Observation of Topological Spin Textures in Ferrimagnetic Mn_{2 − x} Zn _x Sb

Abstract

Ferrimagnets, which have both ferromagnetic and antiferromagnetic coupling, are attracting increased attention in the realm of spintronic devices due to advantages such as ultrafast dynamics and a suppressed skyrmion Hall effect. Thus, understanding the behavior of nontrivial spin textures in ferrimagnets is crucial; however, comprehensive reports on this topic remain limited. Here, the magnetic spin textures of ferrimagnetic Mn_{2 − x} Zn _x Sb (x = 0.85) is explored as a function of temperature and applied magnetic field. The spin textures can be tuned to a variety of states, including stripes, skyrmion bags, and a skyrmion lattice. Chiral Néel‐type magnetic structures are visualized using Lorentz transmission electron microscopy. Mn(I) ions are slightly shifted toward the Sb sites, which may be due to a strong electrostatic interaction between Mn and Sb ions. This local structural distortion breaks the inversion symmetry and introduces an effective Dzyaloshinkii–Moriya interaction. This work thus provides a pathway to use doping and heterogeneity in a ferrimagnet to control and generate chiral nontrivial spin textures.

Mn_{2 − x} Zn _x Sb crystal has ferrimagnetic order due to the anti‐aligned spins at two inequivalent Mn sites. Magnetic property of the ferrimagnet can be tuned by external stimuli (such as the temperature and the magnetic field), resulting in a variety of spin textures. The observation of topological chiral spin states in this crystal suggests promising applications in future spintronic devices.

1. Introduction

Magnetic skyrmions are topologically nontrivial spin textures that are fascinating not only due to their fundamental physics arising from symmetry breaking but also their technological potential for future spintronics applications.^{[ 1} , ² , ³ , ^{4 ]} The majority of the research on magnetic skyrmions has focused on ferromagnetic (FM) materials with broken symmetries either due to a chiral crystal lattice, such as MnSi,^{[ 5 ]} FeGe,^{[ 6 ]} Co‐Mn‐Zn^{[ 7 ]}; or to asymmetric interfaces in heterostructures, for example, in Ta/CoFeB/TaOx^{[ 8 ]} or Pt/Co/X, where X is a heavy metal.^{[ 9} , ^{10 ]} The interplay between the Heisenberg exchange, antisymmetric exchange and Dzyaloshinkii‐Moriya interaction (DMI) leads to the formation of skyrmions of Bloch or Néel type.^{[ 11 ]} Bloch‐type chiral spin textures are stabilized due to inversion symmetry breaking of the bulk crystal, while Néel‐type chiral spin textures are formed due to broken inversion symmetry at interfaces.^{[ 12 ]} Recently, skyrmions have also been observed in achiral materials, which are stabilized by long‐range dipolar interactions. In particular, materials with achiral crystal lattices and competing types of magnetic order, such as ferrimagnetic (FiM) order, are extremely interesting as they provide additional degrees of freedom that can lead to a larger variety of topological spin textures and a rich phase space with respect to temperature and magnetic field.^{[ 4 ]} Ferrimagnets have unbalanced antiparallel‐aligned magnetic spins at inequivalent sublattices, simultaneously possessing antiferromagnetic (AFM) and ferromagnetic (FM) orders. This leads to unique magnetic properties: small stray field, small net magnetization and ultrafast dynamics.^{[ 13} , ^{14 ]} Although bulk and interfacial DMI have been reported in FiM multilayers^{[ 15} , ^{16 ]} and amorphous alloys,^{[ 17 ]} the presence of DMI in FiM crystals is still relatively unknown and has only recently garnered interest.

One of the outstanding issues with skyrmions in FM materials is the skyrmion Hall effect, which results in a non‐collinear motion of skyrmions with respect to an applied electric current.^{[ 18} , ^{19 ]} This is not desirable for spintronic applications such as skyrmion racetrack memories. Here again, it has been predicted and observed that the use of FiM materials can lead to the suppression of the skyrmion Hall effect due to competing magnetic order between different sublattices in the material.^{[ 20} , ^{21 ]} The formation of skyrmions and chiral domains in FiM materials due to the presence of a DMI has only recently been reported.^{[ 21} , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ^{29 ]} However, a majority of these materials are based on rare‐earth metals, which are not earth‐abundant and are considered critical raw materials, such as Gd, Tb, and Dy in multilayers or alloys such as GdFeCo.

Mn₂Sb is a rare earth‐free FiM material that crystallizes in a layered structure with a P4/nmm space group. It has two inequivalent Mn sites, Mn(I) and Mn(II), which have different magnetic moments and are antiferromagnetically coupled, leading to FiM order.^{[ 30} , ³¹ , ^{32 ]} The difference in magnetization of the two distinct Mn sublattices results in exotic temperature‐dependent magnetic properties, such as the switching of the magnetic easy axis from the basal plane at low temperatures (< 240 K) toward the c axis at higher temperatures (> 240 K).^{[ 30 ]} Doping Mn₂Sb with transition metals such as Co,^{[ 33} , ^{34 ]} Cr^{[ 35 ]} and Zn^{[ 32} , ³⁶ , ³⁷ , ³⁸ , ^{39 ]} can also be used to control the magnetic behavior. FiM Mn_{2 − x} Zn _x Sb, in which Zn atoms only substitute for the Mn(II) sites, displays rich temperature‐dependent phase transitions and electronic properties as a function of the Zn content:^{[ 32} , ^{36 ]} for example, when Zn atoms occupy all Mn(II) sites, MnZnSb becomes FM ordered at room temperature.^{[ 37 ]} As a result, Mn_{2 − x} Zn _x Sb offers a unique material platform to explore the effect of competing magnetic orders (i.e., the ferromagnetic and antiferromagnetic coupling) on the emergence of nontrivial magnetic spin textures.

In this work, we explore the way in which temperature and applied field influence the formation of a variety of topological spin textures in FiM Mn_{2 − x} Zn _x Sb (x = 0.85). We determine the type of spin texture and its havior using a combination of magneto‐optic Kerr effect (MOKE) microscopy and Lorentz transmission electron microscopy (LTEM). The observation of diverse spin textures (including stripe domains, skyrmion lattices and skyrmion bags) in the bulk crystal is attributed to the variation of magnetic parameters, such as the uniaxial anisotropy, coercive field and saturation magnetization, as a function of temperature. Chiral Néel‐type domains were seen via LTEM. The Mn atoms at the Mn(I) sites were found to be closer to the Sb atoms than to the Mn(II) sites, determined using atomic‐resolution scanning TEM (STEM) high‐angle annular dark‐field (HAADF) imaging. The displacement of Mn(I) sites could be responsible for breaking the inversion symmetry, thereby introducing the effective DMI to form the Néel‐type spin textures.

2. Results and Discussion

2.1. Temperature‐Dependent Magnetic Properties

In order to determine the magnetic behavior of Mn_1.15Zn_0.85Sb, we measured the temperature‐dependent magnetization and hysteresis loops that determine the magnetic parameters, such as coercive field, remanent magnetization and perpendicular anisotropy, and the associated phase transitions. Figure  1b shows the out‐of‐plane (H∥c) and in‐plane (H∥ab) magnetization as a function of temperature during zero‐field cooling (ZFC) and field cooling (FC) in a 50 mT magnetic field. The details of the Mn_{2 − x} Zn _x Sb crystal orientation in our work is sketched in Figure 1a.^{[ 36 ]} It can be seen that there are three regions showing different temperature‐dependent magnetization behavior across the temperature range from 2 to 330 K, which are labeled as Regions I, II, and III, with transition temperatures at 170 and 286 K, as shown in the inset in Figure 1b. The higher transition temperature corresponds to the transition from a paramagnetic state (Region I) to a FiM state (Region II). Please note that the transition temperature of 286 K is defined as the midpoint of the phase transition (the dM(dT)⁻¹ versus T in the inset of Figure 1b) and, thus, the magnetization is decaying into the paramagnetic state in Region I. When the temperature is above 320 K (Curie temperature), the magnetization is completely zero. As the temperature is lowered, there is a gradual increase in magnetization along the c‐axis (Region II) until approaching 170 K, below which the magnetization along the c‐axis decreases abruptly (Region III). In Region II, Mn_1.15Zn_0.85Sb shows a strong perpendicular magnetic anisotropy, as measured from hysteresis loops (Figure S2, Supporting Information), which decreases below 170 K (Region III) along with a decrease in magnetization. We also measured the magnetization in the ab plane which shows a slight increase near the lower transition temperature of 170 K. These measurements suggest that there could be a spin reorientation occurring near 170 K which tilts the magnetic moment of the Mn ions away from the c‐axis and toward the ab plane.^{[ 30} , ³² , ^{36 ]} The temperature‐dependent behavior of magnetization under varying magnetic fields are detailed in Section S1 (Supporting Information). In addition, according to the M versus T curve, except in the paramagnetic region, the net magnetization never reaches zero from 320 to 2K. Therefore, magnetic compensation, i.e., zero magnetization, may not occur in this system in the studied temperature range.

Figure 1.

Temperature‐dependent magnetic properties of a Mn_1.15Zn_0.85Sb bulk crystal. a) Schematic of the crystal structure of Mn_{2 − x} Zn _x Sb.^{[ 36 ]} b) Magnetization as a function of temperature for zero‐field‐cooling (ZFC) and field‐cooling (FC) protocols in a 50 mT magnetic field applied along the c axis or in the ab plane. The temperature‐dependent curves can be divided into three temperature regions: I, II, and III. Inset is the derivative of the ZFC curve showing two phase transition temperatures at 170 and 286 K. The background colors highlight the three temperature regions. c) Temperature‐dependent coercive field, H _c , when the net magnetization is 0 Am⁻¹. d) Temperature‐dependence of the remanent magnetization M _r0 (blue) and of the quasi‐saturation magnetization M _qs (red) at a 400 mT applied magnetic field. The external magnetic field was applied along the c axis of the crystal for (c) and (d).

Based on isothermal hysteresis measurements with the magnetic field along the c axis,^{[ 36 ]} we also determined the coercive field, the remanent and quasi‐saturation magnetization of Mn_1.15Zn_0.85Sb, which are also temperature dependent. The definitions of these three magnetic parameters are shown in Figure S2 (Supporting Information). Figure 1c shows that the value of the coercive field (H _c ) is very low in Regions I and II, and then increases as the temperature reduces into Region III. The temperature‐dependent remanent magnetization (M _r0) (Figure 1d) slowly increases with decreasing temperature within each region but shows a significant change across the transition between regions. The increase in the remanent magnetization coincides with a more square hysteresis loop (Figure S2, Supporting Information). We also measured the magnetization at μ₀ H = 400 mT applied along the c axis as a function of temperature (Figure 1c), which we refer to as the quasi‐saturation magnetization (M _qs ) since the upper and lower branches of the hysteresis loop almost overlap for all temperatures (see Figure S2, Supporting Information). The behavior of this magnetic parameter shows a similar trend as the M versus T curve in Figure 1a: the value of M _qs reaches a maximum of 1.04 × 10⁻⁵ Am⁻¹ in Region II and decreases as the temperature is reduced. These findings show that the FiM coupling in Mn_1.15Zn_0.85Sb is strongly dependent on temperature, which results in the variation of the magnetic parameters of the bulk crystal.

2.2. Diverse Magnetic Spin Textures

To gain further insight into the effect of varying magnetic parameters on the spin textures, we systematically studied the temperature‐ and field‐driven behavior in each of the three regimes. Polar MOKE microscopy was utilized to directly visualize real‐space magnetic spin textures of a bulk Mn_1.15Zn_0.85Sb crystal. The sample was cooled to a given temperature in the absence of magnetic field. At the given temperature, magnetic field was then applied perpendicular to the sample surface along the c axis, varying the strength between 0 and 135 mT. Figure  2 shows the magnetic spin textures observed at specific applied field values and temperatures. Although Region I exhibits paramagnetic order at high temperatures, the magnetization is zero only when the temperature is above the 320 K (Curie temperature). 300 K is close to the phase transition and the net magnetic moment is not completely zero. At 300 K (region I), when the magnetization is very weak, we observe the formation of stripe domains in a low applied field as shown in Figure 2a. As the applied field is increased (center and right panes of the figures), the stripe domains break down and initially form a mixed state of short stripes and skymionic bubbles at 67 mT, with a disorder skyrmion lattice forming at 87 mT magnetic field. All magnetic spin textures are polarized in an applied field of 97 mT. Note that these skyrmionic bubbles are approximately 700 nm in diameter at 87 mT magnetic field (see more details in Figure S3, Supporting Information). We find that the skyrmions prefer to form at the intersection of a couple of stripe domains or at the end of stripe domains, and a few skyrmions are created in the vicinity of structural defects (Video S1, Supporting Information).

Figure 2.

Magnetic spin textures observed at the surface of a bulk Mn_1.15Zn_0.85Sb crystal. MOKE images showing evolution of the magnetic spin textures as a function of a magnetic field applied perpendicular to the sample and along the c axis, at temperatures of a) 300 K (Region I), b) 200 K (Region II), and c) 120 K (Region III). SkX refers to a skyrmion lattice and “Sky bag” to a skyrmion bag. Scale bars:5 µm for (a), 10 µm for (b) and (c).

In Region II at a temperature of 200 K, as discussed before, the perpendicular anisotropy and saturation magnetization are higher than those in Region I, resulting in the formation of mixed states consisting of stripes and bubbles at a lower field (μ₀ H < 124 mT), as shown in Figure 2b and Figure S4 (Supporting Information). As the field is increased to 81 mT, we observe an interesting transition of the spin texture to skyrmion lattices that are each enclosed in a large closed‐loop stripe domain; these are referred to as skyrmion bags. The skyrmion bag configuration, which has a high topological charge, has been reported in a 2D liquid crystal^{[ 40 ]} as well as in materials with an intrinsic DMI,^{[ 41} , ^{42 ]} such as FeGe. Interestingly, unlike the isolated skyrmion bags in other published work, connected skyrmion bags emerge in Mn_1.15Zn_0.85Sb. As the field is increased up to 103 mT, the skyrmion bag configuration remains stable, and the connected multiple domains shrink to a single looped stripe. The skyrmion bag configuration eventually breaks down to form a skyrmion lattice again at a field of 124 mT.

In the low‐temperature regime (Region III) at 120 K and below, where the magnetization decreases significantly, we only observe the formation of stripe domains in an applied field range from 0 to 135 mT, as shown in Figure 2c. Increasing magnetic field results in narrowing of the stripe domains. The sample was not fully saturated at the maximum applicable field in our experimental setup (135 mT). The formation of bubbles is not seen. This suggests that the out‐of‐plane anisotropy significantly decreases. The black spots in the images are surface contamination and could not be removed by image processing (details in the Methods section).

Based on our extensive imaging of the magnetic spin textures, we can establish a magnetic phase diagram for Mn_1.15Zn_0.85Sb showing various spin textures that form as a function of temperature and magnetic field, as shown in Figure  3 . The phase diagram explicitly demonstrates that the magnetic‐field‐driven spin textures are strongly associated with the three temperature regimes. In Region I, at higher temperature, the spin texture gradually evolves forming stripes, then a mixed state, then skyrmion lattices, and finally a uniformly magnetized state as a function of applied field. However, in Region II, the perpendicular anisotropy increases, and thus the net magnetization along the c‐axis is dramatically enhanced. This leads to the formation of skyrmions at a lower magnetic field, μ₀ H = 5 mT (Figure S4, Supporting Information) or even μ₀ H = 0 mT.^{[ 43 ]} The zero‐field skyrmions induced by the increase in the perpendicular anisotropy were also reported in synthetic Pt/CoGd/Pt ferrimagnetic multilayers.^{[ 44 ]} Similar mixed bubbles and stripe domains have been observed on the surface of a bulk cobalt crystal due to the effect of stray field.^{[ 45 ]} In addition, a unique skyrmion bag structure forms in the intermediate field range, along with a skyrmion lattice created at a higher magnetic field.

Figure 3.

Magnetic phase diagram as a function of applied magnetic field at varying temperature, showing the formation of diverse spin textures, including stripe, mixed stripe and skyrmion (mix), skyrmion (Sky) bag, skyrmion lattice (SkX) and uniform FM states. The background colored gradients highlight the three temperature regimes, and the black dashed lines indicate the two phase transition temperatures (170 and 286 K, respectively). The red dashed curve marks the phase region where the Sky bag configuration is observed.

Finally in Region III, due to a decrease in net magnetization along the c‐axis, we only observe the formation of stripes across the entire applied field range. These findings show that the variation of FiM coupling as a function of temperature and applied field in Mn_1.15Zn_0.85Sb can be leveraged to create a diverse variety of spin textures.

2.3. In‐Situ Temperature Dependent Imaging of Néel Spin Textures

To understand the nature of magnetic spin textures, we employed LTEM for imaging the magnetization distribution in Mn_1.15Zn_0.85Sb. LTEM can efficiently determine whether the magnetic spin textures are Néel‐ or Bloch‐type in a magnetic sample with strong perpendicular anisotropy, based on changes in image contrast as a function of sample tilt.^{[ 46 ]} A TEM lamella was fabricated along the ab plane (thickness < 200 nm) such that the c − axis (the easy axis of magnetization) was aligned with the electron beam direction. Figure  4a–c shows out‐of‐focus LTEM images at varying tilt angles (‐20°, 0° and 21°) at 250 K (temperature Region II). Skyrmions are visible in the images at non‐zero tilt, but the magnetic contrast disappears when the sample is tilted to 0°, with the only contrast being due to bend contours. The projected in‐plane magnetic induction from the two opposite tilt angles results in the domain contrast reversing as indicated by the blue and orange line plots shown in Figure 4d. The LTEM results indicate that the spin textures in Mn_1.15Zn_0.85Sb are Néel‐type, suggesting the presence of a Dzyaloshinkii–Moriya interaction (DMI) that results in the chiral domains. This agrees with previous work which has shown that Mn_1.15Zn_0.85Sb exhibits a finite topological Hall effect.^{[ 36 ]} This is quite surprising since the crystal structure of Mn_1.15Zn_0.85Sb has been reported to be tetragonal and centrosymmetric, belonging to the P4/nmm space group.^{[ 36 ]}

Figure 4.

Evolution of Néel magnetic spin textures in a thin Mn_1.15Zn_0.85Sb lamella, viewed along the [001] zone axis, as a function of temperature. a−c) LTEM images recorded at 250 K of a thin lamella of Mn_1.15Zn_0.85Sb as a function of tilt angle, α, showing the Néel‐type magnetic spin texture. d) Average intensity profile along the orange and the blue lines across the Néel‐type skyrmions at tilt angles of α = −20° and α = +21°. LTEM images of the evolution of a stripe spin texture as a function of temperature during e) a ZFC run and f) a ZFH run.

However, it is worth noting that the thicknesses of the lamella for the LTEM and the bulk sample for the MOKE measurements are different, the former being less than 200 nm and the latter being around 130 µm. The difference in thickness may significantly alter the density, size and nature of spin textures.^{[ 47} , ⁴⁸ , ^{49 ]} It has been reported that increased thickness can lead to transformation from Néel to Bloch spin textures.^{[ 50 ]} Increasing thickness results in greater dipolar energy, which would favor the formation of Bloch domains.^{[ 45} , ^{49 ]} Therefore, although the Néel spin texture is observed in the thin lamella, the nature of spin texture in the bulk crystal might vary. Besides, the reduction of dimensionality of the lamella would introduce boundary effects which can impact the formation of spin textures. For example, the creation of stripe domains in the ab‐plane starts at the edge of the lamella (Figure S5, Supporting Information).

In the previous section, we discussed the field‐driven behavior of the spin textures in Mn_1.15Zn_0.85Sb at a given fixed temperature in each of the three temperature regimes. It is also interesting to gain insight into how the spin textures evolve continuously as a function of temperature, and we can explore this at high spatial resolution using LTEM. We performed in situ ZFC and zero‐field heating (ZFH) experiments and recorded LTEM images as displayed in Figure 4e,f. During the ZFC experiment, at 295 K the magnetic contrast is not clearly evident, while the spin textures at 300 K in the MOKE experiment were clearly visible. This is most likely a result of sample thickness; the thickness of the LTEM sample is less than 200 nm, while the MOKE specimen was a bulk crystal with thickness of 130 µm. A similar scenario also occurs when the temperature is less than 155 K, as the magnetic moment is too weak in Region III to give rise to detectable LTEM contrast. A stripe spin texture is observed at 277 K, and as the temperature decreases, the width of the stripe domains is observed to increase with a corresponding decrease in domain density.

The spin texture during the ZFH experiment shows the reverse temperature‐dependent behavior. The LTEM contrast of the stripe domains appears when the temperature increases to 162 K (Figure 4f). Interestingly, when the stripe domains are seen to nucleate at the low temperature, their width is small, and the domain walls are wavy. As the temperature is increased to 195 K, the width of the stripe domains greatly increases and the domain walls become smoother. The increased width of domains observed during heating at 250 K is very close to the one observed during cooling at 250 K, which shows that the domain growth and shrinking is a reversible process without any hysteresis. When the temperature reaches 280 K, the stripe domain width again decreases and the density increases. The LTEM contrast finally disappears at 290 K. These results agree with the change in the component of magnetization along the c‐axis as a function of temperature (Figure 1b). Below the paramagnetic‐FM transition temperature, the magnetization component along the c‐axis increases with decreasing temperature, resulting in the initial domains that are nucleated being small and gradually increasing in size to decrease the domain wall energy, which is dependent on M _s . Similarly while heating, the initial domains that are formed are small and they grow in size, eventually becoming smaller again before disappearing at 290 K.

One possibility in Region III is that a spin reorientation may occur, which can change the direction of magnetic moment from pointing along the c‐axis to the ab plane.^{[ 30} , ³² , ^{36 ]} To explore this possibility, we imaged magnetic domains in a TEM lamella fabricated with the c‐axis in the plane of the TEM sample (Figure S5, Supporting Information). In this orientation, due to the strong magnetocrystalline anisotropy of Mn_1.15Zn_0.85Sb, we observe the magnetization to be in the plane of the lamella oriented along the c‐axis. As the temperature was decreased to below 180 K, we did not observe any changes in the magnetization orientation, which suggests that there is no evident spin reorientation from the c axis to the ab plane, or the reoriented net magnetic moment at temperature Region III is too weak to be measured in the thin TEM lamella.

2.4. Origin of Effective DMI

In order to elucidate the origins of the DMI that results in the Néel‐type spin textures, we performed atomic resolution STEM HAADF imaging to determine atomic positions. The STEM HAADF image seen in Figure  5a displays the atomic‐resolution structure of the Mn_1.15Zn_0.85Sb sample viewed along the [010] zone axis. The Mn(I), Zn/Mn(II), and Sb atomic column positions agree very well with the reference crystal structure shown in the left schematic of Figure 5a.^{[ 36 ]} It should be noted here that Zn is known to replace the Mn atoms at the Mn(II) atomic sites in the crystal structure, as discussed earlier in this paper; however, it is not known whether they form an ordered or a disordered structure. Surprisingly, the Mn(I) atoms are not aligned in a straight line, but form a zig‐zag trajectory (the white circles in Figure 5b). It can be seen that the Mn(I) sites are preferentially located closer to the Sb ions than to the Zn/Mn(II) sites, as shown in Figure 5b and from the average intensity profiles shown in Figure 5c. We statistically evaluated the interatomic distances between the Sb and Mn(I) positions (d _{Sb − Mn} ), the Zn/Mn(II) and Mn(I) positions (d _{Zn − Mn} ) and the Zn and Sb positions (d _{Sb − Zn} ) as shown in the histograms in Figure 5e–g. The average values of the three projected distances are: d _{Sb − Mn} = 1.68(±0.15) Å, d _{Zn − Mn} = 1.77(±0.17) Å and d _{Sb − Zn} = 2.80(±0.07) Å. The quantitative analysis further illustrates that the Mn(I) ions prefer sitting further away from Zn/Mn(II) sites and closer to the Sb ions. The physical mechanism to form this local structure distortion may be complicated, which involves electrostatic interaction and magnetic correlation from neighboring ions, as well as atom size, during the growth of crystal. For example, this distortion may occur because electrostatic interaction between Mn(I)⁺¹ and Sb⁻³ is attractive and stronger compared to that between Mn(I)⁺¹ and Zn⁺² (Mn(II)⁺²) which is repulsive.^{[ 37 ]} In addition, we observe that the Mn(II) substitution by Zn is not uniform or ordered across the sample. Although Mn(II) and Zn ions have very close atomic numbers of Z = 25 and Z = 30, respectively, making it difficult to distinguish them in a HAADF image based on intensity, we did careful measurements of the intensity line profiles of several atomic columns as shown in Figure 5d. Based on these measurements, we are able to see that Zn substitution on the Mn(II) sites occurs randomly across the crystal. Therefore, the displacement of Mn(I) ions results in a local symmetry breaking, which induces effective DMI. Local defects have been reported to enhance the DMI.^{[ 51 ]} A similar phenomenon was also reported by C. Liu et al.,^{[ 52 ]} the so‐called effective DMI giving rise to Néel skyrmions.

Figure 5.

Origin of effective DMI. a) STEM HAADF image showing atomic‐resolution crystal structure viewed along the [010] zone axis. The left schematic shows the atomic positions viewed along the [010] zone axis.^{[ 36 ]} b) The positions of Mn(I) (white circles), Mn(II) (magenta circles), Zn (blue circles) and Sb (yellow circles) atoms in the magnified region that is highlighted by the box in (a). The Mn(I) atoms prefer being located close to Sb atoms. c) The average intensity of line profiles for two vertical columns, which are labeled by the pink and blue dash box, showing the peak of Mn(I) sits close to Sb and is away from Zn/(Mn(II)). The gray arrow in (b) indicates the direction of the vertical line profiles. d) The average intensity profile along the horizontal direction for the STEM HAADF image shown in the inset. The black arrow indicates the direction of the line profile. The Mn(II) and Zn atoms can be identified by the intensity difference: Mn(II) with lower atomic number has lower intensity peaks compared to Zn. The two gray dashed lines indicate the maxima of Mn(II) and Zn peak intensity. e–g) Histogram of (a) Sb‐Mn(I) distance (d _{Sb − Mn} ), Zn‐Mn(I) distance (d _{Zn − Mn} ) and Sb‐Zn distance (d _{Sb − Zn} ), where the black curve is the normal distribution. The two black dashed lines in (e) and (f) highlight the average distance of d _{Sb − Mn} and d _{Zn − Mn} .

3. Discussion and Conclusion

Zn‐rich Mn_1.15Zn_0.85Sb exhibits two magnetic phase transitions that are related to temperature. The magnetic properties, such as the magnetic anisotropy, coercive field and remanent magnetization, are also highly dependent on temperature, leading to clear changes in spin texture in the three temperature regimes. The temperature‐dependent magnetic behavior is due to the changes in the magnetic interactions between the two Mn sublattices, thereby affecting the FiM order. The transition from paramagnetic to FiM order occurs at the first transition temperature. Due to the significantly high magnetization, this state is effectively a strong FiM state. At the second transition temperature, the phase transition is from a strong FiM state to a weaker FiM state. It has been reported that out‐of‐plane spins at the Mn(I) and Mn(II) sites reorient to the in‐plane direction in Mn₂Sb across the second phase transition temperature, resulting in decreased magnetization along the c axis.^{[ 30 ]} However, we cannot prove the switch from an out‐of‐plane magnetization to an in‐plane magnetization in thin or bulk crystals at the low‐temperature Region III, using either LTEM or MOKE imaging. We also performed temperature‐dependent X‐ray diffraction, which did not show any changes in the crystal structure, therefore eliminating the possibility of a magneto‐structural transition (see Figure S6, Supporting Information). Thus, the changes in magnetic phase are due to changes in the magnetic interactions as a function of temperature in the Zn‐doped Mn_{2 − x} Zn _x Sb system.

We can further understand the formation of skyrmions in this material based on the critical material parameter for the skyrmion stability,^{[ 53 ]} $\kappa =\pi D{(4\sqrt{A{K}_u})}^{-1}$, where D is the DMI coefficient, A is the micromagnetic exchange constant, and K _u is the uniaxial anisotropy constant. As the temperature changes from Region I to Region III, the effective anisotropy of Mn_1.15Zn_0.85Sb gradually increases as determined from the change in the coercive field and the remanent magnetization. This increase in anisotropy is inversely proportional to κ and hence reduces the tendency of the material to form stable skyrmions. A similar observation was also made for FiM multilayers of [Pt/Fe_{1 − x} Tb _x /Ta].^{[ 27 ]}

In summary, we have explored the temperature‐dependent magnetic properties of Mn_1.15Zn_0.85Sb, and have confirmed the presence of nontrivial chiral Néel‐type spin textures in the thin lamella via direct visualization. The resulting spin textures show very different behavior in three distinct temperature regions. The unique skyrmion bag spin textures are formed only in the presence of a strong perpendicular anisotropy (Region II). The displacement of the Mn(I) atomic sites toward the Sb sites results in an effective DMI that enables the formation of the Néel‐type spin textures. Our work thus demonstrates interesting pathways to introduce a symmetry‐breaking DMI interaction in centrosymmetric crystal structures through doping. Our study shows the existence of rich topological spin textures in FiMs, which can be controlled by temperature and magnetic fields, thereby making this material a promising candidate for future applications in spintronics or information storage.

4. Experimental Section

Crystal Synthesis

Single crystals of Mn_2‐x Zn _x Sb were grown with a self‐flux method using a Zn flux. To initiate the growth process of an Mn_1.15Zn_0.85Sb crystal, Mn powder (99.6%, Alpha Aesar), Zn powder (99.9%, Alpha Aesar), and Sb powder (99.5%, Beantown Chemical) were loaded in an alumina crucible at an atomic ratio of Mn: Zn: Sb = 1.2: 6: 1. The crucible was then sealed in a quartz tube evacuated below 10⁻¹ Pa. The tube was gradually heated over 30 – 40 hours to reach the maximum temperature of 900 °C, held at this temperature for 3 days, slowly cooled down (3 K min⁻¹) to 600 °C, followed by subsequent centrifuge to remove the Zn flux.

Magnetization Characterization

The temperature‐dependent magnetization was measured using a superconducting quantum interference device (SQUID) magnetometer. The crystal was cooled down from 330 to 2 K without (with) an applied magnetic field for the ZFC (FC) run, with the field applied along the c axis of the Mn_1.15Zn_0.85Sb crystal. The strength of the magnetic moment was recorded with a 50 or 100 mT magnetic field applied when heating the sample from 2 to 330 K. The calculated density of the Mn_1.15Zn_0.85Sb crystal (7.33 g cm⁻³) was used to normalize the magnetization to mass.

The field‐dependent magnetization was measured using a physical properties measurement system (PPMS). The sample was mounted in a standard quartz holder for in‐plane magnetization measurements, while a standard brass holder was used for out‐of‐plane magnetization measurements. Isothermal magnetization measurements were performed by sweeping the applied magnetic field between ‐9 and 9 T for hysteresis loop measurements. To ensure accurate magnetization measurements, the background signal from the sample holder was separately measured and subtracted.

MOKE Measurement

Polar‐MOKE images were recorded using a commercial microscope from Evico magnetics. The bulk Mn_1.15Zn_0.85Sb sample was mounted using GE varnish inside an optical cryostat, which was cooled using liquid nitrogen to obtain a minimum temperature of 80 K. An in‐house made solenoid was utilized to apply magnetic fields up to 135 mT, perpendicular to the crystal surface being imaged. Magnetic contrast was optimized by subtracting a MOKE image taken at a saturating field of 135 mT from images acquired at lower fields. However, magnetic domains of the Mn_1.15Zn_0.85Sb crystal cannot be polarized by a 135 mT magnetic field when the temperature is 120 K. Therefore, the magnetic contrast cannot be improved and contaminating black spots cannot be removed using this approach.

TEM Experiment

Thin Mn_1.15Zn_0.85Sb lamellae for TEM analysis were prepared using a Zeiss NVision focused ion beam (FIB) system. The cryo LTEM measurements were carried out using a Gatan liquid nitrogen holder. The experiment to confirm the Néel‐type domains was carried out using a FEI Tecnai F20ST TEM operating in Lorentz mode at 200 kV. The LTEM images as a function of temperature were recorded on a JEOL 2100F TEM with an image corrector. The STEM HAADF experiment to analyse atomic‐resolution structure was carried out in a ThermoFisher Scientific Spectra 200 with 200 kV accelerating voltage.

X‐ray Scattering Measurement

Synchrotron X‐ray scattering measurements were performed at Sector 6‐ID‐D of the Advanced Photon Source at Argonne National Laboratory. Data were collected using an incident energy of 87.1 keV and a Dectris Pilatus 2M detector with the sample continuously rotated about an axis perpendicular to the beam at 1° s⁻¹ over 365°, with images read out every 0.1 s. Data were collected between 100 and 300 K, with samples cooled in a flowing nitrogen gas stream. Three sets of rotation images were collected at each temperature to fill in gaps between the detector chips. These images were combined and transformed into reciprocal space coordinates,^{[ 54 ]} resulting in a continuous volume of measured scattering intensities over approximately ±15 Å⁻¹ in all directions.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supplemental Video 1

Li Y., Nabi M. R. U., Park H., Liu Y., Rosenkranz S., Petford‐Long A. K., Hu J., Velthuis S. G. te, Phatak C., Observation of Topological Spin Textures in Ferrimagnetic Mn_{2 − x} Zn _x Sb. Small 2025, 21, 2406299. 10.1002/smll.202406299

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.