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[Satoshi Sugimoto](https://orcid.org/0000-0002-7148-2372), [Yukiko Takahashi](https://orcid.org/0000-0001-9197-7236), [Shinya Kasai](https://orcid.org/0000-0001-7149-4800)

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[Transition of topological Hall effect for tetragonal Heusler Mn<sub>2</sub>PtSn thin film](https://mdr.nims.go.jp/datasets/fa76c93b-ea94-4c95-a6e0-74cf33db3de3)

## Fulltext

1  Transition of topological Hall effect for tetragonal Heusler 1 Mn2PtSn thin film  2  3 Satoshi Sugimoto,1,* Yukiko Takahashi,1 and Shinya Kasai 1,2 4 1Research Center for Magnetic and Spintronic Materials, National Institute for Materials 5 Science (NIMS), 1-2-1 Sengen, Tsukuba 305-0047, Japan 6 2JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan 7  8 Abstract 9 The large topological Hall effect is observed in Mn2PtSn epitaxial thin films. Non-10 hysteretic topological Hall resistivity is attributed to the canted spins below the 11 reorientation temperature, while the hysteretic topological resistivity at zero field 12 vicinity captures the trend of antiskyrmion formation. A decrease in thickness 13 enhances the contribution of dipolar interaction, leading to the additional 14 antiskyrmion-type signal above the reorientation temperature. The amplitudes of 15 these topological signals are strongly modulated by the film thickness, providing 16 pathways for developing antiskyrmion hosting media via film engineering. 17  18 *Corresponding author: SUGIMOTO.Satoshi@nims.go.jp  19  2  Topological magnetic textures possessing the Berry curvature affect the 20 electronic structure of the host material, leading to distinctive transport properties 21 favorable for future high-performance spintronic devices. [1 ,2   The topological Hall 22 effect (THE) is a transport property in which itinerant electrons are driven in the direction 23 of the Hall effect. [3 ,4   The study of THE has been intrinsically linked to magnetic 24 skyrmions, nanometric bubble domains in which intertwined wrapping spins result in a 25 unit integer topological charge. [5  Magnetic skyrmions were initially discovered in non-26 centrosymmetric crystals with Dzyaloshinskii–Moriya interactions (DMI), [2,3,6,7  and 27 further explored in centrosymmetric systems with frustrated magnetic exchange 28 interactions. [8,9   29 Of late, Mn-based tetragonal Heusler alloys have attracted attention as 30 alternative skyrmion-hosting materials. Antiparticles of skyrmions, known as 31 antiskyrmions (aSks), [10,11  were observed in Mn1.4Pt0.9Pd0.1Sn in a broader field and 32 temperature range. [12  This compound belongs to the D2d symmetry class, where in-33 plane anisotropic DMI cause the stability of the robust aSK phase [13  . Studies on 34 analogous Heusler compounds reported so far include discussions on THE being linked 35 to aSk stabilizations, for example, bulk Mn2PtSn [14  and Mn1.4Pt1−yRhySn. [15 , and thin 36 films of Mn2PtSn [16 , Mn2−xPtSn [17,18 , and Mn2RhSn. [19,20 . Note that for such 37 anti(ferri)-magnetic materials with canted spin configurations, THE can arise in 38 noncoplanar spin structures without links to skyrmions. [21,22,23  Vistoli et al. recently 39 observed large THE in a canted antiferromagnet Ca1−xCexMnO3, [24  and reported that 40 non-“skyrmionic” bubble domains were responsible for THE due to the canted spin 41 gradient [25 . For materials with canted spin configurations, the physical origin of THE 42 needs to be carefully explored. 43  3  In this letter, we report the experimental observation of a large THE in a Heusler 44 Mn2PtSn epitaxial thin film over a wide range of temperatures, magnetic fields, and 45 thicknesses. We propose a discussion that focuses on the hysteretic properties of THE and 46 access the underlying magnetic structures. 47  48 Mn2PtSn thin films (40 nm  100 nm) were grown on MgO (001) substrates with 49 a 20 nm thick MgO buffer layer, using dc magnetron sputtering from a Mn50Pt25Sn25 alloy 50 target. These films were deposited at ambient temperature and post-annealed at 500 C 51 for 30 min. The crystal structures of the Mn2PtSn films were characterized using X-ray 52 diffraction (XRD, Rigaku) with Cu-K radiation (𝜆 = 1.5406 Å). Atomic-scale crystal 53 structures were identified using transmission electron microscopy (TEM, FEI). 54 Magnetization measurements were performed by a vibrating sample magnetometry 55 technique using a magnetic property measurement system (MPMS, Quantum Design). 56 The transport properties were measured by a four-probe method using a physical property 57 measurement system (PPMS, Quantum Design). The variation in magnetic field between 58 MPMS and PPMS is estimated below ± 0.1 mT. 59  60 The Mn2PtSn tetragonal crystal structure is classified in the space group 𝐼4̅𝑚2, 61 no. 119, as shown in Fig. 1(a). [16  The clear (110) and (220) peaks in the out-of-plane 62 XRD spectra in Fig. 1(b) support the formation of this inverse Heusler compound. The 63 cross-sectional TEM images in Fig. 1(c) capture the epitaxial growth of Mn2PtSn crystals 64 for all thicknesses from 40 nm to 100 nm. The sharp spotty patterns of the integrated 65 nanobeam electron diffraction (NBDs), shown in Fig. 1(d), were also identified by the 66  4  𝐼4̅𝑚2 symmetry. The lattice parameters are 𝑎 = 4.49 ± 1Å and 𝑐 = 6.08 ± 2Å for all 67 thicknesses. 68 Figures 1(e) and (f) show the temperature dependences of longitudinal resistivity 69 𝜌𝑥𝑥  and magnetization 𝑀 , respectively. The samples were field-cooled in a 70 perpendicular field of 4 T to investigate saturated magnetization state. The kinks of 𝜌𝑥𝑥 71 and 𝑀  mark the spin reorientation temperature 𝑇s  from the noncoplanar (NCP) 72 ferrimagnet into coplanar (CP) ferrimagnets. [12  The Curie temperatures 𝑇c  are 73 estimated as 𝑇c~350 K from the gradient changes of 𝑀 above room temperature. 74  75 The total Hall resistivity 𝜌𝑥𝑦 is composed of the ordinary Hall effect (OHE) 76 𝜌𝑥𝑦OHE , the anomalous Hall effect (AHE) 𝜌𝑥𝑦AHE , and additional THE 𝜌𝑥𝑦THE , as 𝜌𝑥𝑦 =77 𝜌𝑥𝑦OHE + 𝜌𝑥𝑦AHE + 𝜌𝑥𝑦THE. [2  The OHE is expressed as 𝜌𝑥𝑦OHE = 𝑅0𝐻 with Hall coefficient 78 𝑅0. The AHE, dominated by intrinsic and side-jump scattering contributions [26,27 , is 79 rewritten as 𝜌𝑥𝑦AHE~𝑆A𝜌𝑥𝑥2 𝑀  with scaling coefficient 𝑆A . Hence, the remaining THE 80 contribution is simplified as follows. 81 𝜌𝑥𝑦THE = 𝜌𝑥𝑦 − 𝑅0𝐻 − 𝑆A𝜌𝑥𝑥2 𝑀.                   (1) 82 In Fig. 2(a), the hysteresis curves of 𝜌𝑥𝑦 , 𝜌𝑥𝑥   𝜌𝑥𝑦OHE + 𝜌𝑥𝑦AHE , and 𝜌𝑥𝑦THE 83 measured under a perpendicular field are plotted for a 40 nm thick sample at 150 K. The 84 𝜌𝑥𝑦OHE + 𝜌𝑥𝑦AHE  curve deviates from the 𝜌𝑥𝑦  curve below 𝐻 < 2 T , with a clear 85 emergence of THE. The 𝜌𝑥𝑦THE  curve shows sign inversions between the positive and 86 negative fields as a feature of the inversed topological flux. [17,28   We obtained the 87 maximum THE signal as 𝜌𝑥𝑦 maxTHE = 0.57 𝜇Ω cm for a 40 nm thick sample. 88 Nayak et al. reported that wide-field range THEs are primarily attributed to the 89 noncoplanar canted spins in analogous ferrimagnetic compounds, [12,15  and 90  5  antiskyrmions should be linked at zero field vicinity, appearing as the hysteretic 91 component of THE. To present the essence of these discussions, we introduce a process 92 to separate the non-hysteretic and hysteretic topological contributions described below. 93 The non-hysteretic component of THE labeled as 𝜌𝑥𝑦tTHE  can be extracted by 94 adding 𝜌𝑥𝑦THE  to change the field-sweep direction from +4 T  to −4 T  (𝜌𝑥𝑦 decTHE )  and 95 change the field-sweep direction from −4 T to +4 T (𝜌𝑥𝑦 incTHE ), as follows. 96 𝜌𝑥𝑦tTHE = (𝜌𝑥𝑦 decTHE + 𝜌𝑥𝑦 incTHE )/2.                (2) 97 In addition, the hysteretic component (𝜌𝑥𝑦hTHE) can be calculated by making a difference 98 as   99 𝜌𝑥𝑦hTHE = (𝜌𝑥𝑦 decTHE − 𝜌𝑥𝑦 incTHE )/2.               (3) 100 The quantifications of 𝜌𝑥𝑦tTHE and 𝜌𝑥𝑦hTHE are shown in Figs. 2(b), (d), and (f), for 40 nm 101 thickness at 150 K and 50 K, and for 100 nm thickness at 50 K, respectively. All 𝜌𝑥𝑦tTHE 102 show a similar trend as 𝜌𝑥𝑦THE shown in Figs. 2(a), (c), and (e). In Fig. 2(d), finite 𝜌𝑥𝑦hTHE 103 appears as a positive peak signal near the zero field, corresponding to a converse 104 hysteresis loop in the THE curve. At a converse hysteresis, the sign inversion of 𝜌𝑥𝑦THE 105 occurs after 𝐻 switches to the opposite direction. The sign of 𝜌𝑥𝑦THE is determined by 106 the polarity of the topological charge 𝑄 = 𝑚𝑝 = ±1, which reflects the direction of out-107 of-plane magnetization 𝑝 = ±1 and a structure parameter called the vorticity 𝑚. [2,29  108 The positive 𝜌𝑥𝑦hTHE indicates that 𝑄 will have same sign as 𝐻 with wide-range hump-109 shaped features in 𝜌𝑥𝑦tTHE . It is difficult to distinguish any topological domains from 110 canted spins in such conditions, and we cannot insist on antiskyrmion formations only 111 from these transport properties. 112 On the other hand, 𝜌𝑥𝑦hTHE shown in Fig. 2(d), obtained for a 100 nm thickness 113 at 50 K, appears to be a negative dip 𝜌𝑥𝑦hTHE < 0 as an inverse hysteresis in the THE loop. 114  6  In the same manner, this trend of 𝜌𝑥𝑦hTHE is considered to reflect the polarity inversion of 115 𝑄. Since the field direction stays constant during this process, i.e., 𝑝 = 𝑐𝑜𝑛𝑠𝑡., the sign 116 inversion of vorticity 𝑚  is implied. Sivakumar et al. [20  reported such inversion of 117 vorticity 𝑚  without field switching indicated antiskyrmion formations, because the 118 vorticity in antiskyrmions considers opposite sign as 𝑚 = −1  to that of normal 119 skyrmions as 𝑚 = +1, [11,29,30 . Therefore, this negative 𝜌𝑥𝑦hTHE is considered to be a 120 sufficient condition of antiskyrmion formations in Mn-based Heusler thin films. It should 121 be noted that 𝜌𝑥𝑦hTHE does not represent THE itself induced by antiskyrmions. The total 122 𝜌𝑥𝑦THE in Fig. 2(e) shows asymmetric behavior with respect to field inversion due to the 123 polarity switching. 124 The other notable features are emergences of zero magnetic field topological 125 Hall signals in Figs. 2(d) and (f). The previous report of Mn2PtSn thin film was focused 126 on nonzero magnetic field THE, [16  where stabilizations of antiskyrmions were observed 127 using direct imaging techniques. [12  In these reports, the helical magnetic phases were 128 dominant at zero field vicinities, and THE associated with antiskyrmions were discussed 129 mainly under finite field conditions. On the other hands, zero field topological Hall 130 signals were also reported for the recent studies of thin film Mn2RhSn [20  and Pd-doped 131 Mn1.5PtSn [28  in conditions with low temperature range where relevant dipolar 132 interaction increases. We next present systematic results of 𝜌𝑥𝑦THE  and 𝜌𝑥𝑦hTHE  for 133 different temperature, field, and sample thickness to investigate the relation between 134 antiskyrmion formations and thin film properties. 135  136 Figures 3(a)  (f) show the temperature and field dependences of 137 (𝜌𝑥𝑦tTHE 𝜌𝑥𝑦hTHE) for 100 nm, 60 nm, and 40 nm thin films. The non-hysteretic 𝜌𝑥𝑦tTHE of 138  7  all thicknesses (Figs. 3(a), (c), and (e)) reproduces the bulk nature of ferrimagnetic 139 MnxPtSn. [12,15  The large and constant THE signals appear below the spin reorientation 140 temperature 𝑇 < 𝑇s, and immediately disappear above 𝑇 > 𝑇s. These steep changes in 141 𝜌𝑥𝑦tTHE  in concert with the magnetic phase transition from the NCP to CP phases are 142 common features of the canted spin textures of ferrimagnetic MnxPtSn, independent of 143 any antiskyrmions. 144 On the other hand, the hysteretic 𝜌𝑥𝑦hTHE  captures a trend of antiskyrmion 145 formations, as discussed above, and can be modulated by film thickness. For the 100-nm-146 thick film shown in Fig. 3(b), the negative 𝜌𝑥𝑦hTHE, i.e., inverse hysteresis, appears below 147 𝑇 < 𝑇s. The absolute amplitude of 𝜌𝑥𝑦hTHE decreases with temperature and reaches zero 148 around 𝑇s. A small positive 𝜌𝑥𝑦hTHE remains above 𝑇 > 𝑇s subsequentially. The finite 149 𝜌𝑥𝑦hTHE above 𝑇s may be attributed to the pinned magnetic domains at zero field vicinity 150 due to the crystal incompleteness. 151 For the thinner 60 nm film in Fig. 3(d), on the other hand, the positive 𝜌𝑥𝑦hTHE 152 appears below 𝑇 < 𝑇s, and vanishes above 𝑇 > 𝑇s. This trend is similar to that of 𝜌𝑥𝑦tTHE, 153 as the phase transition from the NCP phase to the CP phase without antiskyrmion 154 formation. 155 For the thinnest 40 nm film shown in Fig. 3(f), the positive 𝜌𝑥𝑦hTHE  appears 156 below 𝑇 < 𝑇s  similarly to results of the 60 nm film. Additionally, antiskyrmion-type 157 𝜌𝑥𝑦hTHE < 0 is observed above 𝑇 > 𝑇s, where no antiskyrmion texture has been reported 158 in bulk compounds. [15  The finite THE above 𝑇s may be attributed to the additionally 159 stabilized antiskyrmions for thin-film engineering, also reported for MnSi and FeGe 160 compounds in cases of skyrmions. [31,32  161  8  The modulation of 𝜌𝑥𝑦hTHE by film thickness feasibly reflects the variations in 162 the dipolar energy, which plays a critical role in antiskyrmion formation. [33  Our 100 163 nm film is thick enough to reproduce the bulk nature, leading to antiskyrmion-type signals. 164 The extension of antiskyrmion-type topological signal to zero field condition is 165 considered due to decrease in perpendicular anisotropy in thin film samples, where the 166 relevant dipolar energy will further increase from bulk samples. Once the thickness 167 decreases, the net magnetization decreases and the contribution of dipolar energy 168 becomes weaker, as is observed with the disappearance of negative 𝜌𝑥𝑦hTHE below 60 nm. 169 Additionally, the formation of a metastable antiskyrmion phase at the limit of a weaker 170 magnetic anisotropy was reported, [ 34   in which dipolar interactions are relatively 171 dominant in domain formations. Such an energy limit is observed at a thickness of 40 nm 172 above 𝑇 > 𝑇s , where an increase in temperature promptly decreases the magnetic 173 anisotropy, and the contribution of dipolar energy is dominant again. 174  175 Finally, we show the thickness dependences of the maximum THE amplitudes 176 for non-hysteretic resistivity 𝜌𝑥𝑦tTHE|max  and hysteretic resistivity 𝜌𝑥𝑦hTHE|max, in Fig. 177 5(a) and Fig. 5(b), respectively. Notably, 𝜌𝑥𝑦tTHE|max increases from 100 nm to 40 nm 178 below 𝑇 < 𝑇s , from 0.1 𝜇Ω cm  to 0.6 𝜇Ω cm . Such a dependence of 𝜌𝑥𝑦tTHE|max  is 179 comparable with that seen in previous reports on Mn2PtSn thin films. Thick epitaxial 180 Mn2PtSn film, i.e., close to the bulk condition, reported negligible THE, which may 181 reflect the inherent crystal structure. [35 . The largest THE more than 0.5 𝜇Ω cm was 182 reported for polycrystalline Mn2PtSn crystal growth on thermally oxidized silicon, with 183 the expectation of large defects and grains compared to epitaxial films. [16  Therefore, a 184  9  complete 𝐼4̅𝑚2 Mn2PtSn thin film is considered to possess an inherently weak THE, 185 and a decrease in thickness breaks the c-axis crystal symmetry and enhances the eventual 186 THE. The thickness dependence of 𝜌𝑥𝑦tTHE|max above 𝑇 > 𝑇s appears to be complicated, 187 showing weak but sign-inverted signals between 40  60 nm. We speculate incomplete 188 coplanar spins above 𝑇 > 𝑇s may trigger such a non-systematic behavior for thinner film 189 samples. The detail study of the magnetic structure will be required to access the origin 190 of these anomalies. 191 The dependence of 𝜌𝑥𝑦hTHE|max is also clear in any temperature range. It shows 192 a monotonic increase from 100 nm to 40 nm for 𝑇 < 𝑇s  and decrease for 𝑇 > 𝑇s , 193 indicating the size and density of nontrivial spin textures, somewhen antiskyrmions, 194 shows direct and systematic dependences on both thickness and temperature. The 195 systematic variation of magnetic anisotropy of thin films is considered to play an essential 196 role here. These results are examples of thin-film engineering to modulate THE, 197 combined with stabilization of the antiskyrmion phase by tuning its dipolar energy. 198  199 In summary, we fabricated epitaxial tetragonal Heusler Mn2PtSn thin films via 200 magnetron sputtering and observed a large THE. The condition of antiskyrmion 201 formations is systematically discussed in relation to the hysteretic properties of THE. 202 Antiskyrmion-type signal was observed at zero field vicinity for the thickest 100 nm thin 203 film at the noncoplanar ferrimagnetic phase. An additional antiskyrmion signal was 204 obtained for the thinnest 40nm film above the reorientation temperature, which is unique 205 to the thin film sample with weak magnetic anisotropy. These topological signals can be 206  10  systematically modulated by temperature and film thickness, providing a route to the 207 realization of skyrmion-based spintronic devices. 208  209 ACKNOWLEDGEMENTS 210 This work was partially supported by the Japan Society for the Promotion of Science 211 (JSPS) KAKENHI grant nos. JP20K14419, JP17K18892, JP18H03787, and JST, 212 PRESTO grant no. JPMJPR18L3, Japan. The authors acknowledge W. Koshibae and X. 213 Z. Yu for fruitful discussions. 214  215 DATA AVAILABILITY 216 The data that support the findings of this study are available within this article. 217  218   219  11  Figure Captions 220 FIG. 1. (a) Crystal structure of tetragonal Mn2PtSn with 𝐼4̅𝑚2 space group. (b) X-ray 221 diffraction pattern of 40 nm Mn2PtSn thin film. (c) Cross-sectional transmission electron 222 microscopy images of 100 nm and 40 nm Mn2PtSn thin films. Positions of Mn, Pt, and 223 Sn atoms are modeled with red, green, and blue colors, respectively. (d) Nanobeam 224 electron diffraction pattern of 40 nm Mn2PtSn thin film along [100  direction. (e) 225 Temperature dependences of longitudinal resistivities of Mn2PtSn. The spin reorientation 226 temperatures 𝑇s are indicated with dashed lines. (f) Temperature dependences of field-227 cooled magnetization of Mn2PtSn at perpendicular fields of 4 T. 228  229 FIG. 2. Hysteresis loops of 𝜌𝑥𝑦 (black), 𝜌𝑥𝑥 (green), 𝜌𝑥𝑦OHE + 𝜌𝑥𝑦AHE (red), and 𝜌𝑥𝑦THE 230 (blue) of (a) 40 nm thick Mn2PtSn at 150 K, (c) 40 nm thick Mn2PtSn at 50 K, and (e) 231 100 nm thick Mn2PtSn at 50 K, respectively. The closed (open) symbols indicate results 232 for the field-sweep from +4 T to −4 T (−4 T to +4 T). Field dependences of 𝜌𝑥𝑦tTHE 233 (black) and 𝜌𝑥𝑦hTHE (blue) of (b) 40 nm thick Mn2PtSn at 150 K, (d) 40 nm thick Mn2PtSn 234 at 50 K, and (f) 100 nm thick Mn2PtSn at 50 K, respectively. 235  236 FIG. 3. Temperature and field dependences of 𝜌𝑥𝑦tTHE and 𝜌𝑥𝑦hTHE, for (a), (b) 100 nm 237 thick Mn2PtSn film, (c), (d) 60 nm thick Mn2PtSn film, and (e), (f) 40 nm thick 238 Mn2PtSn film.  239  240  12  FIG. 4. Film thickness dependences of 𝜌𝑥𝑦tTHE|max  and 𝜌𝑥𝑦hTHE|max obtained (a) below 241 spin reorientation temperature 𝑇 < 𝑇s, and (b) above 𝑇 > 𝑇s. The black and red dotted 242 lines indicate the increase in 𝜌𝑥𝑦tTHE|max and 𝜌𝑥𝑦hTHE|max. 243  244  245 246  13  Fig. 1 Sugimoto et al. 247  248  249   250   14   251 Fig. 2 Sugimoto et al. 252  253  254  255   256   15   257 Fig. 3 Sugimoto et al.  258    16  Fig. 4 Sugimoto et al. 259  260   261    17   262  1 F. Jonietz, S. Mühlbauer, C. Pfleiderer, A. Neubauer, W. Münzer, A. Bauer, T. Adams, R. Georgii, P. Böni, R. A. Duine, K. Everschor, M. 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