Occupancy disorder in the magnetic topological insulator candidate Mn_1−x Sb_2+x Te₄

1 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, Bi₂Te₃ and Sb₂Te₃, exhibit the tetradymite-type (Bi₂STe₂) [4] crystal structure, i.e. they both crystallize in the rhombohedral R 3 ‾ m space group and are built of Te–Bi–Te–Bi–Te quintuple layers which are formed by [BiTe₆] octahedra. The current even hotter than hot topic is to combine long-range magnetic order – a bulk property – with the topologically protected transport – a surface property – and have them influence each other. This has been first achieved in Cr _x (Bi,Sb)₂Te₃, 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 EuIn₂As₂ [6], CuMnAs [7] and TbMn₆Sn₆ [8]. In the case of tetradymite-based compounds magnetic order could be introduced intrinsically by adding Mn²⁺ to the structure, resulting in the intrinsic magnetic topological insulator (IMTI) MnBi₂Te₄ [9, 10]. In contrast to Bi₂Te₃ and Sb₂Te₃, this layered compound is built of septuple Te–Bi–Te–Mn–Te–Bi–Te layers, which also form octahedra [BiTe₆] and [MnTe₆].

Our group developed the first growth protocol and characterized single crystals of MnBi₂Te₄ [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 MnSb₂Te₄). Moreover, the QAHE could be achieved in thin exfoliated flakes of MnBi₂Te₄ 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.

Figure 1:

The average unit cell of MnSb₂Te₄ exhibiting the typical septuple layers including the occupancy disorder. One of the septuple layers is enlarged for better visibility.

MnSb ₂Te₄ is a new isostructural analogue that has rapidly gained interest in the community [12], [13], [14], [15], [16], [17]. Opposed to MnBi₂Te₄, various magnetic behaviors have been reported for MnSb₂Te₄ 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 Mn²⁺ 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 MnSb₂Te₄. 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 MnBi₂Te₄. The present study explores the Mn/Sb intermixing in two distinct Mn_1−x Sb_2+x Te₄ crystals and its implications for magnetism.

2 Experimental

Single crystalline specimens were produced via a solid state reaction. Sample 1 (S1) was prepared by tempering stoichiometric amounts of MnTe and Sb₂Te₃ 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 two-zone 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.

3 Structural studies

MnSb₂Te₄ crystallizes in the R 3 ‾ m (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 MnBi₂Te₄, 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 MnBi₂Te₄ 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 MnSb₂Te₄. Indeed, as in MnBi₂Te₄, 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 MnSb₂Te₄, 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)Te₄. 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)Te₄.

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 MnSb₂Te₄, while S1 shows an overoccupation. The most significant difference between S1 and S2 is seen in the occupancy of the central Mn position (3a) that is more Mn-rich 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.

Figure 2:

Graphic representation of distances and angles in the [(Mn/Sb)Te₆] octahedra. The figure has been constructed from data of Sample 1 but indicates the respective geometries for both samples.

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 MnSb₂Te₄ (ca. 90%) but the sample also contains admixtures of Sb₂Te₃ (ca. 6%) and a small amount of MnSb₄Te₇ (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 Te₄ 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 Sb₂Te₃, and to 6–7 at.% of Mn, which is characteristic for MnSb₄Te₇. 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.

4 Magnetic studies

One of the central reasons why an in-depth study of the intermixing in MnSb₂Te₄ is important, is its impact on the magnetic ordering in these compounds. As alluded to in the introduction, the magnetism found in MnSb₂Te₄ differs from MnBi₂Te₄ not only by anti-versus ferromagnetism, but also by its robustness. As can be seen in Table 2, the Néel temperature of T _N  ≈ 24 K is very consistent over various measurements on MnBi₂Te₄, albeit slight variations of the occupancy values. Hence, there are two points which strongly differ between our MnBi₂Te₄ and MnSb₂Te₄ samples: 1. The intermixing in our MnBi₂Te₄ crystals is reproducible (Table 2), 2. The amounts of intermixing in MnBi₂Te₄ are relatively small in comparison with MnSb₂Te₄.

On the other hand, for MnSb₂Te₄ there is a wide range of critical temperatures reported in the literature as shown in 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.

Figure 3:

Temperature-dependent magnetization measurements of (a) S1 and (b) S2 powder samples obtained at various fields after field-cooled (FC) and zero-field-cooled (ZFC) procedures. The vertical dashed lines indicate the transition temperature T _C determined from the inflection point of the low field data.

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 MnSb₂Te₄ only. Ferromagnetic or ferrimagnetic behavior has also been reported in MnSb₂Te₄ in other sources as cited above, where they find the following compositions: MnSb_1.4Te₄, T _C  = 25 K [14]; Mn_0.846(6)Sb_2.154(6)Te₄, T _N  = 19 K or Mn_0.99(1)Sb_2.01(1)Te₄, T _C  = 34 K, single crystal [13]; Mn_1.07Sb_1.9Te₄, T _C  = 45–50 K, MBE thin films [16]. As evidenced, different amounts of intermixing and possible vacancies can lead to dramatic changes in the magnetic ordering transition. Our S1 hence excellently adds another data point to this collection of varying composition versus magnetic response. On the other hand, since S2 contains admixed phases that are magnetically active (MnSb₄Te₇ AFM with T _N  = 13.5 K [27] and Mn-doped Sb₂Te₃ FM with transition temperatures between T _C  = 9–17 K depending on amount of Mn in Sb₂Te₃ and publication []), 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 MnSb₂Te₄ with varying tempering routes and starting materials and we propose that MnSb₂Te₄ is not a line phase but exhibits a certain phase width.

While for MnBi₂Te₄ reported starting-material compositions vary (Bi₂Te₃-rich melts versus 1:1 MnTe:Bi₂Te₃ 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 MnSb₂Te₄. On one hand, the wide homogeneity range of MnSb₂Te₄ can lead to severe problems with reproducibility. On the other hand, the variability in MnSb₂Te₄ 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.