We investigate the relationship between structural parameters, magnetic ordering, and the anomalous Hall effect (AHE) of Mn3+xSn1−x (−0.42 ≤ x ≤ +0.23) thin films annealed at various temperatures Ta. The crystal structure changes with x and Ta, and at Ta ≥ 500 °C near the stoichiometric composition (−0.08 ≤ x ≤ +0.04), epitaxial single-phase D019-Mn3+xSn1−x(101̄0) is obtained. At room temperature, a larger AHE is obtained when the single-phase epitaxial Mn3Sn with the lattice constant closer to that of bulk is formed. The temperature dependence of the AHE shows different behaviors depending on Ta and can be explained by considering the variation of magnetic ordering. A close inspection into the temperature and composition dependence suggests a variation of magnetic phase transition temperature with composition and/or a possible correlation between the AHE and Fermi level position with respect to the Weyl points. Our comprehensive study on (101̄0)-oriented epitaxial Mn3Sn thin films would provide the basis for utilizing the unique functionalities of non-collinear antiferromagnetic materials.

Antiferromagnets (AFMs) show unique physical properties and functionalities, such as ultra-fast dynamics, robustness against external perturbation, and no stray field generation, which are not seen in ferromagnets (FMs). These characteristic features allow the AFMs to expand the realm of spintronics based on FMs and form a new paradigm, so-called antiferromagnetic spintronics.1–7 Magnetic orderings of typical collinear AFMs are electrically invisible due to the zero net magnetization. On the other hand, non-collinear AFM materials with a chiral-spin ordering are attracting considerable attention as they exhibit a large anomalous Hall effect (AHE), i.e., they are electrically visible, despite their vanishingly small net magnetization. The large AHE is attributed to the non-vanishing integration of the Berry curvature in momentum space,8–11 which also exhibits anomalous Nernst and magneto-optical Kerr effects.12–17 

A non-collinear AFM D019-Mn3Sn has a hexagonal Ni3Sn-type structure with a space group of P63/mmc. The Mn sublattice in the 0001 plane of D019-Mn3Sn constitutes the kagome lattice. Due to a geometric frustration of magnetic moments and the Dzyaloshinskii–Moriya interaction, the magnetic moments in the kagome lattice of Mn3Sn form a non-collinear spin configuration, as shown in Fig. 1(a) at room temperature (RT). In this configuration, Mn3Sn has an uncompensated magnetization of a few mT, allowing the chiral-spin structure with the AHE to be switched by an external magnetic field.18–21 Mn3Sn also belongs to Weyl semimetals with the Weyl points in the vicinity of the Fermi level.9,22–24 In the momentum space, Berry curvature or a fictitious field emerges between a pair of Weyl points, whose chirality is opposite to each other. As the crystal structure and the magnetic ordering determine the position of Weyl points and the direction of the fictitious field, the resultant topological responses, e.g., AHE, also depend on them.

FIG. 1.

(a) Top view along the c-axis of the Mn3Sn crystal structure with an inverse triangular spin ordering. A layer shown in monochrome represents the plane in c/2. XRD spectra of (b) 2θθ scan for MgO(110) sub./W/Ta/Mn2.92Sn1.08/MgO/Ru annealed at various Ta and (c) ϕ scan for a sample annealed at 600 °C. (d) Ta dependence of lattice constant a. a of bulk Mn3Sn, abulk = 5.665 Å, is indicated by a red dashed line. The inset in (d) shows a magnified view of the 2θθ scan at 2θ = 36°–37°, where the arrows and a dashed line indicate the positions of Mn3Sn(202̄0) peaks and that of bulk, respectively. (e) Ta dependence of order parameter S.

FIG. 1.

(a) Top view along the c-axis of the Mn3Sn crystal structure with an inverse triangular spin ordering. A layer shown in monochrome represents the plane in c/2. XRD spectra of (b) 2θθ scan for MgO(110) sub./W/Ta/Mn2.92Sn1.08/MgO/Ru annealed at various Ta and (c) ϕ scan for a sample annealed at 600 °C. (d) Ta dependence of lattice constant a. a of bulk Mn3Sn, abulk = 5.665 Å, is indicated by a red dashed line. The inset in (d) shows a magnified view of the 2θθ scan at 2θ = 36°–37°, where the arrows and a dashed line indicate the positions of Mn3Sn(202̄0) peaks and that of bulk, respectively. (e) Ta dependence of order parameter S.

Close modal

For utilizing the functionalities of Mn3Sn, many studies focusing on the AHE in thin-film samples have been carried out.25–30 In particular, it is of importance to fabricate epitaxial thin films with the c-axis lying in the film plane because observations of intriguing phenomena such as anomalous Hall, anomalous Nernst, and magneto-optical Kerr effects require this crystalline orientation. In addition, chiral-spin rotation and domain wall propagation due to spin–orbit torque are possible in this configuration,31–34 as experimentally demonstrated very recently.34 

Recently, the first epitaxial growth of a (101̄0)-oriented Mn3Sn thin film has been reported with appropriate single crystal substrates and underlayers.28 However, the magnitude of anomalous Hall resistance was smaller than that reported for bulk Mn3Sn, probably due to the structural factor associated with thin films. Therefore, it is of importance to clarify the critical factors in thin films to effectively utilize the characteristic functionalities of non-collinear AFMs. Several factors likely relating to the AHE, such as crystalline phase, strain, and order parameter of the alloy, are sensitively affected by the preparation conditions and the compositions. Previous studies on polycrystalline Mn3Sn thin films showed a strong dependence of the AHE on annealing temperature and Mn–Sn composition.26,27 However, since the AHE depends on crystal orientation, it is difficult to disentangle the factors governing the AHE in polycrystalline samples.

In this study, we systematically evaluate the crystal structures and magneto-transport properties of Mn3+xSn1−x thin films and discuss the critical factors governing the magnitude of the AHE. We prepare various samples based on a growth technique to form epitaxial thin films28 while varying the annealing temperatures Ta and Mn–Sn compositions and investigate the correlation of the AHE with structural parameters, magnetic ordering, and other factors.

All films are deposited on MgO(110) substrates by DC and RF magnetron sputtering. The stacks consist of, from the substrate side, W (3 nm)/Ta (2 nm)/Mn3+xSn1−x (50 nm)/MgO (1.5 nm)/Ru (1 nm). During sputtering, substrates are put on a heating stage with a nominal temperature of 400 °C. The composition x in the Mn3+xSn1−x layer is controlled by co-sputtering of Mn and Sn targets and is determined by inductively coupled plasma mass spectrometry. After deposition, films are annealed for an hour at a Ta of 300–600 °C in a vacuum. We use an x-ray diffractometer for the structural analysis. A Cu-Kα1 x-ray with a wavelength of 0.154 06 nm is used. To measure the transport properties, films are processed into the Hall bar by photolithography and Ar ion milling.

First, we study the Ta dependence of the crystalline structure in a stack with x = −0.08. Figure 1(b) shows x-ray diffraction (XRD) spectra of the stack annealed at various Ta. As Ta increases, diffraction peaks of (101̄0), (202̄0), and (303̄0) planes of the ferrimagnetic B82-Mn1.75Sn diminish, whereas those of (101̄0), (202̄0), and (404̄0) planes of the non-collinear antiferromagnetic D019-Mn3Sn appear at a Ta of 400 °C. The peaks from D019-Mn3Sn increase with Ta, whereas the peaks from B82-Mn1.75Sn disappear above Ta of 500 °C. Figure 1(c) shows the ϕ scan pattern of the 101̄1 plane of Mn3Sn, indicating that the D019-Mn3Sn is epitaxially grown along the W/Ta underlayers. An epitaxial relationship is identified as MgO110001W211011̄Mn3Sn101̄00001, which can exhibit the AHE.28 We then quantify the lattice constant a and order parameter S of D019-Mn3Sn from the results of the 2θθ scan. Lattice constant a is determined by the position of the Mn3Sn(202̄0) peak as shown in the inset of Fig. 1(d). The order parameter S of Mn3Sn is evaluated from integrated intensities of (101̄0) and (202̄0) peaks, corresponding to the superlattice and fundamental peaks, respectively. The structural (structure, multiplicity, Lorentz-polarization, thermal, and film thickness) factors are included to calculate the theoretical intensities of the (101̄0) and (202̄0) peaks.35,36 As Ta increases, a decreases and approaches that of bulk (abulk) at Ta ≥ 550 °C [Fig. 1(d)]. On the other hand, S slightly decreases with Ta [Fig. 1(e)], probably due to the diffusion from/to the adjacent layers.

Next, we investigate transport properties of the prepared films. The transport measurements are performed on 30-μm-wide Hall bar devices with a four-probe method as shown in Fig. 2(a). Figure 2(b) shows the transverse resistivity ρxy as a function of out-of-plane magnetic field Hz for the Mn2.92Sn1.08 film with various Ta. Negative Hall-resistance loops are observed at Ta ≥ 450 °C in the measured field range, where the x-ray diffraction peaks from D019-Mn3Sn were found to be dominant [Fig. 1(b)]. On the other hand, the only linear response, due to the ordinary Hall effect, is observed at Ta ≤ 400 °C. We then evaluate transverse conductivity σxyρxy/ρxx2, where ρxx is a longitudinal resistivity of the Mn–Sn layer. Figure 2(c) shows the Ta dependence of the saturated value of σxy (σxysat) together with aabulk determined by XRD. σxysat increases and almost saturates at Ta ≥ 550 °C. Importantly, an increase in σxysat coincides with the approach of a to abulk with increasing Ta, suggesting a correlation between the lattice constant and magnitude of the AHE in Mn3Sn thin films.

FIG. 2.

(a) Measurement circuit with a 30-μm-wide Hall bar device. (b) ρxy vs Hz for various Ta measured at 300 K. (c) Ta dependence of σxysat and aabulk measured at 300 K. Crystalline phases deduced from XRD are indicated by background colors. (d) ρxx, (e) σxysat, and (f) M/μ0H as a function of measurement temperature for samples annealed at various Ta. Left (right)-half of the plots in (d) is filled for the minus (plus)-sign slope. Star plots in (e) indicate that an antiferromagnetic phase transition takes place just below these points. The inset in (f) shows M vs Hz for Ta of 400 and 600 °C measured at 150 and 300 K.

FIG. 2.

(a) Measurement circuit with a 30-μm-wide Hall bar device. (b) ρxy vs Hz for various Ta measured at 300 K. (c) Ta dependence of σxysat and aabulk measured at 300 K. Crystalline phases deduced from XRD are indicated by background colors. (d) ρxx, (e) σxysat, and (f) M/μ0H as a function of measurement temperature for samples annealed at various Ta. Left (right)-half of the plots in (d) is filled for the minus (plus)-sign slope. Star plots in (e) indicate that an antiferromagnetic phase transition takes place just below these points. The inset in (f) shows M vs Hz for Ta of 400 and 600 °C measured at 150 and 300 K.

Close modal

Subsequently, we measure the temperature dependence of the transport and magnetic properties. The magnetic properties are measured by a vibrating sample magnetometer. Figure 2(d) shows ρxx as a function of measurement temperature T. The sign of slope changes from minus to plus, suggesting a change in the conduction mechanism, at Ta = 400 °C, where the formation of D019-Mn3Sn was found to start. The temperature dependence of σxysat for various Ta summarized in Fig. 2(e) reveals that the behavior of the Hall effect drastically changes as well as the longitudinal conductance with the transition of the dominant crystalline phase from B82-Mn1.75Sn to D019-Mn3Sn. The temperature dependence of the susceptibility M/μ0H and M vs Hz curves for various Ta summarized in Fig. 2(f) are also consistent with this scenario, that is, the ferrimagnetic B82-Mn1.75Sn possessing uncompensated moment below the Curie temperature TC reported as ∼250 K37,38 is formed for low Ta, whereas the non-collinear antiferromagnetic D019-Mn3Sn with a small net magnetic moment ∼0.003 μB per Mn atom is formed for high Ta. For stacks annealed at Ta ≥ 500 °C, positive σxysat originating from the non-collinear AFM increases with decreasing T from 300 to 250 K and then vanishes at 200–250 K. M/μ0H is small even at low temperatures, where the transport property drastically changes. σxysat vs T of our single-phase Mn3Sn films annealed at higher Ta could therefore be explained by a transition between the inverse triangular spin state and the spiral spin state at a certain temperature TAFM,39,40 the latter preserving the inversion symmetry and thus showing no AHE.39–41 We also note that TAFM of our Mn3Sn films depends on Ta, while such a variation is observed in bulk Mn3Sn as well.21,40 Meanwhile, stacks annealed at Ta ≤ 350 °C, where the XRD peaks only from B82-Mn1.75Sn were observed [Fig. 1(b)], show no AHE at 300 K and negative σxysat is observed below 250 K. This result can be attributed to the conventional anomalous Hall effect of the ferrimagnetic B82-Mn1.75Sn with the TC of ∼250 K as shown in Fig. 2(f). For stacks annealed at 400–450 °C, where XRD peaks from both D019-Mn3Sn and B82-Mn1.75Sn are observed, positive σxysat is obtained at RT and negative σxysat below 250 K. This result can be explained by the contribution from both crystalline phases.

We then turn to the composition dependence of structural and transport properties in Mn–Sn films. Figure 3(a) shows XRD spectra of Mn3+xSn1−x thin films with various x. Films are annealed at 600 °C for an hour after the deposition. As x increases, the dominant phase changes from B8-Mn3Sn2 to D019-Mn3Sn. The ferrimagnet B8-Mn3Sn2 has an orthorhombic Ni3Sn2-type structure, a superstructure composed of disordered hexagonal NiAs(B81)–Ni2In(B82)-type structure.42–44 The epitaxial and single-phase Mn3Sn is formed near stoichiometric composition (−0.08 ≤ x ≤ +0.04), whereas a polycrystalline Mn3Sn is formed at x ≥ +0.15. Figures 3(b) and 3(c) show the lattice constant a and order parameter S as a function of x. a decreases with x, whereas S shows no significant dependence with x.

FIG. 3.

(a) XRD spectra of the 2θθ scan for MgO(110) sub./W/Ta/Mn3+xSn1−x/MgO/Ru annealed at 600 °C. (b) Composition x dependence of lattice constant a. a of bulk Mn3Sn, abulk = 5.665 Å, is indicated by a red dashed line. The inset in (b) shows a magnified view of the 2θθ scan at 2θ = 36°–37°. Arrows and a dashed line indicate the positions of Mn3Sn(202̄0) peaks and that of bulk, respectively. (c) Composition x dependence of order parameter S.

FIG. 3.

(a) XRD spectra of the 2θθ scan for MgO(110) sub./W/Ta/Mn3+xSn1−x/MgO/Ru annealed at 600 °C. (b) Composition x dependence of lattice constant a. a of bulk Mn3Sn, abulk = 5.665 Å, is indicated by a red dashed line. The inset in (b) shows a magnified view of the 2θθ scan at 2θ = 36°–37°. Arrows and a dashed line indicate the positions of Mn3Sn(202̄0) peaks and that of bulk, respectively. (c) Composition x dependence of order parameter S.

Close modal

We then measure the transport properties of Mn3+xSn1−x as in the Ta dependence described earlier. x dependences of σxysat and aabulk are summarized in Fig. 4(a). σxysat shows the highest value of ∼13 Ω−1cm−1 at x = −0.04, where the epitaxial and single-phase Mn3Sn(101̄0) was found to be formed and decreases as the composition is far away from the stoichiometric composition. Small σxysat of ∼5 Ω−1cm−1 at x < −0.08 is probably due to the presence of the B8-Mn3Sn2 phase because TC of B8-Mn3Sn2 is ∼262 K.45,46 On the other hand, small σxysat at x > +0.04, where polycrystalline Mn3Sn was found to be formed, can be attributed to the existence of crystallites with other orientations, e.g., (0002) orientation exhibiting no AHE, and/or the large aabulk.

FIG. 4.

(a) Composition x dependence of σxysat and aabulk measured at 300 K. Crystalline phases deduced from XRD are indicated by the background color. (b) and (c) ρxy vs Hz curves measured at 300 and 200 K, respectively, for −0.08 ≤ x ≤ +0.04. (d) Composition x dependence of σxysat at 300 and 200 K. The inset shows the corresponding ρxx.

FIG. 4.

(a) Composition x dependence of σxysat and aabulk measured at 300 K. Crystalline phases deduced from XRD are indicated by the background color. (b) and (c) ρxy vs Hz curves measured at 300 and 200 K, respectively, for −0.08 ≤ x ≤ +0.04. (d) Composition x dependence of σxysat at 300 and 200 K. The inset shows the corresponding ρxx.

Close modal

Finally, we focus on the temperature dependence of the AHE for the epitaxial and single-phase region of −0.08 ≤ x ≤ +0.04 [red-colored region in Fig. 4(a)] in which the crystalline structure is regarded as invariable. Figures 4(b) and 4(c) show ρxyHz loops at 300 and 200 K, respectively, and Fig. 4(d) summarizes the x dependence of σxysat in this composition range. Interestingly, x showing the maximum σxysat shifts to the Mn-rich side as the temperature decreases. It is also notable that ρxx slightly decreases with x in this range [inset of Fig. 4(d)]. Considering the fact that the crystalline structure has no perceivable variation in this range, this result could be attributed to an electronic origin, i.e., the position of Fermi level EF with respect to the Weyl points,9,23 and/or a variation of TAFM with x. According to the first-principles calculations, Weyl points nearest to EF are located slightly above EF,22,23 while the AHE should increase as EF approaches the Weyl points due to a large fictitious field conduction electrons feel, as was experimentally observed in bulk Mn3+xSn1−x.12,22 In addition, the extra Mn atoms are reported to increase the conduction electron density,22 meaning the lift up of EF. Accordingly, our result can be understood by considering that the Mn-richer composition lifts EF up closer to the Weyl point generating a large AHE although this effect is not dominant at higher temperatures where conduction electrons in a wider energy window contribute to the transport and the relative number of electrons feeling the large fictitious field decreases. Note that the observed decrease in ρxx with x, meaning an increase in the number of electrons, supports this scenario. However, one also needs to consider a possibility that TAFM changes with x; when TAFM is higher for smaller x, the present experiment can be explained as well. Further measurements such as AC susceptibility measurement and neutron diffraction are necessary to distinguish these two effects.

In summary, we systematically investigate Ta and the Mn–Sn composition dependence of the AHE in Mn3+xSn1−x thin films deposited with a technique of epitaxial growth. Integrating all the obtained results, we conclude that the factors crucial to achieve a large AHE originating from the chiral-spin ordering in the Mn–Sn thin film are, in the order of importance, (1) formation of a single-D019-phase (101̄0)-epitaxial structure and (2) lattice constant closer to that of bulk. In our samples, factor (1) is satisfied at Ta ≥ 500 °C and near the stoichiometric composition (−0.08 ≤ x ≤ +0.04). The lattice constant [factor (2)] is found to also depend on Ta and x; Ta ≥ 550 °C is preferable and it is composition sensitive. In addition, the temperature dependence of the AHE for samples with various compositions around the stoichiometry suggests that the (3A) Fermi level closer to the Weyl point and (3B) sufficiently lower magnetic ordering transition point TAFM compared with the measurement temperature may also be important factors to obtain a large AHE. We also note that factor (3A) could be, if any, significant only at lower temperature, where electrons dominantly contributing to the transport properties should be limited in a narrower energy window near EF. Our experimental results with the thin films show good agreement with those with bulk Mn3Sn in terms of factors (1) and (3), indicating high quality of our (101̄0)-oriented epitaxial Mn3Sn thin films. Additionally, it is clarified that factor (2), which is difficult to disentangle in polycrystalline thin films, is also an important factor that determines the magnitude of the AHE in the single-phase D019-Mn3Sn. Our work provides a comprehensive understanding of the correlation between the crystal structures and AHE in the non-collinear antiferromagnetic thin film, facilitating the exploration of unraveled functionalities as well as development of novel devices.

The authors thank R. Takechi, B. Jinnai, J. Nitta, and S. Kim for their technical support and fruitful discussions. This work was partly supported by JSPS Kakenhi (Grant Nos. 19H05622, 19J13405, and 20K22409), Iketani Science and Technology Foundation (Grant No. 0331108-A), and RIEC Cooperative Research Projects. J.-Y.Y. acknowledges financial support from the GP-Spin at Tohoku University. Figure 1(a) is partly created by VESTA.47 

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

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