Magnetic tunability in tetragonal Mn–Rh–Ir–Sn inverse Heusler compounds

Gaining control over magnetic structure has been an ongoing challenge in materials that form complex, nanoscale, and non-collinear magnetic configurations. Recently, it was predicted that tuning the ratio of the Dzyaloshinskii–Moriya interaction to the uniaxial magnetic anisotropy in tetragonal inverse Heuslers through changes in composition could allow a range of interesting magnetic states to be accessed, from simple ferrimagnetism, to helical and antiskyrmionic phases. Here, we show tunability of the magnetic phase behavior in the Mn–Rh–Sn system through Ir substitution on the Rh substructure. Iridium substitution correlates to an increase in the strength of ferromagnetic exchange couplings, at the expense of antiferromagnetic exchange couplings. However, we do not observe the complex non-collinear magnetic phases proposed previously, likely due to the extremely narrow composition window where these phases are predicted to form in a bulk sample. This work highlights the sensitivity of complex magnetic structures to stoichiometry, which makes them difficult to discover empirically.


Introduction
The realization of spintronic devices requires precise control over exotic magnetic states, beyond that available today.Skyrmions are an attractive option for developing next generation, high-density, non-volatile magnetic data storage through mechanisms including racetrack memory [1][2][3].Utilizing skyrmions rather than magnetic domains solves several problems associated with racetrack memory, as skyrmions are * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Skyrmions are challenging to detect from both an experimental and a material standpoint.Their small magnetic moments can be below the limit of detection of traditional magnetometry and they are easily field polarized, particularly in the case of anti-skyrmions [2,14].The primary experimental methods to detect sykrmions are time intensive and difficult to access, such as Lorentz Transmission Electron Microscopy and small angle neutron scattering [4,[15][16][17].Magnetoentropic mapping, which can be accomplished through a transformation of magnetometry data, has been proposed as a solution but has yet to be widely adopted [18,19].In addition to methodology challenges most skyrmion hosts have narrow temperature and field windows of skyrmion stability, increasing the time and instrument resources necessary to evaluate candidate materials [4,14,20,21].These experimental limitations motivate the development of rapid experimental or computational screening methods.
The driving forces for skyrmion formation are complex.Skyrmions are two-dimensional magnetic nano-structures often described as 'vortex-like' or 'screw-like'.References [2,23,24] These circular structures are characterized an outer domain and an anti-parallel skyrmion core, separated by progressively rotating moments [24].To host a skyrmion, materials must crystallize with chiral symmetry, e.g.lack an inversion center, which allows a non-zero magnitude of the Dzyaloshinskii-Moriya interaction (D).D describes the propensity of moments to cant, diverging from totally parallel or anti-parallel orientations [25][26][27].Weak unaxial anisotropy (A), which will encourage moment reorientation, works with D to encourage skyrmion formation [28].Gaining control over skyrmion formation necessitates control over D and A.
Tetragonal inverse Heuslers are an ideal material class to tune D and A. Structural distortions, often stimulated through composition based changes in bonding, are known to lead to new functionality within the parent Heusler phase [29].The structural distortion that links the parent Heusler and tetragonal inverse Heusler structure types removes the inversion center to yield D 2d symmetry [30].The magnetic ion, generally Mn, occupies sites within both the rock salt site and interstitial tetrahedral site (figure 1).This generates competing magnetic interactions, which lead to exotic magnetic ground states [22,31].Composition tunes the magnetic ground state and phase evolution within tetragonal inverse Heusler materials [32][33][34].Recent computational results suggest that composition changes both the atomistic magnetic exhange couplings and the values of D, A, and the magnetic anisotropy (K) [31].These results indicate that there are critical ratios of D, A, and K that promote the formation of long-range helical, conical, and antiskyrmion spin textures [31].
Lorentz transition electron microscopy experiments have recently demonstrated the presence of antiskyrmions in the tetragonal inverse Heusler Mn 2 Rh 0.95 Ir 0.05 Sn [4].The precise composition of this material and need for substitution suggest that this material has the critical combination of magnetic exchange couplings, D, A, and K proposed in the computational work [31].
Here, we examine the magnetic behavior of several members of the solid solution series Mn 2 Rh 1−x Ir x Sn.We demonstrate that Ir substitution modifies the magnetism of the Mn 2 RhSn parent structure, strengthening the ferromagnetic character of the material and weakening its antiferromagnetic components.However, our magnetic data show no evidence of the long-range spin-textures reported previously, likely due to the extremely narrow composition range where these The tetragonal inverse Heusler structure.The most electropositive metal (Mn) occupies the rock-salt layer with the most electronegative metal (Sn).The remaining equivalent of Mn occupies half of the tetrahedral interstitial sites between the rock-salt layers, while the third metal (Rh/Ir) occupies the other half.Typically, Mn is the only magnetic element.As it occupies two different sites, one tetrahedral and one octahedral, there are several distinct magnetic coupling constants J i .In all known materials in this class, J 1 is such that the layers perpendicular to the c-axis couple antiferromagnetically, favoring a net ferrimagnetic spin structure [22].J 2 and J 3 are less fixed and can compete with J 1 to modify the local spin order and form a range of possible magnetic ground states.
phases are predicted to occur in bulk samples.Our results highlight the sensitivity of magnetic phase formation to composition variations, highlighting the importance of computational screening and suggesting that skyrmion-host candidate materials should be tested and optimized for error tolerance in material formation.

Sample preparation
Rh, Ir, and Sn powders were used as received.Sn was stored in a desiccator under vacuum.Mn pieces were cleaned by heating to 800 • C for 8 h in an evacuated silica ampoule.The series Mn 2 Rh 1−x Ir x Sn was prepared through traditional solid state methods.Stoichiometric ratios of the metals were ground, pressed into a pellet, and sealed into a silica ampoule under vacuum.The samples were then heated to 1100 • C, held at temperature for one hour, cooled to 900 • C over an hour, held at temperature for 18 h, and then water quenched.Samples were then ground and powder annealed at 900 • C for one hour.

Diffraction
Laboratory diffraction data were collected on a Panalytical Empyrean Powder Diffractometer.Temperature-dependent high-resolution synchrotron powder x-ray diffraction studies were performed on beamline 11-BM-B at the Advanced Photon Source, Argonnne National Laboratory.Using Apiezon N-grease as an adhesive, powdered samples were adhered to a small diameter polyimide tube, which was then inserted into a larger diameter polyimide tube and sealed using modeling clay.Time-of-flight neutron powder diffraction patterns were collected on the diffractometer POWGEN at the Spallation Neutron Source, Oak Ridge National Laboratory.X-ray diffraction patterns were fit with the TOPAS suite.Neutron and joint neutron-x-ray refinements were performed in GSAS-II.

Energy dispersive x-ray spectroscopy
Images and spectra were collected on a Hitatchi TM4000Plus tabletop Microscope.Data were analyzed using the automated processes in AztexOne.

Magnetic measurements
Magnetic data were collected on a Quantum Design MPMS3.Milligrams of powdered samples were packed into propylene containers.All temperature-dependent data were collected on heating at a rate of 2 K per minute.Data analysis was performed in python.

Results
Mn 2 RhSn crystallizes in the tetragonal inverse Heusler structure at room temperature, as do the members of the Mn 2 Rh 1−x Ir x Sn solid solution series.As Mn is more electropositive than Rh, it occupies the rock salt layers with tin.Rhodium and the other equivalent of Mn occupy the tetrahedral interstitial sites.
We have prepared several members of the solid solution series Mn 2 Rh 1−x Ir x Sn.The substitution level x was determined through energy dispersive x-ray spectroscopy (EDX) and is shown in table 1.The nominal concentration of Ir based on the molar ratio of the precursors is lower than the value detected in EDX for samples with a large Ir content.The amount of Mn is also larger than the nominal molar ratio, perhaps suggesting Sn vacancies.For the remainder of the text, samples will be referred to as Mn 2 Rh 1−x Ir x Sn, where x is the molar ratio of Ir measured through EDX as expressed in the resulting formula in table 1.
Despite these discrepancies, all members of the series crystallize in the tetragonal inverse Heusler structure, including the parent material Mn   percentages of Rh and Ir from EDX result in a good visual fit during Rietveld refinement.Heusler materials have several known disorder pathways that can be differentiated by the low angle reflections [22].Here, we observe only one reflection below Q = 3 Å −1 , consistent with the tetragonal inverse structure.There are some discrepancies between the intensity of the data and the fit for several reflections that could indicate disorder, but allowing the occupanices to refine from the values ascertained from EDX does not improve the fit visually or statistically.Mn 2 RhSn undergoes two known magnetic transitions [21].At base temperature, Mn 2 RhSn is in a canted ferrimangetic state, where spins are aligned ferromagnetically in their respective ab planes, antiferromagnetically between these planes, and are not constrained to be parallel to the c axis.This structure is consistent with the computed values of J 1 − J 2 − J 3 for Mn 2 RhSn listed in table 2. While J 1 < 0 favors an antiferromagnetic coupling between the Mn planes, both J 2 < 0 and J 3 < 0 frustrate this order by penalizing the resulting collinear ferrimagnetic structure.Evidently, this frustration is significant enough to lead to a canted-spin ground state.Consistent with previous neutron diffraction studies [21], we find that on heating to 80 K, the susceptibility the magnetization exhibits a discontinuity as Mn 2 RhSn transitions to a collinear ferrimagnetic state where spins align ferromagnetically in the ab plane and antiferromagnetically along the caxis.Further heating above 270 K leads to a further reduction in the magnetic susceptibility as the material transitions to a paramagnetic state.These transitions are apparent in the temperature-dependent magnetization in figure 3 as a Néel type feature in magnetization near 80 K and as a decrease in the magnetic susceptibility (χ) at 270 K on heating.
The Ir substituted members of the Mn 2 Rh 1−x Ir x Sn series exhibit similar qualitative magnetic behavior to the parent material Mn 2 RhSn.In the temperature-dependent magnetic susceptibility (figure 4), all materials show the same Néel type feature on heating from base temperature, followed by a dramatic decrease in χ near room temperature.The field-cooled (FC) and zero field-cooled (ZFC) susceptibility diverge at temperatures below the paramagnetic to ferrimagnetic transition, suggesting significant domain formation.The high temperature feature is quite broad, which makes determining the Curie temperature challenging.Therefore we calculated the derivative δM δH , where the high temperature feature is a well-resolved negative peak.We assign the Curie temperature as this peak minimum.The Néel transition manifests as a peak in the susceptibility in all samples and a similar low intensity peak in the derivative of the magnetization.We assign the Néel temperature as the peak maximum of the feature in the field cooled susceptibility and the high temperature side of the feature in the derivative of the zero-field magnetization.
The derivative of the magnetization becomes increasingly noisy and the features wider with increasing Ir content.We  attribute this to the disorder that stochastic substitution brings to the system.In the highly substituted samples there are many possible configurations of Rh and Ir around the Mn magnetic centers, leading to a range of local environments that can affect the magnetism.
Field dependent measurements collected at temperatures below both magnetic phase transitions (figure 5) show the characteristic saturated 'S' shape of an uncompensated system.The saturation magnetization for Mn 2 RhSn is 2 µ B per Mn, which is consistent with the known ferrimagnetic state [21].All samples can be classified as soft magnets, with coercive fields below 1 kOe.
The sample with x = 0.06 has a composition quite close to the known antiskyrmion host Mn 2 Rh 0.95 Ir 0.05 Sn.The small net moment of antiskyrmions make detecting them through traditional magnetometry quite challenging.However, complex spin structures tend to be associated with clear entropic signatures that can be observed by transforming temperaturedependent magnetization into isothermal entropy change upon magnetization ∆S M (H, T) [18].Briefly, the temperature dependent magnetization is differentiated and re-integrated according to the formula: Figure 6(a) shows temperature-dependent magnetization data spanning the known antiskyrmion pocket for Mn 2 Rh 0.95 Ir 0.05 Sn previously observed through LTEM [4].These data were then numerically differentiated (figure 6(b)) and integrated according to equation ( 1), giving the entropic curves shown in figure 6(c).In the region of interest, the raw, differentiated, and integrated terms are smooth.This analysis suggests a lack of change to the magnetic structure, particularly the formation of large magnetic bodies.

Discussion
The observation of antiskyrmions in Mn 2 Rh 0.95 Ir 0.05 Sn supported theoretical claims that tetragonal inverse Heusler materials could host such topologies [4].Computational efforts to explain why this specific composition was needed to form antiskyrmions suggested that one needed a precise balance of magnetic coupling strengths (J i ) as well as critical values of D and K [31].Changes in composition was one proposed method to manipulate these values in real materials.The magnetic data presented above indicate that composition changes in Mn 2 Rh 1−x Ir x Sn change the magnetic coupling strengths.Both magnetic phase transitions vary in temperature monotonically with x (figures 4 and 7(a), (b)).The Curie temperature decreases with increasing Ir content, while the Néel temperature increases with increasing Ir content.The trend in Curie temperature is consistent with the relative values of the exchange constants computed for the pure-Rh and pure-Ir endmembers.All exchange constants J i are weaker in Mn 2 IrSn compared to Mn 2 RhSn as shown in table 2, which absent any discontinuous changes in magnetic structure suggests a lowering of the Curie temperature.Furthermore, the saturation magnetization from the field-dependent studies (figure 5) also increases with increasing Ir content (figure 7(c)), indicating an increase in uncompensated spins.These trends indicate an effective strengthening of ferromagnetic and weakening of antiferromagnetic interactions.This trend, as well as the evolution of the Néel temperature, is consistent with a smaller degree of frustration between J 1 and J 2,3 in the Mn 2 IrSn endpoint as compared to Mn 2 RhSn, quantified by the ratios  tabulated for Mn 2 RhSn and Mn 2 IrSn from this previous work and reproduced in table 2 we can plot 2 × K × A × D −2 as a function of x.In the Rh-rich regime, this relationship has a steep slope (figure 8).The composition range in which skyrmion formation is possible is therefore quite narrow and centered near x = 0.05, consistent with the previous observation of antiskyrmions in Mn 2 Rh 0.95 Ir 0.05 Sn [4].In our bulk samples, the nominal stoichiometry is outside of this ideal skyrmion window, and local inhomogeneities from the bulk, particulate nature of the samples removes us further from the sykrmion window.

Conclusion
Developing control over the formation of complex spin structures in materials necessitates a deep understanding of the physical driving forces for their formation and competing ground states.These forces span atomistic to microscopic scales, from magnetic coupling strengths to the Dzyaloshinskii-Moriya interaction strength and magnetic anisotropy.Tetragonal inverse Heusler materials have been host complex spin structures, including antiskyrmions in the Mn 2 Rh 1−x Ir x Sn system.Here, we have demonstrated that Ir substitution changes the magnetic coupling strengths between Mn magnetic centers.Additionally, our magnetic data are qualitatively consistent with computational results to predict compositional windows in tetragonal inverse Heusler materials for skyrmion formation using only the Dzyaloshinskii-Moriya interaction strength, unaxial anisotropy, magnetic anisotropy values.

Figure 1 .
Figure 1.The tetragonal inverse Heusler structure.The most electropositive metal (Mn) occupies the rock-salt layer with the most electronegative metal (Sn).The remaining equivalent of Mn occupies half of the tetrahedral interstitial sites between the rock-salt layers, while the third metal (Rh/Ir) occupies the other half.Typically, Mn is the only magnetic element.As it occupies two different sites, one tetrahedral and one octahedral, there are several distinct magnetic coupling constants J i .In all known materials in this class, J 1 is such that the layers perpendicular to the c-axis couple antiferromagnetically, favoring a net ferrimagnetic spin structure[22].J 2 and J 3 are less fixed and can compete with J 1 to modify the local spin order and form a range of possible magnetic ground states.
2 RhSn (figures 2(a) and (b)).Synchrotron x-ray and neutron diffraction patterns of Mn 2 Rh 0.7 Ir 0.4 Sn and Mn 2 Rh 0.4 Ir 0.6 Sn, shown in figures 2(c)-(f) respectively, closely resemble that of the Rh parent material.The

Figure 2 .
Figure 2. Selected Q range of synchrotron x-ray and neutron diffraction patterns collected at room temperature for several members of the series Mn 2 Rh 1−x IrxSn.The data are represented as black circles, the fit from joint x-ray and neutron Rietveld refinements is shown in orange, and the difference is shown in grey.

Figure 3 .
Figure 3. FC and ZFC temperature-dependent magnetic susceptibility of Mn 2 RhSn collected on warming under an external field of (a) 1 kOe, (b) 100 Oe, and (c) 10 Oe.

Figure 4 .
Figure 4. FC and ZFC temperature-dependent magnetic susceptibility compared to the differentiated magnetization of the series Mn 2 Rh 1−x IrxSn collected under a 100 Oe external field.The temperature of each transition was determined from the features in both the susceptibility and the differentiated magnetization and is indicated by a vertical dashed grey line.

Figure 5 .
Figure 5. Field-dependent magnetization collected at a temperature of 2 K for several members of the series Mn 2 Rh 1−x IrxSn.

Figure
Figure (a) Temperature-dependent magnetization of Mn 2.2 Rh 0.98 Ir 0.06 Sn collected under applied fields of 200 Oe, 600 Oe, 900 Oe, 1250 Oe, and 1750 Oe.(b) The derivative of the data in panel (a), calculated numerically.(c) The magnetic entropy change ∆S M calculated according to equation (1) based on panels (a) and (b).

Figure 7 .
Figure 7.The change in (a) Curie temperature, (b) Néel temperature, and (c) saturation magnetization with increasing amounts of Ir in the series Mn 2 Rh 1−x IrxSn.Markers indicate experimentally determine values and dashed lines are guides to the eye.

J 2 /
|J 1 | and J 3 /|J 1 | [31].Kitchaev et al propose that antiskyrmions will form when the value of 2 × K × A × D −2 is close to zero.Using the values

Table 2 .Figure 8 .
Figure 8. K × A × D −2 as a function of Ir substitution near the critical composition for antiskyrmion formation.For antiskyrmions to form, K × A × D −2 should be close to zero; the steep slope shown here suggests that the window for antiskyrmion formation is quite narrow.

Table 1 .
Atomic ratios based on EDX and the resulting chemical formula normalized to tin.The percentages listed result from automated fitting and are accurate within 2%.Nominal x % Mn % Rh % Ir % Sn resulting formula