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[Kazuaki Kobayashi](https://orcid.org/0000-0002-3440-5730), [Masato Shimono](https://orcid.org/0000-0003-2386-4111), [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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This is the Accepted Manuscript version of an article accepted for publication in Japanese Journal of Applied Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.35848/1347-4065/add0bc.[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Various magnetic properties of <i>M</i>-doped CoSb<sub>3</sub> (<i>M</i> = Sc, Ti, V, and Mn) thin films](https://mdr.nims.go.jp/datasets/2b7b9edb-b41e-4ea5-9dd1-102326454a9b)

## Fulltext

Various Magnetic Properties of M-doped CoSb3 (M = Sc, Ti, V,and Mn) Thin FilmsKazuaki Kobayashi1 ∗, Masato Shimono1, and Takao Mori1,21Research Center for Materials Nanoarchitechtonics (MANA), National Institute for Materials Science,Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan2Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki305-8671, JapanM-doped CoSb3 and related compound thin films (M = Sc, Ti, V, and Mn) have been calculated inorder to investigate their electronic and magnetic properties by using the total energy calculation method.All calculated thin films are free-standing in the supercell and their internal structures are fully relaxed. Avacuum region and slab as a thin film were periodically repeated in the supercell. We considered symmetricand unusual slab structures. Various dopants (Sc, Ti, V, and Mn) are considered in order to search novelelectronic and magnetic properties and to compare them with each other. We have found various magneticproperties. Although V and Mn dopants have large magnetic moments, those of Sc and Ti dopants arequite small with the exception of one Ti doped case. One of the magnetic states in the Ti-doped unusualthin films is antiferromagnetic. As a result of calculations, total magnetic moments of thin films and themagnetic moment of Mn dopant are enhanced in the unusual thin film case. Most thin films calculatedin the present work have ferromagnetic properties. The total energies of the ferromagnetic thin films arelower than those of the nonmagnetic thin films with the exception of Sc- and Ti-doped cases. The magneticproperties generated by the dopants depend on their atomic kinds and positions.∗KOBAYASHI.Kazuaki@nims.go.jp11. IntroductionCoSb3 (bulk) is a famous skutterudite compound and its thin films have been investi-gated both theoretically and experimentally.1–11) Bulk CoSb3 (Im3̄ crystal symmetry) isa semiconductor and its magnetic property is nonmagnetic. In the previous work, Si- andTe-doped CoSb3 (skutterudite) compounds under high pressure9) and Cr-doped CoSb3thin films10) have been extensively investigated in detail. In addition to above studies, alarge number of experimental and theoretical studies12–37) of CoSb3 bulk and thin filmshave been devoted to elucidate and control their electronic properties. CoSb3 thin filmshave been studied for potential and useful thermoelectric materials.13, 15, 19–28, 30–33, 36)Furthermore, the electronic states of CoSb3 thin films12–28, 30–33, 36) are nonmagnetic.Therefore, there is a general lack of studies on magnetic CoSb3 thin films.We focus on the CoSb3 thin films with transition metal dopants in this work. A thinfilm is one of the typical nanostructures. It is expected to realize novel electronic andmagnetic properties of transition metal atom doped CoSb3 thin films to enhance thethermoelectric properties.M-doped CoSb3 and related compound thin films (M= Sc, Ti,V, and Mn) have been considered and their electronic, lattice, and magnetic propertieswere obtained and investigated vigorously in this work. Previously, we have alreadystudied the magnetic properties of Cr-doped CoSb3 thin films.10) The purpose of thiswork is to find the new and novel feature of electronic and magnetic properties of CoSb3thin films with dopants (Sc, Ti, V, and Mn). These dopants (Sc, Ti, V, Cr,10) and Mn)have been investigated systematically owing to the various numbers of valence electronsas Sc (3d14s2), Ti (3d24s2), V (3d34s2), Cr10) (3d54s1), and Mn (3d54s2) to compare theirelectronic and magnetic properties with each other. We have found various magneticproperties and they are expected to control and tune the electronic properties aroundthe Fermi level. This will lead to enhancing the thermoelectric properties.38)We considered two slab structures as symmetric and unusual in this work. Theyhave been used in the previous work.10) Total magnetic moments of the “unusual” slabstructures are remarkably enhanced. This trend is consistent with the previous results.10)An analysis of Stoner’s criterion39–43) for magnetic properties of most thin films havebeen investigated in this work. The total and partial densities of states (TDOSs andPDOSs) at the Fermi level in the nonmagnetic states are fairly important to analyzethe stability of magnetic properties using Stoner’s criterion.22. Calculation MethodOur code44, 45) was used in this work. It is the electronic structure calculation code usingthe optimized pseudopotential,46, 47) which is based on the local density approximation(LDA) in density functional (DF) theory.48, 49) The exchange-correlation formula byPerdew and Zunger50, 51) was considered. Pseudopotentials46, 47) of Sc, Ti, V, Mn, Co,and Sb were used. Their nonlocal parts were tuned into Kleinman-Bylander separableforms52) without ghost bands. Nonlinear core corrections53) were considered in Sc, Ti,V, and Mn pseudopotentials. The wave functions were expanded in plane waves and thecutoff energy for them was set at 81 Ry. The number of k-points for sampling (Nk) was16 (= 4×4×1) in the whole Brillouin zone. The magnetic moments were obtained fromthe electron density differences between majority and minority spin states. The TDOSsand PDOSs were obtained from the electronic band structures.54) We have assumeda periodically repeated slab model, where slab and vacuum regions were periodicallyrepeated and the slab is free-standing in the supercell. The internal atoms in the slabwere governed by Hellmann-Feynman forces.55, 56) These repeated slabs correspond tothin films and their internal atoms were structurally optimized where the maximumforce acting on each atom is less than 2.0 × 10−3 Ry/Bohr.We considered two slab structures in the present work. One is constructed fromthe crystal structure of bulk skutterudite. The calculated equilibrium lattice constantof bulk CoSb3 (skutterudite) are 8.953 Å (9.036 Å[Experiment]5)) and the number ofatoms in the primitive unit cell is 16. This slab consists of the cubic unit cell (= 2primitive unit cells) and one Sb layer (= 4 atoms) and its number of atoms is 36 (seeFig. 1 (a)). Its composition is Co7M1Sb28 (M-doped atoms as M = Sc, Ti, V, and Mn)and slab structure is symmetric. The other which corresponds to the related compoundwas constructed accidentally in the process of constructing the CoSb3 slab.10) Its com-position as Co7M1Sb24 (M-doped atoms as M = Sc, Ti, V, and Mn) was considered. Itsslab structure is asymmetric and unusual and its atom number in the supercell is 32.Figures 1 (a) and (b) show above two slab structures without dopants in the supercellwhere some atoms are duplicated due to periodicity in depicting the slab structureshereafter. Co atoms are numbered as shown in Figs. 1 (a) and (b). The M-doped sitecorresponds to that of the Co atom (“1”). We denote Co atom (“1”) as Co (1), Co atom(“2”) as Co (2), etc. hereafter. These symmetric and unusual slab structures are thesame as previous work.10) We denote these slabs as M-doped CoSb3 (symmetric) and3M-doped CoSb3 (unusual) (M = Sc, Ti, V, and Mn) hereafter. Cutoff energy, numberof k-points, and number of atoms are listed in Table I.3. Results and Discussion3.1 StabilityWe calculated nonmagnetic (NM) and ferromagnetic (FM) cases where T = 0 K inthe DFT-LDA calculation. Slab structures in the supercell are fully relaxed. Figures2 and 3 are bird’s eye views of Sc-doped and Ti-doped CoSb3 (unusual) thin films innonmagnetic and ferromagnetic states, respectively. Those of Sc- and Ti-doped CoSb3(symmetric) thin films in nonmagnetic and ferromagnetic states are shown in Fig. 4.The total energy differences (∆EFM−NM) and average atomic position differences peratom (∆DFM−NM) between the nonmagnetic and ferromagnetic cases are listed in Ta-ble I. Their total magnetic moments are also shown in Table I. ∆EFM−NM values ofCoSb3 (symmetric),10) Sc-doped CoSb3 (symmetric), and Ti-doped CoSb3 (symmetric)thin films are fairly small within 0.03 eV. Therefore, their total magnetic momentsin the ferromagnetic cases are also small within approximately 0.04 µB and they aresubstantially equal to nonmagnetic. µB is the Bohr magneton. ∆EFM−NM values ofthe unusual thin films are energetically lower than those of the symmetric thin films.∆DFM−NM values of the unusual thin films are fairly larger than those of the symmetricthin films. Larger ∆DFM−NM values lead to more stable slab structures in the ferromag-netic unusual thin films. In unusual cases, ferromagnetic states are more favorable thannonmagnetic states with the exception of Sc doped case. The nonmagnetic Sc-dopedCoSb3 (unusual) thin film is energetically more stable by 3.61 eV than the ferromagneticcase. The relaxed structure of the nonmagnetic Sc-doped CoSb3 (unusual) thin film isremarkably different from other unusual cases as shown in Figs. 2 (a) and 3 (a). It leadsto more stable structure in the relaxation since the unusual thin film has high degrees ofstructural freedom. This is inconsistent with the relaxed structure of the ferromagneticSc-doped CoSb3 (unusual) thin film. Further consideration is necessary to obtain moresuitable relaxed structure of the nonmagnetic Sc-doped CoSb3 (unusual) thin film.The relaxed symmetric thin films with dopants are structurally similar to each otheras shown in Fig. 4. This trend is consistent with other dopant cases (Ti [see Figs. 4(c) and (d)], V, and Mn [see Fig. S1 in supplementary data] ). Although the relaxedunusual thin films with dopants (Ti, V, and Mn) are also structurally similar to eachother, the relaxed structures of nonmagnetic unusual thin films are slightly different4from those of ferromagnetic thin films as shown in Figs. 3 (a) and (b). The evidentlydifferent atomic positions between Figs. 3 (a) and (b) are labeled by red numbers andthose between Figs. 3 (b) and (c) are labeled by red (1 and 6) and black numbers(11). The ∆DFM−NM between Figs. 3 (a) and (b) is 0.571 Å (see Table I) and that ofthe Ti-doped CoSb3 (symmetric) thin film is 0.006 Å. The relaxed unusual thin filmswith dopants (V and Mn) are shown in Fig. S2 (see supplementary data) and evidentlydifferent atomic positions between NM and FM cases are labeled by red numbers. Thesedifferences are independent of the atomic kind of dopant.3.2 Magnetic momentsAll the calculated thin films in this work are metallic regardless of their magnetic andlattice structures. The total magnetic moments and magnetic moments of dopants (Sc,Ti, V, Cr,10) and Mn) are shown in Table II. The magnetic moments of V and Mn arelarge and those of Sc and Ti are fairly small within approximately 0.1 µB in all caseswith the exception of the replaced case. A detailed description of the replaced case willbe mentioned in the later. Total magnetic moments of the ferromagnetic unusual thinfilms are large. The magnetic moments of Cr10) and Mn dopants are enhanced in theunusual thin film cases from Table II although that of V dopant decreases slightly inthe unusual thin film. Although the magnetic moments of V and Mn dopants in thesymmetric cases are large, those of Co and Sb are small and less than 0.16 µB (absolutevalue).To confirm these magnetic properties, the magnetic moment of each atom in theV- and Mn-doped CoSb3 (unusual) thin films is shown in Figs. 5 and 6. From Figs. 5and 6, the V and Mn dopants in the CoSb3 (unusual) thin films have large magneticmoments. A dopant is substituted for Co (1) in Co (“1”, “4”, “6”, and “7”) atoms as“lower” (see Fig. 1 and insets of Figs. 5 and 6, see Fig. 3 for numbered Sb atoms).The figures 5 and 6 clearly show that the magnetic moments of V and Mn dopants andCo (“2”, “3”, “5”, and “8”) as “upper” (see Fig. 1) are large. Those of other three Coatoms as “Co (lower)” and Sb atoms are fairly small and negligible in all cases.The magnetic moments of V, Cr,10) and Mn dopants in the unusual cases are largealthough their positions correspond to those of Co (1) and the unusual thin films areenergetically quite unfavorable.10) The magnetic moments of Sc and Ti dopants whosepositions correspond to Co (1) are small regardless of their thin film structures. There-fore, we focus on structurally relaxed ferromagnetic Sc- and Ti-doped CoSb3 (unusual)5thin films as initial structures. We replace the Sc (1) and Ti (1) dopants with Co (2)in ferromagnetic unusual cases to analysis the variation of their magnetic properties asshown in Fig. 1 (c), respectively. The thin film structures with the replacements arestructurally relaxed. The magnetic moment of Co (2) is large before replacing. Fromtable II, the magnetic moments of the replaced Co atoms (= Co (1)) without relaxationare large and those are fairly decreased with less than 0.15 µB after relaxation. Themagnetic moments of the replaced Sc atom with and without relaxation are small withless than 0.1 µB (absolute value) as shown in Fig. S3 (see supplementary data). In con-trast, the magnetic moments of the replaced Ti atom without and with relaxation areantiferromagnetic and their absolute values are large as shown in Fig. 7 and table II.Therefore, the total magnetic moment of the unusual thin film replaced Ti (1) with Co(2) after structural relaxation is smallest in the unusual thin films. The antiferromag-netic behavior in this work is induced by the Ti dopant. The total energies of unusualthin films with the replacement of Sc (1) - Co (2) and Ti (1) - Co (2) are lower by 0.93eV and 0.30 eV than those of Sc- and Ti-doped unusual thin films without replacement,respectively. This replacement is almost equal to the substitution of Co (2) for dopantin the CoSb3 thin film. It is revealed that the magnetic properties of dopants are variedby their atomic kinds and positions. In particular, the magnetic state of the replacedTi dopant indicates antiferromagnetic behavior. As for magnetic properties, there is adistinctly difference among Sc, Ti, V, Cr,10) and Mn. Their numbers of valence electronsmay play a important role. Therefore, further investigations will be necessary to clarifythe mechanism of the antiferromagnetic behavior in the Ti doped case and other variousmagnetic properties.3.3 TDOS and PDOSWe calculated the total and partial densities of states (TDOSs and PDOSs) of thestructurally relaxed thin films in this work. The TDOSs and PDOSs for the Mn-dopedCoSb3 (symmetric) and (unusual) thin films are plotted in Fig. 8. The TDOSs andPDOSs of Sc- and Ti-doped CoSb3 (unusual) thin films in nonmagnetic cases are shownin Figs. S4 and S5, respectively (see supplementary data). The TDOSs and PDOSs ofSc-, Ti-, and V-doped CoSb3 (symmetric) thin films in ferromagnetic cases are shownin Figs. S6, S7, and S8, respectively (see supplementary data). The TDOS and PDOSsof V-doped CoSb3 (unusual) thin films in the ferromagnetic case are shown in Fig. S9(see supplementary data). The features of TDOSs and PDOSs in each symmetric (see6Figs. 8 (b), S6, S7, and S8) or unusual (see Figs. 8 (d), 9 (a), 10 (a), and S9) thinfilm are similar to each other. This is consistent with the similarity between relaxedthin film structures. The PDOS of Mn is remarkably spin polarized in the symmetriccase although the PDOSs of Co and Sb are almost unpolarized as shown in Fig. 8(b). In contrast, the PDOSs of Mn and Co are fairly polarized in the unusual thinfilm as shown in Fig. 8 (d). These trends are the same for V-doped and Cr-doped10)CoSb3 (symmetric) and (unusual) thin films. The TDOSs and PDOSs of Sc- and Ti-doped CoSb3 (unusual) thin films in ferromagnetic cases are shown in Figs. 9 and 10,respectively. The replacement cases are also plotted in Figs. 9 (b) and 10 (b). ThePDOSs of Sc and Ti are almost unpolarized in all cases (see Figs. 9 (a), 9 (b), 10 (a),S6, and S7) with the exception of the replacement of Ti (1) -Co (2). The PDOS of Ti(2) in the thin film with the replacement of Ti (1) - Co (2) is antiferromagneticallypolarized in Fig. 10 (b).The PDOSs of Sb at the Fermi level in the nonmagnetic Mn-doped CoSb3 (symmet-ric) thin films are larger than those of Co as shown in Fig. 8 (a) (see inset). In contrast,the contribution of both PDOSs of Co and Sb at the Fermi level in nonmagnetic unusualand ferromagnetic (minority spin) unusual thin films are large and nearly equal to eachother as shown in Figs. 8 (c) and (d) (see insets). This trend is consistent with otherdoped cases (Sc, Ti, V [see Fig. S9], and Cr10)) and inconsistent with the Fe2VAl thinfilm cases57) where Fe states are dominated at the Fermi level.3.4 Stoner’s criterionWe analyze the stability of the ferromagnetic states using the Stoner’s criterion39–43)as a rough estimate. In this criterion, the DOS per spin at the Fermi level (D(Ef)) isan important factor. We calculated the D(Ef) values of thin films with dopants (Sc, Ti,V, Cr,10) Mn, and Co10)) to clarify the stability of the ferromagnetism. We calculatedID(Ef), where I is the exchange parameter,40) to determine if Stoner’s criterion is satis-fied. The ID(Ef) value greater than one (ID(Ef) > 1) is favorable for ferromagnetism.We used the values43) of exchange parameters (I, see Table III) of Sc, Ti, V, Cr, Mn, andCo. They are insensitive to the chemical environment41) because they depend primarilyon intra-atom interactions. The calculated ID(Ef) values are tabulated in Table III.The ID(Ef) values of bulk Sc (bcc), Sc (fcc), Sc (hcp), Ti (hcp), V (bcc), Cr (bcc), Mn(fcc), Co (fcc), and Co (hcp) are obtained and most of them are consistent with the cal-culated magnetic properties with the exception of Co (fcc) and Sc (bcc). The magnetic7states of Sc (bcc) is ferromagnetic although Sc (bcc) is energetically more unfavorablethan Sc (fcc) and Sc (hcp). In the previous work,10) ID(Ef) value of Co (hcp) was 0.9,that is 1.2 in the present work as a result of recalculation. The ferromagnetic states ofbulk Sc (fcc), Sc (hcp), Ti (hcp), V (bcc), and Cr (bcc)10) are unstable and they areconsistent with the ID(Ef) value smaller than one.From Table III, the ID(Ef) values in the nonmagnetic cases are 0.1 ∼ 0.7 and theyare smaller than those (0.8 ∼ 1.2) in the ferromagnetic cases with the exception ofthe Mn dopant in the symmetric thin film (ID(Ef) = 0.5). The smallest ID(Ef) value(0.1) of Sc dopant in the Sc-doped CoSb3 (unusual) thin film may be invalid becauseits relaxed structure is quite different from that of the ferromagnetic case as mentionedabove. The magnetic moments of V, Cr,10) and Mn dopants are large and ferromagneticin all thin film cases. The ID(Ef) values of V, Cr,10) and Mn dopants (symmetric) andCr10) and Mn dopants (unusual), and Sc (bcc) and Co (fcc) bulk in Table III do notsatisfy Stoner’s criterion. However, their ID(Ef) values (0.8 ∼ 0.9) are so close to onethat they imply ferromagnetic states are stable. This inconsistency leads to beyond theStoner theory. Some values of Cr, Co, CoSb3 and Cr-doped CoSb3, which are listed inTables I, II, and III, are improved and slightly different from the previous work10) asthe results of recalculation using denser energy meshes for all cases and denser k-pointmeshes for bulk metals. The differences of recalculations are fairly small within 0.08 µB(or within 10 %) in the magnetic moments.4. SummaryIn this work, the electronic and magnetic properties of M-doped CoSb3 thin films (M= Sc, Ti, V, and Mn) have been calculated. Various magnetic properties have beenpresented in this work. It is found that the ferromagnetic states for most thin filmsare energetically more stable. It is revealed that the total magnetic moments of thinfilms and the magnetic moments of the Mn dopant are enhanced in the unusual thinfilms. This trend is consistent with previous Cr-doped case.10) It may be significant tobreak the symmetry of the thin films for varying the magnetic properties. The magneticmoments of Sc and Ti dopants and Co (lower) and Sb atoms are fairly small with theexception of the Ti (1) - Co (2) replacement case. The replacement of Ti (1) - Co (2)with structural relaxation induces the antiferromagnetic state of Ti dopant althoughthe magnetic moments of Sc in the replacement of Sc (1) - Co (2) with and withoutrelaxation are fairly small. Various magnetic behavior is remarkable and it is expected8to control and tune the electronic and magnetic properties around the Fermi level. Inparticular, TDOS shapes at the Fermi level are very important for the thermoelectricproperties. This will be enhanced the thermoelectric properties.38)The stability of the ferromagnetic states for dopants in the thin films is analyzedusing Stoner’s criterion39–43) as a rough estimate. It is not sufficient to describe theferromagnetic states using Stoner’s criterion although their ID(Ef) values (0.8 ∼ 1.2)are larger than those (0.1 ∼ 0.7) in the nonmagnetic cases with the exception of theMn-doped case. The analysis of Stoner’s criterion in this work is possible to describethe magnetic properties qualitatively to a certain extent, whereas it is still insufficient.Therefore, it is necessary to further investigation to clarify the mechanism of the largemagnetic moments in the ferromagnetic cases.More extensive calculations of various slab structures, defects, dopants, co-doping,11, 36, 37) and introducing disorder are needed to tune and enhance the magneticmoments in the thin films. The slabs were terminated by Sb atom layers in all thin filmsand a layer number of each slab was not varied in the present calculations. Althoughother asymmetric slab cases have been investigated in the previous work,10) they are notconsidered in this work. It is necessary to consider Co-terminated and/or other variousthickness of slab cases in order to investigate the stability of the thin films in the futurenext task.It is not clear and needs further consideration to the origin of antiferromagnetic be-havior of the Ti dopant (Ti (2)) in the Ti (1) - Co (2) replacement case. It is necessaryto replace V, Cr, and Mn dopants with Co atoms to investigate and compare with thepresent results of Sc (1) - Co (2) and Ti (1) - Co (2) replacements. In addition, it isexpected that the experimental synthesis and observation of thin films with transitionmetal dopants calculated in this work will be realized. Their thermoelectric proper-ties (thermal conductivity, Seebeck coefficient, and power factor, etc.) will be obtainedtheoretically in the future task.AcknowledgmentsThis work was supported by the JST-Mirai Program, Grant Number JPMJMI19A1,Japan. 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Bird’s eye views of (a) the CoSb3 (symmetric) thin film, (b) the CoSb3(unusual) thin film, and (c) the CoSb3 (unusual) thin film with the replacement of Co(1) - Co (2) indicated by the red arrow. Co and Sb are depicted in blue and green,respectively. Co atoms are numbered as “1” ∼ “8”. “Lower” and “Upper” indicate thesites of “1, 4, 6, and 7” and “2, 3, 5, and 8”, respectively.Fig. 2. Bird’s eye views of the (a) nonmagnetic, (b) ferromagnetic, and (c) replace-ment of Sc (1) - Co (2) in Sc-doped CoSb3 (unusual) thin films. Sc, Co, and Sb aredepicted in pink, blue, and green, respectively.Fig. 3. Bird’s eye views of the (a) nonmagnetic, (b) ferromagnetic, and (c) replace-ment of Ti (1) - Co (2) in Ti-doped CoSb3 (unusual) thin films. Ti, Co, and Sb aredepicted in grey, blue, and green, respectively. The evidently different atomic positionsbetween (a) and (b) are labeled by red numbers and those between (b) and (c) arelabeled by red (1 and 6) and black numbers (11).Fig. 4. Bird’s eye views of the (a) nonmagnetic Sc-, (b) ferromagnetic Sc-, (c) non-magnetic Ti-, and (d) ferromagnetic Ti-doped CoSb3 (symmetric) thin films. Sc, Ti,Co, and Sb are depicted in pink, grey, blue, and green, respectively.Fig. 5. Magnetic moment of each atom in the V-doped CoSb3 (unusual) thin film. V,Co, and Sb atoms are denoted by 1, 2-8, and 9-32 on the horizontal axis, respectively.The inset shows the bird’s eye view of the V-doped CoSb3 (unusual) thin film whereV and Co atoms are numbered. V, Co, and Sb are depicted in red, blue and green,respectively.Fig. 6. Magnetic moment of each atom in the Mn-doped CoSb3 (unusual) thinfilm. Mn, Co, and Sb atoms are denoted by 1, 2-8, and 9-32 on the horizontal axis,respectively. The inset shows the bird’s eye view of the Mn-doped CoSb3 (unusual) thinfilm where Mn and Co atoms are numbered. Mn, Co, and Sb are depicted in magenta,blue and green, respectively.Fig. 7. Magnetic moment of each atom in the Ti-doped CoSb3 (unusual) thin filmwith the replacement. The Ti dopant is denoted by 2 on the horizontal axis. Co atomsare denoted by 1 and 3-8 on the horizontal axis. Sb atoms are denoted by 9-32 on thehorizontal axis. The inset shows the bird’s eye view of the Ti-doped CoSb3 (unusual)thin film with the replacement where Ti and Co atoms are numbered. Ti, Co, and Sbare depicted in grey, blue and green, respectively.Fig. 8. Total and partial DOSs (states/eV cell) of (a) nonmagnetic and (b) ferro-magnetic Mn-doped CoSb3 (symmetric) thin films. Total and partial DOSs (states/eV13cell) of (c) nonmagnetic and (d) ferromagnetic Mn-doped CoSb3 (unusual) thin films.The DOS curves of Total, Mn, Co, and Sb are plotted by magenta, red, blue, and green,respectively. The vertical scale is “states/eV cell” and linear. The Fermi level (Ef) isindicated by “0” on the horizontal axis. The insets show the expanded DOS around theFermi level.Fig. 9. Total and partial DOSs (states/eV cell) of (a) ferromagnetic and (b) replace-ment of Sc (1) - Co (2) in Sc-doped CoSb3 (unusual) thin films. The DOS curves ofTotal, Sc, Co, and Sb are plotted by magenta, red, blue, and green, respectively. Thevertical scale is “states/eV cell” and linear. The Fermi level (Ef) is indicated by “0” onthe horizontal axis.Fig. 10. Total and partial DOSs (states/eV cell) of (a) ferromagnetic and (b) re-placement of Ti (1) - Co (2) in Ti-doped CoSb3 (unusual) thin films. The DOS curvesof Total, Ti, Co, and Sb are plotted by magenta, red, blue, and green, respectively. Thevertical scale is “states/eV cell” and linear. The Fermi level (Ef) is indicated by “0” onthe horizontal axis.14Table I. Total energy differences, average atomic position differences, and total magnetic moments.Thin films, cutoff energy [Ry] (Cutoff), number of k-points (Nk), number of atoms (Na) in thesupercell, magnetic states (“MS”; NM: Nonmagnetic, FM: Ferromagnetic), total energy differencesper the supercell (= cell) (eV/cell) as ∆EFM−NM, average atomic position differences per atom (Å)between the nonmagnetic and ferromagnetic cases as ∆DFM−NM, and total magnetic moment values(µB) as “Total”. Negative (positive) values of ∆EFM−NM indicate more stable (more unstable).Thin film Cutoff Nk Na MS ∆EFM−NM ∆DFM−NM Total (µB)CoSb3 (symmetric)10) 81 16 36 NM 0.0 - -CoSb3 (symmetric)10) 81 16 36 FM 0.001 0.002 0.033Sc-doped CoSb3 (symmetric) 81 16 36 NM 0.0 - -Sc-doped CoSb3 (symmetric) 81 16 36 FM -0.03 0.120 0.021Ti-doped CoSb3 (symmetric) 81 16 36 NM 0.0 - -Ti-doped CoSb3 (symmetric) 81 16 36 FM 0.005 0.006 0.042V-doped CoSb3 (symmetric) 81 16 36 NM 0.0 - -V-doped CoSb3 (symmetric) 81 16 36 FM -0.35 0.028 2.000Cr-doped CoSb3 (symmetric)10) 81 16 36 NM 0.0 - -Cr-doped CoSb3 (symmetric)10) 81 16 36 FM -0.52 0.049 2.940Mn-doped CoSb3 (symmetric) 81 16 36 NM 0.0 - -Mn-doped CoSb3 (symmetric) 81 16 36 FM -0.27 0.042 2.449CoSb3 (unusual)10) 81 16 32 NM 0.0 - -CoSb3 (unusual)10) 81 16 32 FM -2.40 0.205 8.291Sc-doped CoSb3 (unusual) 81 16 32 NM 0.0 - -Sc-doped CoSb3 (unusual) 81 16 32 FM 3.61 1.168 8.485Ti-doped CoSb3 (unusual) 81 16 32 NM 0.0 - -Ti-doped CoSb3 (unusual) 81 16 32 FM -1.87 0.571 8.639V-doped CoSb3 (unusual) 81 16 32 NM 0.0 - -V-doped CoSb3 (unusual) 81 16 32 FM -1.94 0.511 10.001Cr-doped CoSb3 (unusual)10) 81 16 32 NM 0.0 - -Cr-doped CoSb3 (unusual)10) 81 16 32 FM -2.04 0.442 11.100Mn-doped CoSb3 (unusual) 81 16 32 NM 0.0 - -Mn-doped CoSb3 (unusual) 81 16 32 FM -1.80 0.448 11.65515Table II. Total magnetic moments and magnetic moments of dopants. Thin films, total magneticmoment values (µB) of thin films as “Total”, magnetic moment values (µB/atom) of dopants as“Dopant”, and magnetic moment values (µB/atom) of replaced Co atoms as “Replaced Co atom”.Thin film Total Dopant Replaced Co atomCoSb3 (symmetric)10) 0.033 - -Sc-doped CoSb3 (symmetric) 0.021 0.0006 -Ti-doped CoSb3 (symmetric) 0.042 -0.041 -V-doped CoSb3 (symmetric) 2.000 2.163 -Cr-doped CoSb3 (symmetric)10) 2.940 3.071 -Mn-doped CoSb3 (symmetric) 2.449 3.005 -CoSb3 (unusual)10) 8.291 - -Sc-doped CoSb3 (unusual) 8.485 0.006 -Ti-doped CoSb3 (unusual) 8.639 0.102 -V-doped CoSb3 (unusual) 10.001 1.970 -Cr-doped CoSb3 (unusual)10) 11.100 3.328 -Mn-doped CoSb3 (unusual) 11.655 3.601 -Sc-Co replaced (unusual, nonrelaxed) 6.704 -0.090 2.179Sc-Co replaced (unusual, relaxed) 5.711 -0.059 0.097Ti-Co replaced (unusual, nonrelaxed) 5.015 -1.636 1.424Ti-Co replaced (unusual, relaxed) 3.685 -1.969 0.133Fig. 1. Bird’s eye views of (a) the CoSb3 (symmetric) thin film, (b) the CoSb3 (unusual) thin film,and (c) the CoSb3 (unusual) thin film with the replacement of Co (1) - Co (2) indicated by the redarrow. Co and Sb are depicted in blue and green, respectively. Co atoms are numbered as “1” ∼ “8”.“Lower” and “Upper” indicate the sites of “1, 4, 6, and 7” and “2, 3, 5, and 8”, respectively.16Table III. Stoner’s criterion. Atom, exchange parameters (I, eV), density of states per spin at theFermi level (D(Ef), states/eV atom spin), the values of ID(Ef), “SC”, and “calc.”. “SC” indicateswhether Stoner’s criterion is satisfied (ferromagnetic, FM) or not satisfied (nonmagnetic, NM).“calc.” indicates the calculated magnetic moment (µB/atom) of bulk and dopants. “(FM)” indicatesthe ferromagnetic behavior where the calculated magnetic moment is greater than 0.7.Atom I (eV) D(Ef) ID(Ef) SC calc.Co(fcc)10) 0.9792 0.9 0.9 NM 1.97 (FM)Co(hcp)10) 0.9792 1.2 1.2 FM 1.88 (FM)Sc(bcc) 0.68 1.2 0.8 NM 0.72 (FM)Sc(fcc) 0.68 1.0 0.7 NM -Sc(hcp) 0.68 1.0 0.7 NM -Ti(hcp) 0.68 0.5 0.3 NM -V(bcc) 0.7072 0.9 0.6 NM 0.0003Cr(bcc)10) 0.7616 0.7 0.5 NM -Mn(fcc) 0.816 0.7 0.6 NM -Doped Sc atom (symmetric) 0.68 0.2 0.1 NM 0.0006Doped Ti atom (symmetric) 0.68 0.6 0.4 NM -0.041Doped V atom (symmetric) 0.7072 1.3 0.9 NM 2.163 (FM)Doped Cr atom (symmetric)10) 0.7616 1.2 0.9 NM 3.071 (FM)Doped Mn atom (symmetric) 0.816 0.6 0.5 NM 3.005 (FM)Doped Sc atom (unusual) 0.68 0.2 0.1 NM 0.006Doped Ti atom (unusual) 0.68 1.0 0.7 NM 0.102Doped V atom (unusual) 0.7072 1.5 1.1 FM 1.970 (FM)Doped Cr atom (unusual)10) 0.7616 1.2 0.9 NM 3.328 (FM)Doped Mn atom (unusual) 0.816 1.0 0.8 NM 3.601 (FM)17Fig. 2. Bird’s eye views of the (a) nonmagnetic, (b) ferromagnetic, and (c) replacement of Sc (1) -Co (2) in Sc-doped CoSb3 (unusual) thin films. Sc, Co, and Sb are depicted in pink, blue, and green,respectively.Fig. 3. Bird’s eye views of the (a) nonmagnetic, (b) ferromagnetic, and (c) replacement of Ti (1) -Co (2) in Ti-doped CoSb3 (unusual) thin films. Ti, Co, and Sb are depicted in grey, blue, and green,respectively. The evidently different atomic positions between (a) and (b) are labeled by red numbersand those between (b) and (c) are labeled by red (1 and 6) and black numbers (11).18Fig. 4. Bird’s eye views of the (a) nonmagnetic Sc-, (b) ferromagnetic Sc-, (c) nonmagnetic Ti-,and (d) ferromagnetic Ti-doped CoSb3 (symmetric) thin films. Sc, Ti, Co, and Sb are depicted inpink, grey, blue, and green, respectively.Fig. 5. Magnetic moment of each atom in the V-doped CoSb3 (unusual) thin film. V, Co, and Sbatoms are denoted by 1, 2-8, and 9-32 on the horizontal axis, respectively. The inset shows the bird’seye view of the V-doped CoSb3 (unusual) thin film where V and Co atoms are numbered. V, Co, andSb are depicted in red, blue and green, respectively.19Fig. 6. Magnetic moment of each atom in the Mn-doped CoSb3 (unusual) thin film. Mn, Co, andSb atoms are denoted by 1, 2-8, and 9-32 on the horizontal axis, respectively. The inset shows thebird’s eye view of the Mn-doped CoSb3 (unusual) thin film where Mn and Co atoms are numbered.Mn, Co, and Sb are depicted in magenta, blue and green, respectively.20Fig. 7. Magnetic moment of each atom in the Ti-doped CoSb3 (unusual) thin film with thereplacement. The Ti dopant is denoted by 2 on the horizontal axis. Co atoms are denoted by 1 and3-8 on the horizontal axis. Sb atoms are denoted by 9-32 on the horizontal axis. The inset shows thebird’s eye view of the Ti-doped CoSb3 (unusual) thin film with the replacement where Ti and Coatoms are numbered. Ti, Co, and Sb are depicted in grey, blue and green, respectively.21Fig. 8. Total and partial DOSs (states/eV cell) of (a) nonmagnetic and (b) ferromagneticMn-doped CoSb3 (symmetric) thin films. Total and partial DOSs (states/eV cell) of (c) nonmagneticand (d) ferromagnetic Mn-doped CoSb3 (unusual) thin films. The DOS curves of Total, Mn, Co, andSb are plotted by magenta, red, blue, and green, respectively. The vertical scale is “states/eV cell”and linear. The Fermi level (Ef) is indicated by “0” on the horizontal axis. The insets show theexpanded DOS around the Fermi level.22Fig. 9. Total and partial DOSs (states/eV cell) of (a) ferromagnetic and (b) replacement of Sc (1)- Co (2) in Sc-doped CoSb3 (unusual) thin films. The DOS curves of Total, Sc, Co, and Sb areplotted by magenta, red, blue, and green, respectively. The vertical scale is “states/eV cell” andlinear. The Fermi level (Ef) is indicated by “0” on the horizontal axis.23Fig. 10. Total and partial DOSs (states/eV cell) of (a) ferromagnetic, and (b) replacement of Ti(1) - Co (2) in Ti-doped CoSb3 (unusual) thin films. The DOS curves of Total, Ti, Co, and Sb areplotted by magenta, red, blue, and green, respectively. The vertical scale is “states/eV cell” andlinear. The Fermi level (Ef) is indicated by “0” on the horizontal axis.24