Site Mixing for Engineering Magnetic Topological Insulators

Site Mixing for Engineering Magnetic Topological Insulators

Yaohua Liu,1, ∗ Lin-Lin Wang,2 Qiang Zheng,3 Zengle Huang,4 Xiaoping Wang,1 Miaofang Chi,3 Yan

Wu,1 Bryan Chakoumakos,1 Michael A. McGuire,3 Brian C. Sales,3 Weida Wu,4 and Jiaqiang Yan3, †

1Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA2Division of Materials Science and Engineering, Ames Laboratory, Ames, IA 50011, USA

3Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA4Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA

(Dated: February 3, 2021)

S1. SINGLE CRYSTAL NEUTRONDIFFRACTION

Single crystal neutron diffraction data were collectedat 300 K using the beamline TOPAZ at the SpallationNeutron Source (SNS) to determine the average nuclearstructure. Low temperature measurements were per-formed at the beamline CORELLI at SNS and the Four-Circle Diffractometer (HB-3A) at the High Flux IsotopeReactor (HFIR) to determine the average magnetic struc-ture.

A. Nuclear structure Refinement

Previous studies reported the R3m space group forMnSb2Te4 from powder diffraction experiments. [1, 2].With the high resolution single crystal neutron diffrac-tion data collected at TOPAZ (300 K), we examined thecrystal structures of all three MnSb2Te4 single crystals.Figure S1 shows the refinement results using R3m forTN19K, TC24K and TC34K. Lowering the crystal sym-metry from R3m to its subgroup R3m or C2/m doesnot significantly improve the refinement; rather there arehigh correlated atomic positions and atomic displacementparameters, suggesting that a lower symmetry is unnec-essary to describe the average structure in the presenceof significant Mn/Sb site mixing. The R3m space groupis thus used for all structure refinements below.

B. Mn/Sb site mixing

Table S1 shows the comparison of the structural re-finements on the 300 K TOPAZ data assuming differ-ent chemical formula. All have the same fitting quality.However, the refinements suggest that all three sampleshave significant amount of Mn/Sb site mixing with slightdifferences in the numerical values. Importantly, they allfound more Mn ions on both Mn and Sb sites for sampleswith a ferromagnetic interlayer coupling. Detailed struc-tural refinement results are shown in Tables S2, S3, S4 for

∗ [email protected]† [email protected]

TN19K, TC24K and TC34K, respectively. With increas-ing Mn content, a-lattice parameter decreases slightlywhile c-lattice is less affected.

C. neutron diffraction patterns of TC24K above Tc

Figure S2 shows the neutron scattering patterns in the[H 1 L] plane of the TC24K sample collected at (a) 30 Kand (b) 6.5 K. The observed Bragg peaks match the scat-tering condition -H+K+L = 3n, as required by the spacegroup R3m for the nuclear reflections. The pattern col-lected at 6.5 K is also presented in the main text and it ispresented here to highlight the change cooling below TC .The diffraction pattern collected at 6.5 K is similar tothat collected at 30 K but the intensity of some peaks isenhanced as highlighted by the white arrows, suggestinga magnetic wavevector of kFM = (0 0 0).

D. magnetic structures: ordered moments on Mn,Sb

Reciprocal space mapping from the CORELLI datafound no highly structured diffuse scattering signal,which suggests that MnSb2Te4 remains in the R3m spacegroup at low temperatures. Low-temperature datasetswere collected for TN19K and TC24K. Partially due tothe unavoidable background scattering from the sampleenvironment, the datasets collected at both CORELLIand HB-3A contain much fewer peaks than the 300 KTOPAZ datasets. However, the average nuclear struc-tures determined from the CORELLI and HB-3A data forTN19K and TC24K suggest similar amounts of Mn/Sitesite mixing but with higher uncertainties in comparisonto the TOPAZ results. Table S5 shows the site mixingand ordered moments for TN19K refined using the for-mula A from neutron diffraction data collected at threedifferent beamlines. Interestingly, to achieve satisfactoryrefinements of the magnetic structure, one has to considerthe ordered moments on Mn,

Sb, as shown in Fig. S3 forboth TN19K and TC24K. For TN19K, the ordered mo-ments are 3.71(2) µB per MnMn and 3.46(8) µB per Mn,

Sbusing the chemical formula A and 3.95(2) µB per MnMn

and 3.18(7) µB per Mn,Sb using the chemical formula C.

For TC24K, the ordered moments are 4.08(7) µB perMnMn and 3.5(2) µB per MnSb for the chemical formulaA and 4.12(7) µB per MnMn and 3.3(2) µB per Mn,

Sb

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FIG. S1. (color online) The observed squared structure factors vs the calculated ones from the nuclear structure refinementsusing the space groups R3m for (a) TN19K, (b) TC24K and (c) TC34K, respectively. R1=3.22%, 5.33% and 5.76% for TN19K,TC24K and TC34K, respectively.

TN19K TC24K TC34Ktotal peaks(I ≥ 2δI) 7086 6151 1976

unique peaks forR1 (I ≥ 4δI) 705 666 529

Assumed Formula A B C A B C A B C# of parameters

(constraints) 15(0) 15(1) 16(1) 15(0) 15(1) 16(1) 15(0) 15(1) 16(1)R1 3.22% 3.22% 3.22% 5.33% 5.34% 5.34% 5.76% 5.76% 5.76%

SbSb 0.871(2) 0.871(2) 0.871(2) 0.849 (2) 0.847(2) 0.847(2) 0.842(3) 0.842(3) 0.842(3)Mn,

Sb 0.129(2) 0.129(2) 0.129(2) 0.151(2) 0.153(2) 0.153(2) 0.158(3) 0.158(3) 0.158(3)MnMn 0.588(2) 0.588(2) 0.549 (4) 0.645(2) 0.648(4) 0.637(6) 0.674(6) 0.674(4) 0.672(6)Sb.

Mn 0.412(2) 0.412(2) 0.387 (2) 0.335 (2) 0.352(4) 0.344(4) 0.326(3) 0.326(4) 0.324(3)TeTe 1 0.962(3) 1 1 0.989(3) 1 1 0.997(3) 1Sb,

Te 0 0.038(3) 0 0 0.011(3) 0 0 0.003(3) 0

TABLE S1. Comparison of the refinement quality for all three crystals using different assumed chemical formulas. Formula A:(Mn1−xSbx)(Sb1−yMny)2Te4, formula B: (Mn1−xSbx)(Sb1−yMny)2(TezSb1−z)4, and formula C: (MnxSby)(Sb1−zMnz)2Te4.Charge neutrality was assumed for formulas B and C using the nominal valance state, Mn2+ at Mn and Sb sites, Sb3+ at Mnand Sb sites, Sb3− at Te sites, and Te2− at Te sites.

Atom x y z occ. Ueq (A2) Wyck.Te1 0 0 0.13162(2) 1 0.01710(8) 6cTe2 0 0 0.29212(2) 1 0.02922(2) 6cSb 0 0 0.42559(2) 0.871(2) 0.02028(13) 6c

Mn,Sb 0 0 0.42559(2) 0.129(2) 0.02028(13) 6c

Mn 0 0 0 0.588(4) 0.008(5) 3aSb.

Mn 0 0 0 0.412(2) 0.008(5) 3a

TABLE S2. Refined structural parameters of TN19K. Thecomposition determined from the best fit is Mn0.84Sb2.16Te4and the lattice parameters are a = 4.2543(1) A, c =40.899(2) A, and V = 641.07(4) A3.

for the chemical formula C. The determined ordered mo-ments using different chemical formulas are slightly dif-ferent but agree with each other. We thus use formulaA in the main text to describe the chemical composition


Mn,Sb 0 0 0.42567(2) 0.150(2) 0.01888(19) 6c

Mn 0 0 0 0.635(2) 0.01888(19) 3aSb.

Mn 0 0 0 0.365(2) 0.01888(19) 3a

TABLE S3. Refined structural parameters of TC24K. Thecomposition determined from the best fit is Mn0.93Sb2.07Te4.The lattice parameters are a = 4.2510(2) A , c =40.907(3) A, and V = 640.17(6) A3 .

and occupancy. Table S6 summarizes the nonstoichiom-etry, site occupancy, and magnetic moments for all threecrystals.

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FIG. S2. (color online) Neutron scattering pattern in the [H 1 L] plane of the TC24K sample at (a) 30 K and (b) 6.5 K. Thewhite arrows highlight those Bragg peaks that have small nuclear scattering contributions and gain significant intensities frommagnetic diffraction below TC . The ring- and arc-like features are from the sample environment and sample mount.


Mn,Sb 0 0 0.42571(3) 0.158(3) 0.0156(3) 6c

Mn 0 0 0 0.674(4) 0.017(2) 3aSb.

Mn 0 0 0 0.326(4) 0.017(2) 3a

TABLE S4. Refined structural parameters of TC34K. Thecomposition determined from the best fit is Mn0.99Sb2.01Te4a = 4.2406(7) A , c = 40.826(10) A and V = 635.8(3) A3 .

TOPAZ(300 K)

CORELLI(6.5 K)

Four-Circle(4.5 K)

nuclear peaks(I ≥ 2δI) 7086 189 96

magnetic peaks(I ≥ 2δI) 0 153 35

SbSb 0.871(2) 0.881(6) 0.88(1)Mn,

Sb, p2 0.129(2) 0.119(6) 0.12(1)MnMn, p1 0.588(2) 0.587(7) 0.58(1)

Sb.Mn 0.412(2) 0.414(7) 0.42(1)

MnMn (µB/Mn) - 3.71(2) 3.9(1)Mn,

Sb (µB/Mn) - 3.46(8) 2.7(3)

TABLE S5. Comparison on the refined values on theantisite mixing and ordered moments on TN19K fromthe three neutron diffractometers using the formula A:(Mnp1Sb1−p1)(Sb1−p2Mnp2)2Te4.

S2. TUNABLE MAGNETIC ORDERINGTEMPERATURES

Figure S4a shows the temperature dependence of mag-netic susceptibility of MnSb2Te4 synthesized using dif-ferent ratios of starting elements. All three batches arehomogenized at 1000 ◦ for 12 hours and then annealedat 640 ◦ for a week. The atomic ratio of the start-ing composition is detailed in the figure. Changing the

FIG. S3. (color online) Comparison between the magneticstructure model without (a, c) and with (b, d) consideringordered moments on MnSb sites for the TN19K and TC24K.Refinement results suggests ordered moments of MnSb sites,which are antiparallel to the ordered moments on adjacentMnMnsites within each septuple layer.

Mn/Sb ratio is expected to vary the magnetic proper-ties. MnSb2Te4 crystals grown in this manner are rathersmall and the magnetic measurements were performedusing a cluster of small crystals with a random orienta-tion. The results suggest that TC can be tuned up toaround 50 K. We noticed that there is a small fraction ofunknown magnetic impurity for the composition startingwith Mn:Sb=1.3:1.7. Further increasing Mn content inthe starting materials increases the content of the impu-rity phase.

Figure S4b shows the magnetization measured at 2K in

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TABLE S6. Nonstoichiometry, site occupancy, and magnetic moments for all three crystals. The chemical formula is writtenas (Mnp1Sb1−p1)(Sb1−p2Mnp2)2Te4, where Te occupancy was fixed to be 1 and p1 and p2 are the site occupation of Mn atomsat Mn and Sb sites, respectively, determined from the 300 K TOPAZ data. The ordered moments (in µB/Mn) are determinedfrom the 6.5 K CORELLI data. The average moment within each septuple layer in the ferrimagnetic state was estimated as(mMn@Mn × p1 −mMn@Sb × 2p2)/(p1 + 2p2).

TN19K TC24K TC34KWDS/EDX Mn0.82Sb2.17 (WDS) Mn0.90Sb2.10 (WDS) Mn0.99Sb2.01 (EDS)

neutron Mn0.84Sb2.16 Mn0.93Sb2.07 Mn0.99Sb2.01

p1, Mn×Mn 0.588(2) 0.635(2) 0.674(4)p2, Mn,

Sb 0.129(2) 0.150(2) 0.158(3)

Ordered moment at 6.5K, Mn×Mn 3.71(2) 4.08(7) -Ordered moment at 6.5K, Mn,

Sb 3.46(8) 3.5(2) -Estimated Mseptuple 1.52(4) 1.65(8) -

Saturation moment at 2 K, Ms 1.95(2) 2.00(2) 1.98(2)

FIG. S4. (color online) (a) Temperature dependence of magnetic susceptibility of crystals measured in an applied magneticfield of 100 Oe in a field-cooled mode. (b) Field dependence of magnetization at 2 K.

applied magnetic fields up to 70 kOe. It is interesting thatall samples have a magnetization around 2 µB/Mn at 2 Kand 70 kOe. While detailed nonstoichiometry and atomicoccupancy need to be determined, it is reasonable to ex-pect that they determine the ordering temperature andsaturation moment. The sample with TC around 50 Khas a smaller magnetization possibly due to the presenceof the unknown magnetic impurity.

S3. TRANSPORT PROPERTIES

Figure S5 shows the temperature and field dependenceof the in-plane electrical resistivity, ρxx, measured in thetemperature range 2 K ≤ T ≤ 300 K with the electricalcurrent flowing in the ab-plane. All compounds show ametallic conducting behavior in the paramagnetic state.ρxx shows an abrupt enhancement cooling across TN forTN19K. In contrast, a cusp sitting around TC was ob-

served for TC24K and TC34K, which is similar to thatobserved for MnBi2Te4. All compounds show a nega-tive magnetoresistance in magnetic fields up to 80 kOeapplied along the crystallographic c-axis.

The Hall resistivity was measured at multiple tem-peratures in the temperature range 2 K - 300 K. Alinear field dependence is observed at all temperaturesfor all samples. Figure S6 shows the data collected at50 K and 250 K. The Hall coefficient shows little temper-ature dependence below room temperature. With theassumption that a single band dominates the Hall sig-nal, the coefficient at 250 K gives a carrier density of2.8×1020cm−3, and 3.7×1020cm−3, and 6.0×1020cm−3

for TN19K, TC24K, and TC34K, respectively.

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FIG. S5. (color online) Temperature dependence of in-planeelectrical resistivity with the electrical current flowing in theab-plane and a magnetic field applied along the crystallo-graphic c-axis.

S4. STEM

Figure S7 shows the intensity variation in Mn atomiccolumns along (001) planes indicating the presence ofatomic mixing. The intensity profiles shown in Fig. S7 bare obtained from the representative atomic planes of Teand Mn labeled in (a). Obviously, Mn atomic columnsshow a larger intensity variation than Te columns. Thisagrees with both our diffraction data and previous DFTcalculations[3] that there are significant amount of sitemixing at the Mn site but not at the Te site.

S5. DFT

Figure S8 shows the atomic configurations for half ofthe supercell of MnSb2Te4 with different site-mixing con-figurations. Also shown are two configurations in the

FIG. S6. (color online) Hall resistivity versus applied mag-netic field for temperatures at 50 K and 250 K with the elec-trical current in the ab-plane and the magnetic field along thec-axis.

FIG. S7. (color online) (a) STEM-HAADF images of TC24K.(b) Intensity variation in Mn and Te atomic columns.

larger (3×3×2) supercell with a smaller site-mixing ra-tio. Table S7 shows the energy difference between thefully relaxed FM-like and AFM-like magnetic order cal-culated in PBEsol+U and PBEsol+U+SOC.[4, 5] All thesupercell configurations with site-mixing prefer the FM-like magnetic order. Figure S9 shows the total densityof states (DOS) near EF of the FM-like and AFM-likemagnetic orders with different site-mixing configurations.Figure S10 shows the band structure assuming all mag-

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FIG. S8. (color online) MnSb2Te4 atomic configurations forhalf of the supercell of (a) (1×1×2)-AS0 without site mixing,(b) (2×2×2)-AS1, (c) (2×2×2)-AS2, (d) (2×2×2)-AS3, (e)(2×2×2)-AS4, (f) (2×2×2)-AS5, (g) (3×3×2)-AS1 and (h)(3×3×2)-AS2 with Mn (purple), Sb (orange) and Te (green)atoms.

netic moments on Mn ions at different sites are alignedferromagnetically. The band gap is reduced, but still noband inversion is expected.

S6. STS

To validate the electronic structure from DFT calcula-tions, we measured scanning tunneling spectra (STS) ofTN19K and TC24K at 4.5 K. As shown in Fig. S11, bothsamples have a bulk band gap of about 0.4 eV, with va-lence band maximum at 0.2 eV above EF and conductionband minimum at 0.6 eV. The flat and diminished DOSwithin the bandgap indicates the absence of in-gap statesand trivial topology of the band structures. The sizableband gap measured in the samples agrees with and can beused to justify the DFT-calculated band structure withthe supercell approach as described above.

S7. REFERENCES

[1] J.-Q. Yan, S. Okamoto, M. A. McGuire, A. F. May, R. J.McQueeney, and B. C. Sales, Physical Review B 100,104409 (2019).

[2] T. Murakami, Y. Nambu, T. Koretsune, G. Xiangyu,T. Yamamoto, C. M. Brown, and H. Kageyama, Phys-ical Review B 100, 195103 (2019).

[3] M.-H. Du, J. Yan, V. R. Cooper, and M. Eisenbach, arXivpreprint arXiv:2006.15475 (2020).

[4] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov,G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke,Physical review letters 100, 136406 (2008).

[5] S. Dudarev, G. Botton, S. Savrasov, C. Humphreys, andA. Sutton, Physical Review B 57, 1505 (1998).

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TABLE S7. Energy difference between the fully relaxed FM-like and AFM-like (4EFM−AFM ) calculated in PBEsol+Uand PBEsol+U+SOC for the configurations in the supercellsof (1×1×2), (2×2×2) and (3×3×2). The (1×1×2)-AS0 is theideal configuration without anti-site (AS) mixing. The othersupercell AS configurations in the septuple layer are shown inFig. S8 and named numerically.

Configuration 4EFM−AFM (meV/f.u.) 4EFM−AFM (meV/f.u.)PBEsol+U PBEsol+U+SOC

(1×1×2)-AS0 +3.48 +3.55(2×2×2)-AS1 -0.03 -0.02(2×2×2)-AS2 -0.84 -0.93(2×2×2)-AS3 -0.31 -0.30(2×2×2)-AS4 -0.10 -0.11(2×2×2)-AS5 -0.54 -0.70(3×3×2)-AS1 -0.15 -0.12(3×3×2)-AS2 -0.12 -0.08

FIG. S9. (color online) Total density of states (DOS)near EF of the FM-like and AFM-like magnetic orders for(a) (1×1×2)-AS0 without site mixing, (b) (2×2×2)-AS1,(c) (2×2×2)-AS2, (d) (2×2×2)-AS3, (e) (2×2×2)-AS4, (f)(2×2×2)-AS5, (g) (3×3×2)-AS1 and (h) (3×3×2)-AS2.

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FIG. S10. (color online) PBE+U+SOC band structure witha FM alignment of magnetic moments on Mn ions at differentsites.

FIG. S11. (color online) Scanning tunneling spectra of TC24K(black) and TN19K (Red) samples measured at 4.5 K. Thetunneling setpoint for TC24K is –0.3 V, 0.4 nA, and that forTN19K is –0.3 V, 0.5 nA.

Site Mixing for Engineering Magnetic Topological Insulators

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