Observation of Magnetic Antiskyrmions in the Low Magnetization Ferrimagnet Mn2Rh0.95Ir0.05Sn.

Recently, magnetic antiskyrmions were discovered in Mn1.4Pt0.9Pd0.1Sn, an inverse tetragonal Heusler compound that is nominally a ferrimagnet, but which can only be formed with substantial Mn vacancies. The vacancies reduce considerably the compensation of the moments between the two expected antiferromagnetically coupled Mn sub-lattices so that the overall magnetization is very high and the compound is almost a "ferromagnet". Here, we report the observation of antiskyrmions in a second inverse tetragonal Heusler compound, Mn2Rh0.95Ir0.05Sn, which can be formed stoichiometrically without any Mn vacancies and which thus exhibits a much smaller magnetization. Individual and lattices of antiskyrmions can be stabilized over a wide range of temperature from near room temperature to 100 K, the base temperature of the Lorentz transmission electron microscope used to image them. In low magnetic fields helical spin textures are found which evolve into antiskyrmion structures in the presence of small magnetic fields. A weaker Dzyaloshinskii-Moriya interaction (DMI), that stabilizes the antiskyrmions, is expected for the 4d element Rh as compared to the 5d element Pt, so that the observation of antiskyrmions in Mn2Rh0.95Ir0.05Sn establishes the intrinsic stability of antiskyrmions in these Heusler compounds. Moreover, the finding of antiskyrmions with substantially lower magnetization promises, via chemical tuning, even zero moment antiskyrmions with important technological import.

Magnetic skyrmions (Sks) are topologically protected vortices of magnetization that can be stabilized in magnetic materials with broken inversion symmetry.[1−9] Since the first observation of skyrmion lattices in the helimagnet MnSi,[4] a variety of noncollinear spin textures have been discovered in several distinct families of materials.[10−22] These spin textures have technological potential[23,24] as, for example, magnetic bits in high density storage devices such as racetrack memories[25−27] or for neuromorphic computing applications.[28] Recently, using Lorentz transmission electron microscopy (LTEM) a new topological spin texture that has distinct topological characteristics from that of Bloch and Néel skyrmions was discovered in a noncentrosymmetric inverse tetragonal Heusler compound. This compound with D2 crystal symmetry stabilizes a novel noncollinear spin texture, namely an antiskyrmion (aSk).[29] However, the material in which the antiskyrmions were observed, Mn1.4Pt0.9Pd0.1Sn, could only be stabilized by introducing a large number of Mn vacancies.[29] These vacancies strongly affect the overall magnetization of the compound.

The magnetic structure of Mn2RhSn consists of two ferromagnetically aligned Mn sub-lattices that are antiferromagnetically coupled to each other[30] so leading to a net magnetic moment of ∼2 μB/f.u. at 2 K. By contrast, the magnetization of Mn1.4Pt0.9Pd0.1Sn and its close cousin Mn1.4PtSn is much higher, namely ∼4.5 μB/f.u. at 2 K.[29] Thus, it has been reported that Mn1.4Pt0.9Pd0.1Sn and Mn1.4PtSn are both effectively ferromagnets.[31−33] For spintronic devices, elimination of long-range dipole fields derived from the moments of small magnetic nano-objects is key to their success.[34−39] For application of antiskyrmions low or even zero moment hosting materials are very important. In this study we have explored the possibility of antiskyrmions in Mn2Rh0.95Ir0.05Sn, a Heusler compound that has a significantly reduced magnetization compared to the only previous Heusler material in which antiskyrmions were observed, but with enough magnetization that the antiskyrmions can be observed with Lorentz transmission electron microscopy. Mn2Rh0.95Ir0.05Sn can be formed without any significant Mn vacancies. We directly show the formation of antiskyrmions in this compound. This opens the path to the full exploitation of the considerable tunability of Heusler compounds for zero-moment antiskyrmions.

Polycrystalline samples of Mn2Rh0.95Ir0.05Sn were prepared by inductive melting of stoichiometric amounts of the elements Mn, Ir, Rh, and Sn of purity >99.99% in alumina crucibles. Due to the high melting points of iridium and rhodium, Rh and Ir powders were first prealloyed together with Sn. The alloy was kept in the melted state for approximately a minute before cooling down. This step was repeated three times to ensure good homogenization of the prealloy. Next, Mn chips were added to the Rh/Ir–Sn ingot followed by remelting and turning the ingots several times for better homogeneity. This procedure ensures a low loss of Mn due to evaporation, indeed for the final ingot, the total mass loss was below 0.5 wt % so that the composition of the ingot is close to the desired stoichiometry. The as-prepared ingots were then packed in closed tantalum crucibles that were further encapsulated in an evacuated fused quartz glass ampule. A subsequent heat treatment for 1 week at 900 °C was performed followed by quenching in an ice–water mixture resulting in the final polycrystalline ingot.

Polycrystalline samples were characterized by powder X-ray diffraction (PXRD) using an image-plate Guinier camera (Huber G670, Cu Kα1, λ = 1.54059 Å). Peak search, indexing, and calculation of the diffraction patterns were performed with the aid of the WinXPow package.[40] All Bragg reflections can be indexed to a body-centered tetragonal unit cell with a = 4.293 (3) Å and c = 6.592 (4) Å. Rietveld refinement was carried out using the Jana2006 software.[41] The crystal structure was resolved by analogy with Mn2RhSn, which crystallizes in the I4m2 (D2) space group.[30] Under this symmetry Mn atoms occupy two different Wyckoff positions, namely MnI at 2b and MnII at 2c, while Rh occupies 2d and Sn in the 2a position, respectively. For our refinement Ir was assumed to occupy the Rh position. Cases in which Ir additionally occupies the Sn or Mn sites do not lead to an improvement of the refinement, hence the later possibility is discarded. The Rietveld refinement of the XRD pattern is given in the Supporting Information (SI) (Figure S1). The stoichiometry of the titled compound from inductively coupled plasma optical emission spectrometry (ICP-OES) analysis is found to be Mn1.988Rh0.949Ir0.049Sn1.015 (within estimated standard deviation of 0.1–0.2 at %). In addition, the composition of the sample was also determined from energy-dispersive X-ray spectroscopy (EDXS) analysis that shows that it is stoichiometric (Figure S2).

The temperature and field (H) dependent DC magnetization (M) measurements of the bulk polycrystalline sample were carried out with a SQUID-VSM [MPMS3, Quantum design]. M(H) loops measured at different temperatures are shown in Figure a. The saturation magnetization of this material is calculated from these measurements to be ∼2 μB/f.u. at 2 K and is reduced further to ∼1 μB/f.u. at 250 K. The saturation magnetization is nearly two times smaller than that of the first inverse Heusler material in which antiskyrmions were observed.[29] From the isothermal magnetization data it is apparent that this material is magnetically soft. The temperature dependent magnetization was measured in a field of 0.1 T for the temperature range from 2 to 390 K after both zero-field-cooling (ZFC) and field-cooling (FC) (Figure a). These data shows that the material undergoes a magnetic ordering transition from a paramagnetic to a ferrimagnetic state at ∼270 K with a second magnetic transition at 80 K. The latter transition has been attributed to a spin-canting transition that results from a competition between exchange interactions between Mn moments on neighboring and next nearest planes.[30] The spin-canting transition is suppressed in higher fields as seen from the temperature-dependent magnetization data at 1 T (see the inset of Figure a).

Figure 1

(a) M(H) hysteresis loops at various temperatures. The inset displays ZFC (black color) and FC (green color) temperature dependent magnetization data in the presence of 0.1 T and 1 T fields. (b) Selected area electron diffraction (SAED) pattern from a thin lamella showing the [100] orientation. (c) The upper panel shows the schematic arrangement of Mn, Rh, and Sn atoms, and the lower panel shows a simulated STEM pattern with superimposed Mn, Rh, and Sn atoms as a guide to the eye. (d) Experimental STEM image along [100]: the inset shows an expanded view.

For in-situ transmission electron microscopy (TEM) investigations, using a FEI TITAN 300 keV microscope, single crystalline lamellae, oriented along different crystal directions, were prepared from individual grains from within the polycrystalline Mn2Rh0.95Ir0.05Sn bulk sample. The small grain size (∼10 μm) meant that this was nontrivial (Figure S3). The lamellae were prepared using a Ga-focused ion beam (FIB) milling at an acceleration voltage of 30 keV [FEI, Nova nano Lab]. Final polishing was carried out on both sides of the lamella using a low energy beam (2 keV) to reduce surface amorphization. In this way a [100] oriented lamella, approximately 60 nm thick, was prepared, as confirmed by the exemplary selected area electron diffraction pattern (SAED) shown in Figure b. A schematic atomic arrangement of the Sn, Rh, and Mn atomic columns along this zone axis is shown in Figure c. The schematic unit cell for this tetragonal structure is shown in the upper panel. In the lower panel, a simulated scanning transmission electron microscopy (STEM) image using the aforementioned space group is shown.[42] This simulated image is in agreement with the experimental STEM image given in Figure d. An enlarged portion of the image from the experimental STEM is shown in the inset of Figure d.

For crystals with D2 symmetry,[29,30] an aSk lattice is stabilized within the tetragonal basal plane, so that it is necessary to carry out measurements on lamellae oriented along [001] in order to observe any aSk. High resolution TEM (HRTEM) images of such a lamella obtained in TEM mode are shown in Figure showing (020) and (200) lattice planes. A fast Fourier transform (FFT) is given in Figure b together with the SAED (inset): these show that the lamella was [001] oriented.

Figure 2

(a) High resolution transmission electron microscope image for a [001] oriented lamella and (b) the corresponding fast Fourier transform. The inset of Figure b shows the [001] oriented selected area electron diffraction (SAED) pattern. (c) Schematic of an antiskyrmion spin texture. (d) LTEM image of a single antiskyrmion at 150 K in the presence of a magnetic field of 83 mT. Inset shows the intensity profile of the contrast along [010] (blue color) and [100] (orange color) directions.

To explore magnetic textures within the lamellae, Lorentz TEM (LTEM) was carried out using a GATAN double tilt liquid nitrogen sample holder that allows for variable temperatures between 100 K and room temperature. Clear evidence for the presence of aSk in the sample was found. A typical LTEM image of a single aSk at 150 K and 83 mT is shown in Figure d. This image is consistent with the schematic aSk spin structure shown in Figure c in which Bloch domain walls of opposite chirality are formed along the [100] and [010] directions, while Néel domain walls of opposite chirality are formed along the [110] and [1-10] directions. The inset of Figure d shows the LTEM contrast profile along the [010] and [100], respectively.

The magnetic field driven evolution of the aSk spin textures at a constant temperature (150 K) is examined after cooling the sample in zero magnetic field from 300 K. After stabilizing the temperature at 150 K, the LTEM images were recorded in zero field. These images show patterns in the form of alternating dark and light stripes, as shown in Figure a, which are characteristic of a helical spin structure. The direction of propagation of the helix is oriented along either [010] or [100] which are the directions along which Bloch domain walls are formed. The presence of magnetic dislocations is observed as the branching of helix marked by arrows in Figure a.[5,43,44] The movement and annihilation of these dislocations are observed upon application of a magnetic field (Figure S4). To apply a magnetic field to the sample, the sample was first tilted away from the [001] direction by ∼25°, and a magnetic field was applied along the microscope column by adjusting the current in the objective lens. The sample was tilted back to a near zero degree tilt to record the LTEM images. This process of tilting, which allows for the application of a small in-plane magnetic field at the sample, was successively repeated to allow for LTEM images to be recorded at various perpendicular magnetic fields (zero degree tilt). This tilting procedure is needed to stabilize the aSk lattice.[29] Upon increasing the magnetic field following the aforementioned protocol, aSks were found to start to emerge from the helical spin texture at a field of ∼75 mT and to coexist with the helical spin texture for fields up to ∼83 mT (Figure b,c). Further increments of the magnetic field (90–94 mT) lead to the formation of a pure aSk lattice, as shown in Figure d,e, which is a slightly distorted hexagonal array. We note that a well-defined strong hexagonal lattice is not found: the likely reason is the low moment of the antiskyrmions here which leads to weak magnetostatic interactions between them. With increasing the magnetic field up to ∼99–104 mT the density of aSks decreases (Figure f–g) and finally transforms to a fully field-polarized state at ∼112 mT (Figure h).

Figure 3

Lorentz transmission electron microscopy images of magnetic spin-textures at (a) zero magnetic field and (b–h) various magnetic fields at 150 K. Scale bar for all figures is identical and is given in (h).

The evolution of the aSk texture as a function of magnetic field was performed at several temperatures. The results are summarized in the form of a magnetic phase diagram in Figure a. This phase diagram was constructed by cooling the sample from 300 to 100 K in zero magnetic field. After stabilizing the temperature at 100 K, the evolution of the helical to aSk lattice was studied using the protocol described in the previous paragraph. The temperature was subsequently increased successively in 25 K steps, and LTEM studies were carried out at each temperature. These results are presented in the magnetic phase diagram shown as a contour map of the aSk density in the temperature (T) - magnetic field (B) plane (Figure a). In the absence of magnetic field the ground state is the helical state. The period of the helix (λ) is in the range of ∼200–235 nm depending on the temperature (Figure S5). This period is larger by ∼50% than that reported for Mn1.4Pt0.9Pd0.1Sn for the same thickness of the LTEM sample. As λ is inversely proportional to DMI[12,45] the larger helical period in Mn2Rh0.95Ir0.05Sn is consistent with a weaker value of the DMI that is expected for the 4d element Rh as compared to the 5d element Pt.[46−48] From Figure a, it is clear that the generation of the aSk lattice from the helical phase requires lower magnetic fields at higher temperature or vice versa. The aSk lattice is stabilized over a wide window of temperature but in a relatively narrow magnetic field range. In Figure b the effect of magnetic field on the aSk size at different temperatures is shown. The aSk size was found using procedures discussed in reference (49). From this figure, we observe that at each temperature, there is a minute change in the size of aSks with field.

Figure 4

(a) Magnetic phase diagram of Mn2Rh0.95Ir0.05Sn. (b) Antiskyrmion size as a function of perpendicular magnetic field at various temperatures. The error bars correspond to standard deviation in the aSk size. Here aSk, H, and FP correspond to antiskyrmion, helical, and field polarized states, respectively.

In conclusion, we have successfully identified the existence of magnetic aSks in an inverse ferrimagnetic Heusler compound, Mn2Rh0.95Ir0.05Sn, that is fully stoichiometric, as compared with our earlier observations of aSks in the compound, Mn1.4Pt0.9Pd0.1Sn, that contains substantial Mn vacancies and which, as a consequence, is nearly ferromagnetic. Antiskyrmions, in this second compound, are observed in a narrower region of field but, nevertheless, over a wide range of temperature. These results prove the intrinsic stability of a ground state composed of arrays of antiskyrmion in compounds that have D2 symmetry and, moreover, show that antiskyrmions can be found in materials with low saturation magnetization as well as smaller DMI. Our work opens the path to the observation of antiskyrmions in the large number of materials that have D2 symmetry, allowing for optimizing the properties of the host compounds, especially tuning the magnetization to zero, that would make them highly useful for various technological applications.