#
Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB_{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Crystal Growth

#### 3.2. Structural and Composition Analysis

#### 3.3. Magnetisation

#### 3.4. Resistivity

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

RE | Rare earth |

TKI | Topological Kondo insulator |

FZ | Floating zone |

EDX | Energy dispersive X-ray spectroscopy |

XPS | X-ray photoelectron spectroscopy |

ac | Alternating current |

ZFCW | Zero-field-cooled warming |

FCC | Field-cooled cooling |

## References

- 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] - 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 YB
_{6}. Phys. Rev. B**2006**, 73, 024512. [Google Scholar] [CrossRef] [Green Version] - Flachbart, K.; Gabáni, S.; Kačmarčik, J.; Mori, T.; Otani, S.; Pavlík, V. Low Temperature Properties and Superconductivity of YB
_{6}and YB_{4}. AIP Conf. Proc.**2006**, 850, 635. [Google Scholar] - Coles, B.R.; Griffiths, D. Antiferromagnetic behaviour of GdB
_{6}. Proc. Phys. Soc. (1958–1967)**1961**, 77, 213–215. [Google Scholar] [CrossRef] - Nozaki, H.; Tanaka, T.; Ishizawa, Y. Magnetic behaviour and structure change of GdB
_{6}single crystals at low temperatures. J. Phys. C Solid State Phys.**1980**, 13, 2751. [Google Scholar] [CrossRef] - Semeno, A.V.; Gil’manov, M.I.; Sluchanko, N.E.; Shitsevalova, N.Y.; Filipov, V.B.; Demishev, S.V. Antiferromagnetic Resonance in GdB
_{6}. JETP Lett.**2018**, 108, 237–242. [Google Scholar] [CrossRef] - Fujita, T.; Suzuki, M.; Komatsubara, T.; Kunii, S.; Kasuya, T.; Ohtsuka, T. Anomalous specific heat of CeB
_{6}. Solid State Commun.**1980**, 35, 569–572. [Google Scholar] [CrossRef] - Takase, A.; Kojima, K.; Komatsubara, T.; Kasuya, T. Electrical resistivity and magnetoresistance of CeB
_{6}single crystal. Solid State Commun.**1980**, 36, 461–464. [Google Scholar] [CrossRef] - 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 CeB
_{6}. Nat. Commun.**2012**, 3, 830. [Google Scholar] [CrossRef] [Green Version] - 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 CeB
_{6}from photoemission tomography. Nat. Commun.**2016**, 7, 10876. [Google Scholar] [CrossRef] - Guy, C.N.; von Molnar, S.; Etourneau, J.; Fisk, Z. Charge transport and pressure dependence of T
_{c}of single crystal, ferromagnetic EuB_{6}. Solid State Commun.**1980**, 33, 1055–1058. [Google Scholar] [CrossRef] [Green Version] - Goodrich, R.G.; Harrison, N.; Vuillemin, J.J.; Teklu, A.; Hall, D.W.; Fisk, Z.; Young, D.; Sarrao, J. Fermi surface of ferromagnetic EuB
_{6}. Phys. Rev. B**1998**, 58, 14896–14902. [Google Scholar] [CrossRef] [Green Version] - Nie, S.; Sun, Y.; Prinz, F.B.; Wang, Z.; Weng, H.; Fang, Z.; Dai, X. Magnetic semimetals and quantized anomalous Hall effect in EuB
_{6}. Phys. Rev. Lett.**2020**, 124, 076403. [Google Scholar] [CrossRef] [PubMed] [Green Version] - 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 LaB
_{6}. Phys. Rev. B**1977**, 13, 5240–5247. [Google Scholar] [CrossRef] [Green Version] - Bai, L.; Ma, N.; Liu, F. Structure and chemical bond characteristics of LaB
_{6}. Phys. B Condens. Matter**2009**, 404, 4086–4089. [Google Scholar] [CrossRef] - Kasai, H.; Nishibori, E. Spatial distribution of electrons near the Fermi level in the metallic LaB
_{6}through accurate X-ray charge density study. Sci. Rep.**2017**, 7, 41375. [Google Scholar] [CrossRef] [PubMed] - Wolgast, S.; Kurdak, Ç.; Sun, K.; Allen, J.W.; Kim, D.J.; Fisk, Z. Low-temperature surface conduction in the Kondo insulator SmB
_{6}. Phys. Rev. B**2013**, 88, 180405(R). [Google Scholar] [CrossRef] [Green Version] - 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] - 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] - Stackelberg, M.; Neumann, F. Die kristallstruktur der boride der zusammensetzung MeB
_{6}. Zeitschrift für Physikalische Chemie**1932**, B19, 314. [Google Scholar] - Aivazov, M.I.; Aleksandrovich, S.V.; Mkrtchyan, V.S. Magnetic susceptibility of Ce
_{x}La_{1−x}B_{6}, Ce_{x}Eu_{1−x}B_{6}, Sm_{x}La_{1−x}B_{6}, and Sm_{x}Ce_{1−x}B_{6}solid solutions. Phys. Status Solidi**1980**, 62, 109–114. [Google Scholar] [CrossRef] - 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] - Aeppli, G.; Fisk, Z. Kondo insulators. Comments Condens. Matter Phys.
**1992**, 16, 155–165. [Google Scholar] - Riseborough, P.S. Heavy fermion semiconductors. Adv. Phys.
**2000**, 49, 257–320. [Google Scholar] [CrossRef] - 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] - 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] - Roy, R. Topological phases and the quantum spin Hall effect in three dimensions. Phys. Rev. B
**2009**, 79, 195322. [Google Scholar] [CrossRef] [Green Version] - Dzero, M.; Sun, K.; Galitski, V.; Coleman, P. Topological Kondo insulators. Phys. Rev. Lett.
**2010**, 104, 106408. [Google Scholar] [CrossRef] [Green Version] - Takimoto, T. SmB
_{6}: A promising candidate for a topological insulator. J. Phys. Soc. Jpn.**2011**, 80, 123710. [Google Scholar] [CrossRef] - Dzero, M.; Sun, K.; Coleman, P.; Galitski, V. Theory of topological Kondo insulators. Phys. Rev. B
**2012**, 85, 045130. [Google Scholar] [CrossRef] [Green Version] - 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 SmB
_{6}. Nat. Commun.**2013**, 4, 2991. [Google Scholar] [CrossRef] [PubMed] - 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] - Menth, A.; Buehler, E.; Geballe, T.H. Magnetic and semiconducting properties of SmB
_{6}. Phys. Rev. Lett.**1969**, 22, 295–297. [Google Scholar] [CrossRef] - Allen, J.W.; Batlogg, B.; Wachter, P. Large low-temperature Hall effect and resistivity in mixed-valent SmB
_{6}. Phys. Rev. B**1979**, 20, 4807–4813. [Google Scholar] [CrossRef] - Cooley, J.C.; Aronson, M.C.; Fisk, Z.; Canfield, P.C. SmB
_{6}: Kondo insulator or exotic metal? Phys. Rev. Lett.**1995**, 74, 1629–1632. [Google Scholar] [CrossRef] [PubMed] - 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 SmB
_{6}. Phys. Rev. X**2014**, 4, 031012. [Google Scholar] - Kasuya, T.; Takegahara, K.; Fujita, T.; Tanaka, T.; Bannai, E. Valence fluctuating state in SmB
_{6}. J. Phys. Colloq.**1979**, 40, 308–313. [Google Scholar] [CrossRef] [Green Version] - Kasuya, T. Mixed-salence state in SmB
_{6}. Europhys. Lett. (EPL)**1994**, 26, 283–287. [Google Scholar] [CrossRef] - Flachbart, K.; Gabáni, S.; Herrmannsdörfer, T.; Konovalova, E.; Paderno, Y.; Pavlík, V. Low-temperature magnetic properties of SmB
_{6}. Phys. B Condens. Matter**2000**, 284–288, 1353–1354. [Google Scholar] [CrossRef] - 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 SmB
_{6}. Phys. Rev. Lett.**2019**, 123, 197203. [Google Scholar] [CrossRef] [Green Version] - Chazalviel, J.N.; Campagna, M.; Wertheim, G.K.; Schmidt, P.H.; Longinotti, L.D. Electronic structure of SmB
_{6}and related rare-earth borides by x-ray photoelectron spectroscopy. Physica B+C**1977**, 86–88, 237–238. [Google Scholar] [CrossRef] - 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 SmB
_{6}: Electronic Conduction and Long Range Magnetic Order. Phys. Rev. Lett.**2005**, 94, 166401. [Google Scholar] [CrossRef] [PubMed] - Miyazaki, H.; Hajiri, T.; Ito, T.; Kunii, S.; Kimura, S.I. Momentum-dependent hybridization gap and dispersive in-gap state of the Kondo semiconductor SmB
_{6}. Phys. Rev. B**2012**, 86, 075105. [Google Scholar] [CrossRef] [Green Version] - Hall, D.; Fisk, Z.; Goodrich, R.G. Magnetic-field dependence of the paramagnetic to the high-temperature magnetically ordered phase transition in CeB
_{6}. Phys. Rev. B**2000**, 62, 84–86. [Google Scholar] [CrossRef] [Green Version] - 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 CeB
_{6}. Phys. Rev. B**2004**, 69, 054415. [Google Scholar] [CrossRef] [Green Version] - Terzioglu, C.; Ozturk, O.; Kilic, A.; Goodrich, R.; Fisk, Z. Magnetic and electronic measurements in CeB
_{6}. J. Magn. Magn. Mater.**2006**, 298, 33–37. [Google Scholar] [CrossRef] - 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 CeB
_{6}. Phys. Rev. X**2020**, 10, 021010. [Google Scholar] [CrossRef] [Green Version] - 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 SmB
_{6}. Nat. Phys.**2018**, 14, 166–172. [Google Scholar] [CrossRef] - Aivazov, M.I.; Aleksandrovich, S.V.; Evseev, B. Physical properties of solid solutions Sm
_{x}Ce_{1−x}B_{6}. Inorg. Mater.**1980**, 16, 300–303. [Google Scholar] - Kasaya, M.; Tarascon, J.M.; Etourneau, J. Study of the valence transition in La- and Yb-substituted SmB
_{6}. Solid State Commun.**1980**, 33, 1005–1007. [Google Scholar] [CrossRef] - Liu, B.; Kasaya, M.; Iga, F.; Kasuya, T. Kondo effect in Sm
_{1−y}Yb_{y}B_{6}and Tm_{1/2}Yb_{1/2}B_{6}. J. Magn. Magn. Mater.**1985**, 47-48, 472–474. [Google Scholar] [CrossRef] - Yeo, S.; Song, K.; Hur, N.; Fisk, Z.; Schlottmann, P. Effects of Eu doping on SmB
_{6}single crystals. Phys. Rev. B**2012**, 85, 115125. [Google Scholar] [CrossRef] [Green Version] - Gabáni, S.; Flachbart, K.; Bednarčík, J.; Welter, E.; Filipov, V.; Shitsevalova, N. Investigation of Mixed Valence State of Sm
_{1−x}B_{6}and Sm_{1−x}La_{x}B_{6}by XANES. Acta Phys. Pol. A**2014**, 126, 292–306. [Google Scholar] [CrossRef] - 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 SmB
_{6}. arXiv**2020**, arXiv:1907.07074v2. [Google Scholar] - Otani, S.; Nakagawa, H.; Nishi, Y.; Kieda, N. Floating zone growth and high temperature hardness of rare-earth hexaboride crystals: LaB
_{6}, CeB_{6}, PrB_{6}, NdB_{6}, and SmB_{6}. J. Solid State Chem.**2000**, 154, 238–241. [Google Scholar] [CrossRef] - 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] - Ciomaga Hatnean, M.; Lees, M.R.; Paul, D.M.; Balakrishnan, G. Large, high quality single-crystals of the new Topological Kondo Insulator, SmB
_{6}. Sci. Rep.**2013**, 3, 3071. [Google Scholar] [CrossRef] [Green Version] - 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 SmB
_{6}with embedded aluminum. Phys. Rev. Lett.**2019**, 122, 166401. [Google Scholar] [CrossRef] [Green Version] - Rodríguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B
**1993**, 192, 55–69. [Google Scholar] [CrossRef] - 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] - Vegard, L. Die konstitution der mischkristalle und die raumfüllung der atome. Z. Phys.
**1921**, 5, 17–26. [Google Scholar] [CrossRef] - Tarascon, J.; Isikawa, Y.; Chevalier, B.; Etoumeau, J.; Hagenmuller, P.; Kasaya, M. Valence transition of samarium in hexaboride solid solutions Sm
_{1−x}M_{x}B_{6}(M = Yb^{2+}, Sr^{2+}, La^{3+}, Y^{3+}, Th^{4+}). J. Phys.**1980**, 41, 1135–1140. [Google Scholar] [CrossRef] [Green Version] - 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] - 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] - 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 SmB
_{6}. Sov. Powder Metall. Met. Ceram.**1982**, 21, 820–823. [Google Scholar] [CrossRef] - Chazalviel, J.N.; Campagna, M.; Wertheim, G.K.; Schmidt, P.H. Study of valence mixing in SmB
_{6}by x-ray photoelectron spectroscopy. Phys. Rev. B**1976**, 14, 4586–4592. [Google Scholar] [CrossRef] - Heming, N.; Treske, U.; Knupfer, M.; Büchner, B.; Inosov, D.S.; Shitsevalova, N.Y.; Filipov, V.B.; Krause, S.; Koitzsch, A. Surface properties of SmB
_{6}from x-ray photoelectron spectroscopy. Phys. Rev. B**2014**, 90, 195128. [Google Scholar] [CrossRef] [Green Version] - Mizumaki, M.; Tsutsui, S.; Iga, F. Temperature dependence of Sm valence in SmB
_{6}studied by X-ray absorption spectroscopy. J. Phys. Conf. Ser.**2009**, 176, 012034. [Google Scholar] [CrossRef] - 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 SmB
_{6}. Phys. B Condens. Matter**2018**, 536, 197–199. [Google Scholar] [CrossRef] - Savchenkov, P.S.; Alekseev, P.A.; Podlesnyak, A.; Kolesnikov, A.I.; Nemkovski, K.S. Intermediate-valence state of the Sm and Eu in SmB
_{6}and EuCu_{2}Si_{2}: Neutron spectroscopy data and analysis. J. Phys. Condens. Matter**2018**, 30, 055801. [Google Scholar] [CrossRef] - Paparazzo, E. On the curve-fitting of XPS Ce(3d) spectra of cerium oxides. Mater. Res. Bull.
**2011**, 46, 323–326. [Google Scholar] [CrossRef] - 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] - Gabáni, S.; Flachbart, K.; Pavlík, V.; Herrmannsdorfer, T.; Konovalova, E.; Paderno, Y.; Briančin, J.; Trpčevská, J. Magnetic properties of Sm
_{1−x}B_{6}and Sm_{1−x}La_{x}B_{6}solid solutions. Czechoslov. J. Phys.**2002**, 52, A225–A228. [Google Scholar] [CrossRef] - Nickerson, J.C.; White, R.M.; Lee, K.N.; Bachmann, R.; Geballe, T.H.; Hull, G.W. Physical properties of SmB
_{6}. Phys. Rev. B**1971**, 3, 2030–2042. [Google Scholar] [CrossRef] - Tanaka, T.; Nishitani, R.; Oshima, C.; Bannai, E.; Kawai, S. The preparation and properties of CeB
_{6}, SmB_{6}, and GdB_{6}. J. Appl. Phys.**1980**, 51, 3877. [Google Scholar] [CrossRef] - Ciomaga Hatnean, M.; Lees, M.R.; Ahmad, T.; Balakrishnan, G. University of Warwick: Coventry, UK, 2020; in preparation.

**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 ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ samples used for the physical properties measurements.

**Figure 2.**Powder X-ray diffraction patterns of ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ 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 $Pm\overline{3}m$ 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 ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$. 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 3.**(

**a**) Sm 4d XPS spectrum and (

**b**) Ce 3${d}_{3/2,5/2}$ XPS spectra collected for the ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ (x = 0.05, 0.10, and 0.20) crystal boules.

**Figure 4.**(

**a**) Temperature dependence of the $dc$ magnetic susceptibility, $\chi $ versus T, in the temperature range 1.8–100 K for the ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ ($x=0$, 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 $\chi $ versus T, on a logarithmic scale, in the temperature range 1.8–300 K. (

**b**) Temperature dependence of the reciprocal of the $dc$ susceptibility, ${\chi}^{-1}$ versus T, of ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ for a field applied along the [001] direction. The inset shows the normalised magnetic susceptibilities of ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ samples, with a magnetic field applied along the [001] direction. The $\chi /\chi $ (10 K) versus T data increase rapidly at low temperatures, but with no signature of long-range magnetic order, for all Ce concentrations.

**Figure 5.**Temperature dependence of the bulk $ac$ resistivity, $\rho $ versus T, in the temperature range 1.8–300 K for the ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ (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.

**Table 1.**Lattice parameters calculated from profile matching the powder X-ray diffraction patterns of the ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ ($x=0.05$, 0.10 and 0.20) crystals to the $Pm\overline{3}m$ 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${}_{1-\mathit{x}}$Ce${}_{\mathit{x}}$B${}_{6-\mathit{y}}$ | Chemical Composition | a | Study | |
---|---|---|---|---|

x | y | (Å) | ||

SmB${}_{6}$ | 0 | 0 | 4.1340(2) | Present work |

Sm${}_{0.95}$Ce${}_{0.05}$B${}_{6}$ | 0.05 | 0 | 4.1351(2) | Present work |

Sm${}_{0.90}$Ce${}_{0.10}$B${}_{6}$ | 0.10 | 0 | 4.1384(2) | Present work |

Sm${}_{0.89}$Ce${}_{0.11}$B${}_{5.9}$ | 0.11 | 0.1 | 4.1358 | Ref. [21] |

Sm${}_{0.80}$Ce${}_{0.20}$B${}_{6}$ | 0.20 | 0 | 4.1393(2) | Present work |

Sm${}_{0.78}$Ce${}_{0.22}$B${}_{5.7}$ | 0.22 | 0.3 | 4.1378 | Ref. [21] |

Sm${}_{0.66}$Ce${}_{0.34}$B${}_{5.9}$ | 0.34 | 0.1 | 4.1399 | Ref. [21] |

Sm${}_{0.62}$Ce${}_{0.38}$B${}_{5.7}$ | 0.38 | 0.3 | 4.1403 | Ref. [21] |

Sm${}_{0.50}$Ce${}_{0.50}$B${}_{6}$ | 0.50 | 0 | 4.1418 | Ref. [21] |

Sm${}_{0.35}$Ce${}_{0.65}$B${}_{5.7}$ | 0.65 | 0.3 | 4.1421 | Ref. [21] |

Sm${}_{0.25}$Ce${}_{0.75}$B${}_{5.9}$ | 0.75 | 0.1 | 4.1424 | Ref. [21] |

Sm${}_{0.18}$Ce${}_{0.82}$B${}_{6}$ | 0.82 | 0 | 4.1418 | Ref. [21] |

Sm${}_{0.08}$Ce${}_{0.92}$B${}_{6}$ | 0.92 | 0 | 4.1412 | Ref. [21] |

CeB${}_{6}$ | 1.00 | 0 | 4.1407(1) | Present work |

**Table 2.**Chemical composition and valence of the Sm ions determined by EDX and XPS for the ${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ 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 Composition | Sm:B Ratio | Sm:B Ratio | Sm Valence | |
---|---|---|---|---|

Present Work | Literature | |||

(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) | |

${\mathrm{Sm}}_{1-\mathit{x}}{\mathrm{Ce}}_{\mathit{x}}{\mathrm{B}}_{6}$ | x | x | Sm 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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## Share and Cite

**MDPI and ACS Style**

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 SmB_{6}. *Crystals* **2020**, *10*, 827.
https://doi.org/10.3390/cryst10090827

**AMA Style**

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 SmB_{6}. *Crystals*. 2020; 10(9):827.
https://doi.org/10.3390/cryst10090827

**Chicago/Turabian Style**

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 SmB_{6}" *Crystals* 10, no. 9: 827.
https://doi.org/10.3390/cryst10090827