005–1007. [Google Scholar] [CrossRef]
  51. Liu, B.; Kasaya, M.; Iga, F.; Kasuya, T. Kondo effect in Sm1−yYbyB6 and Tm1/2Yb1/2B6. J. Magn. Magn. Mater. 1985, 47-48, 472–474. [Google Scholar] [CrossRef]
  52. Yeo, S.; Song, K.; Hur, N.; Fisk, Z.; Schlottmann, P. Effects of Eu doping on SmB6 single crystals. Phys. Rev. B 2012, 85, 115125. [Google Scholar] [CrossRef] [Green Version]
  53. Gabáni, S.; Flachbart, K.; Bednarčík, J.; Welter, E.; Filipov, V.; Shitsevalova, N. Investigation of Mixed Valence State of Sm1−xB6 and Sm1−xLaxB6 by XANES. Acta Phys. Pol. A 2014, 126, 292–306. [Google Scholar] [CrossRef]
  54. Miao, L.; Min, C.H.; Xu, Y.; Huang, Z.; Kotta, E.C.; Basak, R.; Song, M.S.; Kang, B.Y.; Cho, B.K.; Kißner, K.; et al. Robust surface states and coherence phenomena in magnetically alloyed SmB6. arXiv 2020, arXiv:1907.07074v2. [Google Scholar]
  55. Otani, S.; Nakagawa, H.; Nishi, Y.; Kieda, N. Floating zone growth and high temperature hardness of rare-earth hexaboride crystals: LaB6, CeB6, PrB6, NdB6, and SmB6. J. Solid State Chem. 2000, 154, 238–241. [Google Scholar] [CrossRef]
  56. Balakrishnan, G.; Lees, M.R.; Paul, D.M. Growth of large single crystals of rare earth hexaborides. J. Cryst. Growth 2003, 256, 206–209. [Google Scholar] [CrossRef] [Green Version]
  57. Ciomaga Hatnean, M.; Lees, M.R.; Paul, D.M.; Balakrishnan, G. Large, high quality single-crystals of the new Topological Kondo Insulator, SmB6. Sci. Rep. 2013, 3, 3071. [Google Scholar] [CrossRef] [Green Version]
  58. Thomas, S.M.; Ding, X.; Ronning, F.; Zapf, V.; Thompson, J.D.; Fisk, Z.; Xia, J.; Rosa, P.F.S. Quantum oscillations in flux-grown SmB6 with embedded aluminum. Phys. Rev. Lett. 2019, 122, 166401. [Google Scholar] [CrossRef] [Green Version]
  59. Rodríguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 1993, 192, 55–69. [Google Scholar] [CrossRef]
  60. Newnham, R.E.; Redman, M.J.; Santoro, R.P. Crystal Structure of yttrium and other rare-earth borates. J. Am. Ceram. Soc. 1963, 46, 253–256. [Google Scholar] [CrossRef]
  61. Vegard, L. Die konstitution der mischkristalle und die raumfüllung der atome. Z. Phys. 1921, 5, 17–26. [Google Scholar] [CrossRef]
  62. Tarascon, J.; Isikawa, Y.; Chevalier, B.; Etoumeau, J.; Hagenmuller, P.; Kasaya, M. Valence transition of samarium in hexaboride solid solutions Sm1−xMxB6 (M = Yb2+, Sr2+, La3+, Y3+, Th4+). J. Phys. 1980, 41, 1135–1140. [Google Scholar] [CrossRef] [Green Version]
  63. Shannon, R.D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. Sect. A 1976, 32, 751–767. [Google Scholar] [CrossRef]
  64. Jia, Y.Q. Crystal radii and effective ionic radii of the rare earth ions. J. Solid State Chem. 1991, 95, 184–187. [Google Scholar] [CrossRef]
  65. Konovalova, E.S.; Paderno, Y.B.; Lundstrem, T.; Finkel’shtein, L.D.; Efremova, N.N.; Dudnik, E.M. Effect of vacancies and foreign metal ions on the valent state of samarium in SmB6. Sov. Powder Metall. Met. Ceram. 1982, 21, 820–823. [Google Scholar] [CrossRef]
  66. Chazalviel, J.N.; Campagna, M.; Wertheim, G.K.; Schmidt, P.H. Study of valence mixing in SmB6 by x-ray photoelectron spectroscopy. Phys. Rev. B 1976, 14, 4586–4592. [Google Scholar] [CrossRef]
  67. Heming, N.; Treske, U.; Knupfer, M.; Büchner, B.; Inosov, D.S.; Shitsevalova, N.Y.; Filipov, V.B.; Krause, S.; Koitzsch, A. Surface properties of SmB6 from x-ray photoelectron spectroscopy. Phys. Rev. B 2014, 90, 195128. [Google Scholar] [CrossRef] [Green Version]
  68. Mizumaki, M.; Tsutsui, S.; Iga, F. Temperature dependence of Sm valence in SmB6 studied by X-ray absorption spectroscopy. J. Phys. Conf. Ser. 2009, 176, 012034. [Google Scholar] [CrossRef]
  69. Emi, N.; Mito, T.; Kawamura, N.; Mizumaki, M.; Ishimatsu, N.; Pristáš, G.; Kagayama, T.; Shimizu, K.; Osanai, Y.; Iga, F. Temperature and pressure dependences of Sm valence in intermediate valence compound SmB6. Phys. B Condens. Matter 2018, 536, 197–199. [Google Scholar] [CrossRef]
  70. Savchenkov, P.S.; Alekseev, P.A.; Podlesnyak, A.; Kolesnikov, A.I.; Nemkovski, K.S. Intermediate-valence state of the Sm and Eu in SmB6 and EuCu2Si2: Neutron spectroscopy data and analysis. J. Phys. Condens. Matter 2018, 30, 055801. [Google Scholar] [CrossRef]
  71. Paparazzo, E. On the curve-fitting of XPS Ce(3d) spectra of cerium oxides. Mater. Res. Bull. 2011, 46, 323–326. [Google Scholar] [CrossRef]
  72. Revoy, M.N.; Scott, R.W.J.; Grosvenor, A.P. Ceria nanocubes: Dependence of the electronic structure on synthetic and experimental conditions. J. Phys. Chem. C 2013, 117, 10095–10105. [Google Scholar] [CrossRef]
  73. Gabáni, S.; Flachbart, K.; Pavlík, V.; Herrmannsdorfer, T.; Konovalova, E.; Paderno, Y.; Briančin, J.; Trpčevská, J. Magnetic properties of Sm1−xB6 and Sm1−xLaxB6 solid solutions. Czechoslov. J. Phys. 2002, 52, A225–A228. [Google Scholar] [CrossRef]
  74. Nickerson, J.C.; White, R.M.; Lee, K.N.; Bachmann, R.; Geballe, T.H.; Hull, G.W. Physical properties of SmB6. Phys. Rev. B 1971, 3, 2030–2042. [Google Scholar] [CrossRef]
  75. Tanaka, T.; Nishitani, R.; Oshima, C.; Bannai, E.; Kawai, S. The preparation and properties of CeB6, SmB6, and GdB6. J. Appl. Phys. 1980, 51, 3877. [Google Scholar] [CrossRef]
  76. Ciomaga Hatnean, M.; Lees, M.R.; Ahmad, T.; Balakrishnan, G. University of Warwick: Coventry, UK, 2020; in preparation.
Crystals 10 00827 g001 550
Figure 1. Crystal boules of (a) Sm 0.95 Ce 0.05 B 6 , (b) Sm 0.90 Ce 0.10 B 6 and (c) Sm 0.80 Ce 0.20 B 6 , prepared by the floating-zone method in argon atmosphere at a growth rate of 18 mm/h. X-ray Laue back reflection photographs show the [001] orientation of aligned Sm 1 − x Ce x B 6 samples used for the physical properties measurements.
Figure 1. Crystal boules of (a) Sm 0.95 Ce 0.05 B 6 , (b) Sm 0.90 Ce 0.10 B 6 and (c) Sm 0.80 Ce 0.20 B 6 , prepared by the floating-zone method in argon atmosphere at a growth rate of 18 mm/h. X-ray Laue back reflection photographs show the [001] orientation of aligned Sm 1 − x Ce x B 6 samples used for the physical properties measurements.
Crystals 10 00827 g001
Crystals 10 00827 g002 550
Figure 2. Powder X-ray diffraction patterns of Sm 1 − x Ce x B 6 with (a) x = 0.05 , (b) x = 0.10 and (c) x = 0.20 ) for samples taken from the crystal boules. The experimental profile (red closed circles) and a full profile matching refinement (black solid line) made using the P m 3 ¯ m cubic structure are shown, with the difference given by the blue solid line. The orange coloured symbols * indicate the impurity peaks belonging to SmBO 3 impurity phases. (d) Evolution of the lattice parameter, a, as a function of the concentration, x, of the Ce-substituent for Sm 1 − x Ce x B 6 . The experimental values obtained in the present work (red open circles) are also given in Table 1. The previously reported values (red, black and orange closed circles) of the crystallographic parameters for the Sm 1 − x Ce x B 6 − y series [21] are given for completeness.
Figure 2. Powder X-ray diffraction patterns of Sm 1 − x Ce x B 6 with (a) x = 0.05 , (b) x = 0.10 and (c) x = 0.20 ) for samples taken from the crystal boules. The experimental profile (red closed circles) and a full profile matching refinement (black solid line) made using the P m 3 ¯ m cubic structure are shown, with the difference given by the blue solid line. The orange coloured symbols * indicate the impurity peaks belonging to SmBO 3 impurity phases. (d) Evolution of the lattice parameter, a, as a function of the concentration, x, of the Ce-substituent for Sm 1 − x Ce x B 6 . The experimental values obtained in the present work (red open circles) are also given in Table 1. The previously reported values (red, black and orange closed circles) of the crystallographic parameters for the Sm 1 − x Ce x B 6 − y series [21] are given for completeness.
Crystals 10 00827 g002
Crystals 10 00827 g003 550
Figure 3. (a) Sm 4d XPS spectrum and (b) Ce 3 d 3 / 2 , 5 / 2 XPS spectra collected for the Sm 1 − x Ce x B 6 (x = 0.05, 0.10, and 0.20) crystal boules.
Figure 3. (a) Sm 4d XPS spectrum and (b) Ce 3 d 3 / 2 , 5 / 2 XPS spectra collected for the Sm 1 − x Ce x B 6 (x = 0.05, 0.10, and 0.20) crystal boules.
Crystals 10 00827 g003
Crystals 10 00827 g004 550
Figure 4. (a) Temperature dependence of the d c magnetic susceptibility, χ versus T, in the temperature range 1.8–100 K for the Sm 1 − x Ce x B 6 ( x = 0 , 0.05, 0.10 and 0.20) crystals, with a magnetic field applied along the [001] (black), [110] (red) and [111] (orange) crystallographic directions. The previously reported susceptibility data for a SmB 6 crystal [57] are given for comparison. The inset shows χ versus T, on a logarithmic scale, in the temperature range 1.8–300 K. (b) Temperature dependence of the reciprocal of the d c susceptibility, χ − 1 versus T, of Sm 1 − x Ce x B 6 for a field applied along the [001] direction. The inset shows the normalised magnetic susceptibilities of Sm 1 − x Ce x B 6 samples, with a magnetic field applied along the [001] direction. The χ / χ (10 K) versus T data increase rapidly at low temperatures, but with no signature of long-range magnetic order, for all Ce concentrations.
Figure 4. (a) Temperature dependence of the d c magnetic susceptibility, χ versus T, in the temperature range 1.8–100 K for the Sm 1 − x Ce x B 6 ( x = 0 , 0.05, 0.10 and 0.20) crystals, with a magnetic field applied along the [001] (black), [110] (red) and [111] (orange) crystallographic directions. The previously reported susceptibility data for a SmB 6 crystal [57] are given for comparison. The inset shows χ versus T, on a logarithmic scale, in the temperature range 1.8–300 K. (b) Temperature dependence of the reciprocal of the d c susceptibility, χ − 1 versus T, of Sm 1 − x Ce x B 6 for a field applied along the [001] direction. The inset shows the normalised magnetic susceptibilities of Sm 1 − x Ce x B 6 samples, with a magnetic field applied along the [001] direction. The χ / χ (10 K) versus T data increase rapidly at low temperatures, but with no signature of long-range magnetic order, for all Ce concentrations.
Crystals 10 00827 g004
Crystals 10 00827 g005 550
Figure 5. Temperature dependence of the bulk a c resistivity, ρ versus T, in the temperature range 1.8–300 K for the Sm 1 − x Ce x B 6 (x = 0, 0.05, 0.10 and 0.20) crystals. The previously reported resistivity data for a SmB 6 crystal [57] are given for comparison.
Figure 5. Temperature dependence of the bulk a c resistivity, ρ versus T, in the temperature range 1.8–300 K for the Sm 1 − x Ce x B 6 (x = 0, 0.05, 0.10 and 0.20) crystals. The previously reported resistivity data for a SmB 6 crystal [57] are given for comparison.
Crystals 10 00827 g005
Table
Table 1. Lattice parameters calculated from profile matching the powder X-ray diffraction patterns of the Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) crystals to the P m 3 ¯ m cubic structure. The previously reported structural parameters quoted for other members of the Sm 1 − x Ce x B 6 − y series [21] are included for completeness.
Table 1. Lattice parameters calculated from profile matching the powder X-ray diffraction patterns of the Sm 1 − x Ce x B 6 ( x = 0.05 , 0.10 and 0.20) crystals to the P m 3 ¯ m cubic structure. The previously reported structural parameters quoted for other members of the Sm 1 − x Ce x B 6 − y series [21] are included for completeness.
Sm 1 − x Ce x B 6 − y Chemical CompositionaStudy
xy(Å)
SmB 6 004.1340(2)Present work
Sm 0.95 Ce 0.05 B 6 0.0504.1351(2)Present work
Sm 0.90 Ce 0.10 B 6 0.1004.1384(2)Present work
Sm 0.89 Ce 0.11 B 5.9 0.110.14.1358Ref. [21]
Sm 0.80 Ce 0.20 B 6 0.2004.1393(2)Present work
Sm 0.78 Ce 0.22 B 5.7 0.220.34.1378Ref. [21]
Sm 0.66 Ce 0.34 B 5.9 0.340.14.1399Ref. [21]
Sm 0.62 Ce 0.38 B 5.7 0.380.34.1403Ref. [21]
Sm 0.50 Ce 0.50 B 6 0.5004.1418Ref. [21]
Sm 0.35 Ce 0.65 B 5.7 0.650.34.1421Ref. [21]
Sm 0.25 Ce 0.75 B 5.9 0.750.14.1424Ref. [21]
Sm 0.18 Ce 0.82 B 6 0.8204.1418Ref. [21]
Sm 0.08 Ce 0.92 B 6 0.9204.1412Ref. [21]
CeB 6 1.0004.1407(1)Present work
Table
Table 2. Chemical composition and valence of the Sm ions determined by EDX and XPS for the Sm 1 − x Ce x B 6 crystal boules grown. The data collected on a pure SmB 6 crystal are included for completeness. The XPS measurements were carried out on a piece of an as-grown SmB 6 crystal boule and on a sample cleaved (in-situ) from the as-grown SmB 6 crystal fragment.
Table 2. Chemical composition and valence of the Sm ions determined by EDX and XPS for the Sm 1 − x Ce x B 6 crystal boules grown. The data collected on a pure SmB 6 crystal are included for completeness. The XPS measurements were carried out on a piece of an as-grown SmB 6 crystal boule and on a sample cleaved (in-situ) from the as-grown SmB 6 crystal fragment.
Chemical CompositionSm:B RatioSm:B RatioSm Valence
Present WorkLiterature
(EDX)(XPS)(XPS)(Refs. [37,41])
SmB 6 1.00(2):5.50(2)1.00(3):6.4(3)+2.80(2)∼2.6–2.7
SmB 6 cleaved-1:00(3):7.30(3)+2.72(2)
Sm 1 − x Ce x B 6 xxSm valence
(EDX)(XPS)(XPS)
Sm 0.95 Ce 0.05 B 6 0.07(2)0.09(3)+2.86(2)
Sm 0.90 Ce 0.10 B 6 0.11(2)0.14(3)+2.86(2)
Sm 0.80 Ce 0.20 B 6 0.21(2)0.23(3)+2.85(2)

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Ciomaga Hatnean, M.; Ahmad, T.; Walker, M.; Lees, M.R.; Balakrishnan, G. Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB6. Crystals 2020, 10, 827. https://doi.org/10.3390/cryst10090827

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Ciomaga Hatnean M, Ahmad T, Walker M, Lees MR, Balakrishnan G. Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB6. Crystals. 2020; 10(9):827. https://doi.org/10.3390/cryst10090827

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Ciomaga Hatnean, Monica, Talha Ahmad, Marc Walker, Martin R. Lees, and Geetha Balakrishnan. 2020. "Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB6" Crystals 10, no. 9: 827. https://doi.org/10.3390/cryst10090827

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