Occupancy disorder in the magnetic topological insulator candidate Mn 1 − x Sb 2 + x Te 4

: MnSb 2 Te 4 is a candidate magnetic topological insulator exhibiting more pronounced cation intermixing than its predecessor MnBi 2 Te 4 . Investigating the cation intermixing and its possible implications on the magnetic order in MnSb 2 Te 4 are currently hot topics in research on quantum materials for spintronics and energy-saving applications. Two single-crystal X-ray diffraction measurements of Mn 1 − x Sb 2 + x Te 4 ( x = 0.06 and x = − 0.1) are presented alongside a detailed discussion of its crystal structure with a spotlight on the apparent occupancy disorder between the two cations. This disorder has been noted by other groups as well, yet never been analyzed in-depth with single-crystal X-ray diffraction. The latter is the tool of choice to receive a meaningful quanti ﬁ cation of antisite disorder. Between the two synthesis procedures we ﬁ nd subtle differences in phases and/or alternation of the cation content which has implications on the magnetic order, as illustrated by bulk magnetometry. Understanding and assessing this disorder in magnetic topological insulators of the MnX 2 Te 4 (X = Bi, Sb) type is crucial to gauge their applicability for modern spintronics. Furthermore, it opens new ways to tune the “ chemical composition – physical property ” relationship in these compounds, creating an alluring aspect also for fundamental science.


Introduction
Today's materials science is driven by the pursuit of novel functional materials to allow for e.g. the ongoing development of computing and energy-saving technologies. These functional materials encompass for instance multiferroics, high-temperature superconductors and topologically non-trivial materials, i.e. materials exhibiting unconventional combinations of electronic conductivity and magnetism. Our interest lies in the pursuit of topological materials, which allow for a dissipationless spin transport on their surfaces, that is not disturbed by structural imperfections or inclusions [1][2][3].
Two archetypes of topological insulators that stimulated an excessive amount of research in the last few years, Bi 2 Te 3 and Sb 2 Te 3 , exhibit the tetradymite-type (Bi 2 STe 2 ) [4] crystal structure, i.e. they both crystallize in the rhombohedral R3m space group and are built of Te-Bi-Te-Bi-Te quintuple layers which are formed by [BiTe 6 ] octahedra. The current even hotter than hot topic is to combine longrange magnetic ordera bulk propertywith the topologically protected transporta surface propertyand have them influence each other. This has been first achieved in Cr x (Bi,Sb) 2 Te 3 , which was the artificial heterostructure on which the quantum anomalous hall effect (QAHE) was discovered [5]. Ongoing pursuit of intrinsic magnetic topological materials, both insulators and semimetals, has yielded a handful of promising candidates, including EuIn 2 As 2 [6], CuMnAs [7] and TbMn 6 Sn 6 [8]. In the case of tetradymite-based compounds magnetic order could be introduced intrinsically by adding Mn 2+ to the structure, resulting in the intrinsic magnetic topological insulator (IMTI) MnBi 2 Te 4 [9,10]. In contrast to Bi 2 Te 3 and Sb 2 Te 3 , this layered compound is built of septuple Te-Bi-Te-Mn-Te-Bi-Te layers, which also form octahedra [BiTe 6 ] and [MnTe 6 ].
Our group developed the first growth protocol and characterized single crystals of MnBi 2 Te 4 [10], which display ferromagnetic (FM) coupling within a layer of manganese and antiferromagnetic (AFM) order between the respective layers (see Figure 1 which shows the layers of Mn on the example of MnSb 2 Te 4 ). Moreover, the QAHE could be achieved in thin exfoliated flakes of MnBi 2 Te 4 under an external magnetic field of 12 T that fully polarized the lattice into a ferromagnet [11]. For QAHE stable at high temperatures and lower magnetic fields (ideally, without any external field), a ferromagnetic bulk magnetic order is highly desirable. MnSb 2 Te 4 is a new isostructural analogue that has rapidly gained interest in the community [12][13][14][15][16][17]. Opposed to MnBi 2 Te 4 , various magnetic behaviors have been reported for MnSb 2 Te 4 ranging from a bulk antiferromagnet to a ferri-or ferromagnet [12][13][14][15][16][17][18][19]. Its synthesis procedures seem to vary greatly between the reports and presumably influence the type of the magnetic order. As outlined in ref. [13], these effects may be connected via the cation intermixing phenomenon. When intermixing is accounted for, Mn is not only found in the center of the septuple layer, but also in the outer cationic positions. Equally, some Sb is populating the central Mn position, leading to some occupancy disorder. Since Mn 2+ carries a magnetic moment (d 5 state), its amounts and placements within the unit cell have a decisive impact on the magnetic exchange coupling and magnetic order in MnSb 2 Te 4 . This intermixing is easiest characterized with single crystal X-ray diffraction as this method is more precise than powder diffraction and depicts a larger sample volume than electron microscopy or tunneling spectroscopy. In our previous work [10], similar cation disorder has been for the first time characterized for MnBi 2 Te 4 . The present study explores the Mn/Sb intermixing in two distinct Mn 1−x Sb 2+x Te 4 crystals and its implications for magnetism.

Experimental
Single crystalline specimens were produced via a solid state reaction. Sample 1 (S1) was prepared by tempering stoichiometric amounts of MnTe and Sb 2 Te 3 at 630°C in an evacuated quartz tube for 10 days and subsequent quenching in water. Sample 2 (S2) was synthesized from the elements with a 10% smaller amount of Te, than demanded by stoichiometry, in a quartz ampule sealed off under vacuum. It was tempered at 594°C for three days, and subsequently quenched in water. The ovens used for these experiments were custom built twozone ovens (Reetz GmbH) with two free moving thermocouples. Those thermocouples were placed directly next to the quartz ampule which contained the sample, allowing for temperature control as precise as ±1 K. After quenching the ampules contained ingots of solidified melt that were cracked open to give two types of samples. On one hand the resulting metallic crumbs were either ground for powder diffraction or pressed to pellets for magnetic measurements. On the other hand the crumbs were inspected through an optical microscope and flat specimens with mirror-like surfaces were selected for single-crystal diffraction and energy dispersive X-ray spectroscopy.
The respective crystals (denoted as S1 and S2 in the text, just as the respective bulk specimens) were measured on a Rigaku Supernova four circle diffractometer, fitted with a molybdenum tube and an AtlasS2 detector. The data was subsequently indexed and integrated in the respective diffractometer software CRYSALISPRO [20] and the crystal structures were solved and refined with SUPERFLIP [21] and JANA2006 [22]. Upon inspection of reciprocal space reconstructions neither data set showed any sign of diffuse scattering or super structure reflections.
The average structure was solved and refined without any special tricks. To allow for some Sb to populate the 3a position and some Mn to populate the 6c position (see Figure 1), both positions were split and populated with 50% Mn and 50% Sb. Furthermore both positions were restrained so that the ADP parameters and coordinates were identical and the occupancies would keep the overall sum of the respective position. When this setup proved stable, the occupancies of Mn and Sb were allowed to refine, while still keeping the above restraints. In a last step, the restraint of the occupancy having to sum up to the site multiplicity was lifted, to allow for the possibility of voids. However neither of the samples showed any significant change of occupancies after this, indicating that no vacancies could be found in our data sets. As a consequence our refined compositions are electroneutral.
Sample 1 additionally shows a small amount (twin volume 2 = 1%) of twinning, which was treated in JANA2006 by a 180°rotation around the b-axis (0, 1, 0) in reciprocal space. Also S2 exhibits twinning that could be directly treated in JANA2006 through a 60°rotation around the c-axis (0, 0, 1) in reciprocal space. Twin 1 accounts for 29% of the data while twin 2 accounts for 71% of the data (see Supplementary Figure 3). The last few cycles of the refinement were performed on F 2 . Powder X-ray diffraction (PXRD) measurements were conducted on a Malvern Panalytical Empyrean 3 diffractometer, fitted with a copper tube and set in Bragg-Brentano geometry. Simple Le Bail decompositions against literature data were performed in JANA2006 [22] to check for phase purity. See Supplementary Figures 1 and 2. Energy-dispersive X-ray spectroscopy (EDX) was conducted on a Hitachi FESEM SU 8020 microscope equipped with a Silicon Drift Detector (SDD) X-Max N (Oxford) at an acceleration voltage of 20 kV and a current of 5 μA. Flat platelet crystalline samples were prepared on a sticky carbon film.
Magnetization measurements were conducted with a commercial Quantum Design superconducting quantum interference device magnetometer (SQUID-VSM) on pressed powder pellets.

Structural studies
MnSb 2 Te 4 crystallizes in the R3m (No. 166) space group, with average lattice parameters a = 4.2 Å and c = 40.8 Å (for more details see Table 1). This structure is built of septuple-layer slabs which are interleaved by a van der Waals gap. The septuple slabs are in turn built of stacks of Te-Sb-Te-Mn-Te-Sb-Te, each layer stretching out infinitely in the ab plane ( Figure 1). In the unit cell Mn is located on the Wyckoff position 3a (0, 0, 0), while the other atoms are situated on 6c Wyckoff positions.
In the parent compound MnBi 2 Te 4 , a certain amount of intermixing between the cationic sites was established previously [10,23,24] with the compositions and magnetic transition temperatures noted in Table 2. Additionally, in this work we have grown and elucidated a MnBi 2 Te 4 crystal following [10] in order to check possible variations of stoichiometry. The present results are very consistent with the previous findings (see Supplementary Material and  Table 2), hinting at a well-defined yet non-stoichiometric composition of the Bi analogue. Therefore intermixing between Mn and Sb was also allowed in our analyses of MnSb 2 Te 4 . Indeed, as in MnBi 2 Te 4 , Mn could be found on the Sb position (6c) as well as Sb could be found on the Mn (3a) position (see Figure 1).
We will in the following present two structure elucidations of MnSb 2 Te 4 , both nominally the same phase, yet they show differences that cannot be ignored. For the respective synthesis routes and single crystal refinement strategies please refer to the Experimental section. The crystal denoted as Sample 1 (S1) exhibits 28 ± 1.0% of Sb on the 3a position and 19 ± 0.3% Mn on the 6c position resulting in the overall composition of Mn 1.11(2) Sb 1.90(2) Te 4 . The second crystal from a different batch (S2) shows 37 ± 1.4% of Sb on the 3a position and 15 ± 0.5% of Mn on the 6c position leading to an overall composition of Mn 0.94(2) Sb 2.07(2) Te 4 .
As mentioned in the Experimental section, neither structure shows vacancies, indicating that the total sum of Mn and Sb in the compound is fixed to three. The difference between the two samples lies in the distribution of Mn and Sb over the respective sites resulting in S2 exhibiting an underoccupation on the Mn as compared to the idealized formula MnSb 2 Te 4 , while S1 shows an overoccupation. The most significant difference between S1 and S2 is seen in the  The a position is the central position in the septuple layer slab which is occupied by Mn in the average structure and the c position is the outer cation position occupied by Bi in the average structure. XRD, X-ray diffraction; ND, neutron diffraction; STM, scanning transmission microscopy; AFM, antiferromagnetic. occupancy of the central Mn position (3a) that is more Mnrich in S1. A close inspection of Table 1 also exhibits large positive and negative residual densities for both samples. This is due to stacking disorder typical for quasi 2D structures and mixed occupancy refinements not allowing to properly account for small atomic movements. When comparing the interatomic distances and angles in Table 3 and Figure 2, the most obvious discrepancies that can be found are connected to the central position of the septuple layer slab. In light of the different atomic radii of Mn and Sb (2.05 Å and 2.2 Å, respectively [25]) this is indeed sensible. If we calculate the interatomic distances from the above values (2.075 Å for Mn-Te and 2.15 Å for Sb-Te) and subsequently calculate the respective difference between samples 1 and 2 after accounting for the occupancy percentages, we find the same difference (0.1%) between the calculated values and the values tabulated in Table 3. The differences in angles are also most visible around the central 3a position and can be connected to the size differences of Mn and Sb and the respective occupancy differences. A qualitative estimation of the size of the van der Waals gap gives the following values: 2.90 Å for S1 and 2.86 Å for S2.
As always with single crystal studies it is important to keep in mind that they only portray a small fraction of the synthesized batch. To receive clarity on the phase purity and elemental composition of the bulk sample we have performed powder X-ray diffraction (PXRD) and energy dispersive X-ray spectroscopy (EDX) overview analyses. While S1 appears phase pure (cf. Supplementary Figure 1), S2 contains additional phases (cf. Supplementary Figure 2). The main phase is indeed MnSb 2 Te 4 (ca. 90%) but the sample also contains admixtures of Sb 2 Te 3 (ca. 6%) and a small amount of MnSb 4 Te 7 (ca 4%) (as compared with ref. [26]). The approximate phase fractions in brackets have been deduced from a very preliminary Rietveld refinement of the S2 powder data (Supplementary Figure 2) without taking the cationic intermixing into account (R p ≈ 12%; GOF ≈ 3; R obs ≈ 13-20%).
EDX analysis of crystallites originating from the S1 batch leads to an average composition of Mn 1.06(1) Sb 1.95(1) Te 4.00 (2) which is in good agreement with the refined composition from the single-crystal measurement. Due to its phase purity seen in PXRD this result is not surprising. Contrary to this, the EDX analysis of S2 shows a range of distinct compositions with various percentages of Mn. The 15 data points that can be attributed to the Mn 1−x Sb 2+x Te 4 phase average up to a composition Mn 0.96(1) Sb 2.14(1) Te 4.00 (2) , which is fairly close to the refined composition of S2 in Table 1. Other elemental compositions found in the S2 batch correspond to ca. 2 at.% of Mn, which could be attributed to Mn-doped Sb 2 Te 3 , and to 6-7 at.% of Mn, which is characteristic for MnSb 4 Te 7 . This distribution of the EDX results coincides well with the phase mixture elucidated from PXRD. This is a telltale example of how single-crystal diffraction can be deceiving and the entire batch of a sample should always be analyzed with several   independent methods. In order to gain solid confidence in our conclusions, we deduced by EDX the elemental composition of the exact single-crystal S2 that was used for the structure refinement: Mn 0.83(2) Sb 2.28(1) Te 4.00(1) as averaged over 10 data points. A stronger deviation from the expected stoichiometry (especially in the Sb:Te ratio) may be connected to an imperfect sample orientation of this tiny crystal.

Magnetic studies
One of the central reasons why an in-depth study of the intermixing in MnSb 2 Te 4 is important, is its impact on the magnetic ordering in these compounds. As alluded to in the introduction, the magnetism found in MnSb 2 Te 4 differs from MnBi 2 Te 4 not only by anti-versus ferromagnetism, but also by its robustness. As can be seen in Table 2 Table 4. As can be seen, not only different critical temperatures but even completely different magnetic ground states are reported. In order to characterize the magnetism of our samples, magnetization measurements as a function of temperature were performed as shown in Figure 3.
Sample S1 (Figure 3a) shows an irreversible behavior in ZFC and FC magnetization curves below 32 K at 100 Oe which is suppressed by increasing the applied magnetic field, finally disappearing at 1000 Oe, suggesting a soft ferromagnetic or ferrimagnetic behavior. In contrast, sample S2 ( Figure 3b) evidences a more complex behavior. Whereas the magnetization initially increases by lowering temperature indicating ferro/ferrimagnetism like in S1, a feature around 18 K is observed, followed by a peak at ca 13 K, a signature for an antiferromagnetic spin alignment/ component. Notably the transition temperature determined from the inflection point is much lower for S2 than for S1, indicating a weakening of the ferro/ferrimagnetic state.
As noted previously, EDX and PXRD revealed that S1 is phase pure while S2 is multi-phase. In that sense, the magnetic behavior observed in S1 can therefore be ascribed to MnSb 2 Te 4 only. Ferromagnetic or ferrimagnetic behavior has also been reported in MnSb 2 Te 4 in other sources as cited above, where they find the following compositions: MnSb 1.4 Te 4 , T C = 25 K [14]; Mn 0.846(6) Sb 2.154(6) Te 4 , T N = 19 K   FM with transition temperatures between T C = 9-17 K depending on amount of Mn in Sb 2 Te 3 and publication [28][29][30]), the interpretation of its magnetic response becomes complex, since the influences from both additional phases contribution plus intermixing effects need to be disentangled. As discussed above, there are various, albeit small, differences in terms of occupancies and amounts of elements that are present in the respective crystals. Referring back to the synthesis procedures for the two samples (see Section 2) and following the principle of Ockham's razor, we put forward the theory that small differences in synthetic conditions (annealing time and temperature) could be the key to tuning variances in occupancy. These findings are corroborated by similar reports from other groups [12][13][14][15][16][17], where especially Liu et al. [13] point out the correlation between synthesis temperature and intermixing. Thus it is possible to grow single crystals and phase pure powders of MnSb 2 Te 4 with varying tempering routes and starting materials and we propose that MnSb 2 Te 4 is not a line phase but exhibits a certain phase width.
While for MnBi 2 Te 4 reported starting-material compositions vary (Bi 2 Te 3 -rich melts versus 1:1 MnTe:Bi 2 Te 3 composition), the tempering profile has been the same in most reports as it is dictated by the high-temperature phase-stability interval. This is at stark contrast to the variability of synthesis conditions for MnSb 2 Te 4 . On one hand, the wide homogeneity range of MnSb 2 Te 4 can lead to severe problems with reproducibility. On the other hand, the variability in MnSb 2 Te 4 may give us more freedom to tailor its physical properties via the composition with the chance of driving the magnetic transition to higher temperatures and confining the magnetic order to ferromagnetism. Furthermore it opens broad possibilities to study the interplay between bulk magnetism and topological surface transport. Corredor returned to IFW-Dresden, where she is currently conducting her research in the Thermodynamics Group headed by Dr. Anja Wolter-Giraud. The research interest of this group focuses in obtaining fundamental insights into the properties of emerging unconventional spin phases through thermodynamic methods like magnetometry, dilatometry and calorimetry in extreme conditions of low temperatures, high fields and high pressures. Particular focus is given to quantum magnets with reduced dimensionality, frustration and the interplay of spin, charge, structure and orbitals in complex transition metal oxide systems, as well as to explore the interplay between magnetism and superconductivity in unconventional hightemperature superconductors.