Antiferromagnets have unique properties such as high-speed dynamics and small stray field, creating a new research field of spintronics, so-called antiferromagnetic spintronics.1–41. T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Nat. Nanotechnol. 11, 231 (2016). https://doi.org/10.1038/nnano.2016.182. V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Rev. Mod. Phys. 90, 015005 (2018). https://doi.org/10.1103/RevModPhys.90.0150053. J. Železný, P. Wadley, K. Olejník, A. Hoffmann, and H. Ohno, Nat. Phys. 14, 220 (2018). https://doi.org/10.1038/s41567-018-0062-74. S. Fukami, V. O. Lorenz, and O. Gomonay, J. Appl. Phys. 128, 070401 (2020). https://doi.org/10.1063/5.0023614 In particular, non-collinear antiferromagnets possessing chiral-spin structures, e.g., Mn3X (X = Sn, Ge, Ir, and Pt), show various intriguing phenomena such as large anomalous Hall effect due to the topologically non-trivial band structure, enabling electrical detection of the magnetic state.5–75. S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212 (2015). https://doi.org/10.1038/nature157236. A. K. Nayak, J. E. Fischer, Y. Sun, B. Yan, J. Karel, A. C. Komarek, C. Shekhar, N. Kumar, W. Schnelle, J. Kübler, C. Felser, and S. S. P. Parkin, Sci. Adv. 2, e1501870 (2016). https://doi.org/10.1126/sciadv.15018707. Z. Q. Liu, H. Chen, J. M. Wang, J. H. Liu, K. Wang, Z. X. Feng, H. Yan, X. R. Wang, C. B. Jiang, J. M. D. Coey, and A. H. MacDonald, Nat. Electron. 1, 172 (2018). https://doi.org/10.1038/s41928-018-0040-1 Such unique properties have been observed not only in bulk but also in thin-film structures in these years,7–127. Z. Q. Liu, H. Chen, J. M. Wang, J. H. Liu, K. Wang, Z. X. Feng, H. Yan, X. R. Wang, C. B. Jiang, J. M. D. Coey, and A. H. MacDonald, Nat. Electron. 1, 172 (2018). https://doi.org/10.1038/s41928-018-0040-18. T. Higo, D. Qu, Y. Li, C. L. Chien, Y. Otani, and S. Nakatsuji, Appl. Phys. Lett. 113, 202402 (2018). https://doi.org/10.1063/1.50646979. T. Ikeda, M. Tsunoda, M. Oogane, S. Oh, T. Morita, and Y. Ando, Appl. Phys. Lett. 113, 222405 (2018). https://doi.org/10.1063/1.505149510. H. Reichlova, T. Janda, J. Godinho, A. Markou, D. Kriegner, R. Schlitz, J. Zelezny, Z. Soban, M. Bejarano, H. Schultheiss, P. Nemec, T. Jungwirth, C. Felser, J. Wunderlich, and S. T. B. Goennenwein, Nat. Commun. 10, 5459 (2019). https://doi.org/10.1038/s41467-019-13391-z11. J. Yoon, Y. Takeuchi, R. Itoh, S. Kanai, S. Fukami, and H. Ohno, Appl. Phys. Express 13, 013001 (2020). https://doi.org/10.7567/1882-0786/ab587412. H. Iwaki, M. Kimata, T. Ikebuchi, Y. Kobayashi, K. Oda, Y. Shiota, T. Ono, and T. Moriyama, Appl. Phys. Lett. 116, 022408 (2020). https://doi.org/10.1063/1.5128241 and this has led to demonstrations of an electrical manipulation of the magnetic state such as a current-induced reversal13–1613. H. Tsai, T. Higo, K. Kondou, T. Nomoto, A. Sakai, A. Kobayashi, T. Nakano, K. Yakushiji, R. Arita, S. Miwa, Y. Otani, and S. Nakatsuji, Nature 580, 608 (2020). https://doi.org/10.1038/s41586-020-2211-214. S. Arpaci, V. Lopez-Dominguez, J. Shi, L. Sánchez-Tejerina, F. Garesci, C. Wang, X. Yan, V. K. Sangwan, M. A. Grayson, M. C. Hersam, G. Finocchio, and P. Khalili Amiri, Nat. Commun. 12, 3828 (2021). https://doi.org/10.1038/s41467-021-24237-y15. B. Pal, B. K. Hazra, B. Göbel, J.-C. Jeon, A. K. Pandeya, A. Chakraborty, O. Busch, A. K. Srivastava, H. Deniz, J. M. Taylor, H. Meyerheim, I. Mertig, S.-H. Yang, and S. S. P. Parkin, Sci. Adv. 8, eabo5930 (2022). https://doi.org/10.1126/sciadv.abo593016. T. Higo, K. Kondou, T. Nomoto, M. Shiga, S. Sakamoto, X. Chen, D. Nishio-Hamane, R. Arita, Y. Otani, S. Miwa, and S. Nakatsuji, Nature 607, 474 (2022). https://doi.org/10.1038/s41586-022-04864-1 and rotation,17,1817. Y. Takeuchi, Y. Yamane, J.-Y. Yoon, R. Itoh, B. Jinnai, S. Kanai, J. Ieda, S. Fukami, and H. Ohno, Nat. Mater. 20, 1364 (2021). https://doi.org/10.1038/s41563-021-01005-318. G. Q. Yan, S. Li, H. Lu, M. Huang, Y. Xiao, L. Wernert, J. A. Brock, E. E. Fullerton, H. Chen, H. Wang, and C. R. Du, Adv. Mater. 34, 2200327 (2022). https://doi.org/10.1002/adma.202200327 showing promise for unconventional devices. Meanwhile, an important issue that has remained to be explored is the stability of the antiferromagnetic spin states against thermal fluctuation. The thermal stability of spin states, generally characterized by the thermal stability factor Δ (=E/kBT; E is the energy barrier, kB is the Boltzmann constant, and T is the absolute temperature), determines the retention time of the stored information and the critical current to switch it at finite temperature in functional devices. Up to now, Δ of nanoscale devices has been well studied in ferromagnetic systems as a function of the device size.19–2419. J. Z. Sun, R. P. Robertazzi, J. Nowak, P. L. Trouilloud, G. Hu, D. W. Abraham, M. C. Gaidis, S. L. Brown, E. J. O’Sullivan, W. J. Gallagher, and D. C. Worledge, Phys. Rev. B 84, 064413 (2011). https://doi.org/10.1103/PhysRevB.84.06441320. H. Sato, M. Yamanouchi, K. Miura, S. Ikeda, H. D. Gan, K. Mizunuma, R. Koizumi, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 99, 042501 (2011). https://doi.org/10.1063/1.361742921. H. Sato, E. C. I. Enobio, M. Yamanouchi, S. Ikeda, S. Fukami, S. Kanai, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 105, 062403 (2014). https://doi.org/10.1063/1.489292422. G. D. Chaves-O’Flynn, G. Wolf, J. Z. Sun, and A. D. Kent, Phys. Rev. Appl. 4, 024010 (2015). https://doi.org/10.1103/PhysRevApplied.4.02401023. L. Thomas, G. Jan, S. Le, Y.-J. Lee, H. Liu, J. Zhu, S. Serrano-Guisan, R.-Y. Tong, K. Pi, D. Shen, R. He, J. Haq, Z. Teng, R. Annapragada, V. Lam, Y.-J. Wang, T. Zhong, T. Torng, and P.-K. Wang, in 2015 IEEE International Electron Devices Meeting (IEDM) ( IEEE, Washington, D.C., 2015), p. 26.4.1–26.4.4.24. E. C. I. Enobio, M. Bersweiler, H. Sato, S. Fukami, and H. Ohno, Jpn. J. Appl. Phys. 57, 04FN08 (2018). https://doi.org/10.7567/JJAP.57.04FN08 For antiferromagnets, on the other hand, experimental investigation on the thermal stability has been limited to a study on a collinear antiferromagnetic Mn2Au film2525. M. Meinert, D. Graulich, and T. Matalla-Wagner, Phys. Rev. Appl. 9, 064040 (2018). https://doi.org/10.1103/PhysRevApplied.9.064040 and an isolated island structured polycrystalline D019-Mn3Sn film,2626. T. Matsuo, T. Higo, D. Nishio-Hamane, and S. Nakatsuji, Appl. Phys. Lett. 121, 013103 (2022). https://doi.org/10.1063/5.0095819 and investigation on a well-defined sample is required.Here, we systematically investigate the thermal stability factor of a Mn3Sn single nanodot with various diameters. Hexagonal D019-Mn3Sn is a prime representative of the non-collinear antiferromagnets. The 0001 plane of Mn3Sn constitutes a kagome lattice of Mn atoms, whose moments form an antiferromagnetic chiral-spin structure due to the geometrical frustration and Dzyaloshinskii–Moriya interaction [Fig. 1(a)]. The magnetic anisotropy of Mn3Sn, which relates to the thermal stability, is known to have three components: local uniaxial anisotropy, which, combined with the Dzyaloshinskii–Moriya interaction, generates a small uncompensated magnetization (MUC) in the kagome plane, a global sixfold anisotropy originating from the kagome lattice structure,27–2927. S. Tomiyoshi and Y. Yamaguchi, J. Phys. Soc. Jpn. 51, 2478 (1982). https://doi.org/10.1143/JPSJ.51.247828. P. J. Brown, V. Nunez, F. Tasset, J. B. Forsyth, and P. Radhakrishna, J. Phys.: Condens. Matter 2, 9409 (1990). https://doi.org/10.1088/0953-8984/2/47/01529. J. Liu and L. Balents, Phys. Rev. Lett. 119, 087202 (2017). https://doi.org/10.1103/PhysRevLett.119.087202 and a global twofold magnetic anisotropy that was found to be induced by a strain in the kagome plane.1616. T. Higo, K. Kondou, T. Nomoto, M. Shiga, S. Sakamoto, X. Chen, D. Nishio-Hamane, R. Arita, Y. Otani, S. Miwa, and S. Nakatsuji, Nature 607, 474 (2022). https://doi.org/10.1038/s41586-022-04864-1 In this study, we prepare a 11¯00-plane oriented epitaxial Mn3Sn film11,17,30,3111. J. Yoon, Y. Takeuchi, R. Itoh, S. Kanai, S. Fukami, and H. Ohno, Appl. Phys. Express 13, 013001 (2020). https://doi.org/10.7567/1882-0786/ab587417. Y. Takeuchi, Y. Yamane, J.-Y. Yoon, R. Itoh, B. Jinnai, S. Kanai, J. Ieda, S. Fukami, and H. Ohno, Nat. Mater. 20, 1364 (2021). https://doi.org/10.1038/s41563-021-01005-330. J.-Y. Yoon, Y. Takeuchi, S. DuttaGupta, Y. Yamane, S. Kanai, J. Ieda, H. Ohno, and S. Fukami, AIP Adv. 11, 065318 (2021). https://doi.org/10.1063/5.004319231. T. Uchimura, J.-Y. Yoon, Y. Sato, Y. Takeuchi, S. Kanai, R. Takechi, K. Kishi, Y. Yamane, S. DuttaGupta, J. Ieda, H. Ohno, and S. Fukami, Appl. Phys. Lett. 120, 172405 (2022). https://doi.org/10.1063/5.0089355 and fabricate Hall devices containing a single nanodot with various diameters. We measure the switching probability under a pulsed magnetic field and quantify the thermal stability factor by applying a developed model. From the dot-size dependence of the thermal stability factor, we discuss the mechanism of thermally activated dynamics of non-collinear antiferromagnetic Mn3Sn.The stack, consisting of, from the substrate side, W(2 nm)/Ta(3 nm)/Mn3Sn(20 nm)/MgO(1.3 nm)/Ru(1 nm) [Fig. 1(b)], is deposited on a MgO(110) single-crystal substrate by DC/RF magnetron sputtering at the substrate temperature of 400 °C. W(2 nm)/Ta(3 nm) is a buffer layer for the epitaxial growth of Mn3Sn, and MgO(1.3 nm)/Ru(1 nm) is a capping layer. The deposited stack is annealed at 500 °C for an hour in a vacuum. With this stack structure and processes, the Mn3Sn layer forms the 11¯00-plane, or M-plane, oriented structure, where the kagome plane is aligned vertically to the film plane,11,17,30,3111. J. Yoon, Y. Takeuchi, R. Itoh, S. Kanai, S. Fukami, and H. Ohno, Appl. Phys. Express 13, 013001 (2020). https://doi.org/10.7567/1882-0786/ab587417. Y. Takeuchi, Y. Yamane, J.-Y. Yoon, R. Itoh, B. Jinnai, S. Kanai, J. Ieda, S. Fukami, and H. Ohno, Nat. Mater. 20, 1364 (2021). https://doi.org/10.1038/s41563-021-01005-330. J.-Y. Yoon, Y. Takeuchi, S. DuttaGupta, Y. Yamane, S. Kanai, J. Ieda, H. Ohno, and S. Fukami, AIP Adv. 11, 065318 (2021). https://doi.org/10.1063/5.004319231. T. Uchimura, J.-Y. Yoon, Y. Sato, Y. Takeuchi, S. Kanai, R. Takechi, K. Kishi, Y. Yamane, S. DuttaGupta, J. Ieda, H. Ohno, and S. Fukami, Appl. Phys. Lett. 120, 172405 (2022). https://doi.org/10.1063/5.0089355 and characterization of fundamental properties was reported elsewhere.3131. T. Uchimura, J.-Y. Yoon, Y. Sato, Y. Takeuchi, S. Kanai, R. Takechi, K. Kishi, Y. Yamane, S. DuttaGupta, J. Ieda, H. Ohno, and S. Fukami, Appl. Phys. Lett. 120, 172405 (2022). https://doi.org/10.1063/5.0089355 The stack is processed into Hall devices with a single nanodot made of Mn3Sn/MgO/Ru layers with various nominal diameters D ranging from 175 to 1000 nm using electron beam lithography and Ar ion milling. Figure 1(c) shows a scanning electron microscopy (SEM) image of a patterned Mn3Sn nanodot with D = 175 nm. The average of the actual diameter observed by SEM is approximately consistent with the nominal D, and its standard deviation evaluated from multiple dots is obtained to be 15 nm. Contact pads with Cr(5 nm)/Au(50 nm) are formed at the ends of the W/Ta Hall bar. To detect the spin state in Mn3Sn, we measure the Hall resistance RH by a four probes method [Fig. 1(d)]. All the measurements are performed at room temperature.Figure 2(a) shows RH as a function of out-of-plane magnetic field H11¯00 for various D. The negative anomalous Hall resistance and clear hysteresis curves are observed, indicating the formation of the non-collinear spin structure in the Mn3Sn nanodot. We also observe a binary state in the RH-H hysteresis curve, which has not been seen in previous studies on Hall bar devices of Mn3Sn.8,9,118. T. Higo, D. Qu, Y. Li, C. L. Chien, Y. Otani, and S. Nakatsuji, Appl. Phys. Lett. 113, 202402 (2018). https://doi.org/10.1063/1.50646979. T. Ikeda, M. Tsunoda, M. Oogane, S. Oh, T. Morita, and Y. Ando, Appl. Phys. Lett. 113, 222405 (2018). https://doi.org/10.1063/1.505149511. J. Yoon, Y. Takeuchi, R. Itoh, S. Kanai, S. Fukami, and H. Ohno, Appl. Phys. Express 13, 013001 (2020). https://doi.org/10.7567/1882-0786/ab5874 The switching field HC vs D is summarized in Fig. 2(b). Here, HC is obtained from several nanodot devices fabricated on the same substrate including the one whose RH–H curve is shown. Reduced HC is obtained at smaller D below 300 nm whose reason will be discussed later. We also note that HC shows the variation of a few hundred mT for each D, probably due to a spatial inhomogeneity of the Mn3Sn film. We then evaluate RH–H loops with the magnetic field H applied along various directions in the 11¯00−112¯0 plane, i.e., in the kagome plane, to investigate the magnetic anisotropy in the nanodot. Figure 2(c) shows the HC, 11¯00-HC, 112¯0 curve in the Mn3Sn nanodot with D = 250 nm, where superscripts to HC denote directions of the magnetic field. While the hexagonal D019-Mn3Sn could exhibit a manifestation of sixfold magnetic anisotropy in the kagome plane for uncompensated magnetization,29,3229. J. Liu and L. Balents, Phys. Rev. Lett. 119, 087202 (2017). https://doi.org/10.1103/PhysRevLett.119.08720232. T. F. Duan, W. J. Ren, W. L. Liu, S. J. Li, W. Liu, and Z. D. Zhang, Appl. Phys. Lett. 107, 082403 (2015). https://doi.org/10.1063/1.4929447 we obtain an astroid curve representing a dominant contribution of a twofold magnetic anisotropy, as was reported in previous studies on bulk3232. T. F. Duan, W. J. Ren, W. L. Liu, S. J. Li, W. Liu, and Z. D. Zhang, Appl. Phys. Lett. 107, 082403 (2015). https://doi.org/10.1063/1.4929447 and thin film devices.1616. T. Higo, K. Kondou, T. Nomoto, M. Shiga, S. Sakamoto, X. Chen, D. Nishio-Hamane, R. Arita, Y. Otani, S. Miwa, and S. Nakatsuji, Nature 607, 474 (2022). https://doi.org/10.1038/s41586-022-04864-1 Based on this finding, we will examine the thermal stability factor of Mn3Sn nanodots considering a co-existence of two- and sixfold anisotropies below.In the following, we determine the thermal stability of the Mn3Sn dot by exploiting the Néel–Arrhenius thermal activation model. To do so, we first theoretically calculate the important parameter of the model, namely, the switching exponent, for the Mn3Sn dot, based on the experimental results described above. We adopt the “rigid-body” approximation, where the antiferromagnetic exchange coupling between the three sublattice magnetizations in Mn3Sn is strong enough to characterize the entire chiral-spin structure by limited parameters.33–3533. T. Dombre and N. Read, Phys. Rev. B 39, 6797 (1989). https://doi.org/10.1103/PhysRevB.39.679734. O. Gomonay, Phys. Rev. B 91, 144421 (2015). https://doi.org/10.1103/PhysRevB.91.14442135. Y. Yamane, O. Gomonay, and J. Sinova, Phys. Rev. B 100, 054415 (2019). https://doi.org/10.1103/PhysRevB.100.054415 Concerning static states of Mn3Sn, the chiral-spin structure can be described only by the direction of the uncompensated magnetization θM in the kagome plane, as long as the external disturbance is sufficiently small. The magnetic energy density u can then be written as u=K62cos 6θM+ K2sin2 θM−MUCH11¯00cos θM.(1)Here, K6 and K2 are positive constants describing the six- and twofold anisotropies for the global rotation of the chiral-spin structure, which originate from the hexagonal crystalline symmetry2929. J. Liu and L. Balents, Phys. Rev. Lett. 119, 087202 (2017). https://doi.org/10.1103/PhysRevLett.119.087202 and the film interface effect or the strain,1616. T. Higo, K. Kondou, T. Nomoto, M. Shiga, S. Sakamoto, X. Chen, D. Nishio-Hamane, R. Arita, Y. Otani, S. Miwa, and S. Nakatsuji, Nature 607, 474 (2022). https://doi.org/10.1038/s41586-022-04864-1 respectively, as described earlier, and MUC is the magnitude of the uncompensated magnetization. Now we define the energy barrier E as the energy required for θM  to switch from a positive-RH state (cos θM<0) to a negative-RH state (cos θM>0). Plotted in Fig. 3(a) is the external field dependence of the energy barrier for the two extreme cases, K6 = 0 and K2 = 0, where E0≡E(H11¯00=0)  and E(H11¯00=HK)=0. Note that the details of the metastable states and the values of E0  and HK depend on K6 and K2, and it is difficult to derive their general expressions. We fit the energy barrier curves by where the switching exponent n is the fitting parameter [broken curves in Fig. 3(a)]. In Fig. 3(b), we show the best-fitting n as a function of the anisotropy constants. We find that n=2.00 in the presence only of K2, as is well known from the Stoner–Wohlfarth approach3636. J. M. D. Coey, Magnetism and Magnetic Materials ( Cambridge University Press, England, 2010). to uniaxial ferromagnets, and n monotonically decreases as the relative value of K6 increases, eventually reaching 1.55 as K2 goes to zero. This fact indicates that the upper and lower bounds of Δ can be determined by assuming n to be 2.00 and 1.55, respectively, when analyzing the experimental results.To evaluate the thermal stability of the Mn3Sn nanodot, we measure the switching probability P as a function of the amplitude of magnetic field pulse H11¯00 with a pulse duration of 1 s. P is derived from 100-times measurement for each H11¯00. Figure 4(a) shows P vs H11¯00 for various D. Based on the Néel–Arrhenius thermal activation model, P can be described as P=1−exp −ττ0exp−Δ1−H11¯00HKn,(3)where τ is the duration of magnetic field pulse, Δ is the thermal stability factor, and τ0 is the inverse of attempt frequency assumed to be 1 ns, following a convention of studies on ferromagnets. Note that a variation of τ0 by an order of magnitude leads to a change in Δ of ∼2.3. Δ can be determined by fitting Eq. (3) to the experimental result.Figure 4(b) shows D dependence of Δ evaluated using n of 2.00 and 1.55. For both cases, Δ decreases with D below ∼300 nm, while no significant change is seen at D ≳ 300 nm, where the Δ value is in the range of about 100–150. Note that D dependences of HC and Δ have similar trends, indicating that the reduction of HC is mainly attributed to the reduction of Δ. Previous studies on ferromagnetic tunnel junctions where the same analysis was executed20,2120. H. Sato, M. Yamanouchi, K. Miura, S. Ikeda, H. D. Gan, K. Mizunuma, R. Koizumi, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 99, 042501 (2011). https://doi.org/10.1063/1.361742921. H. Sato, E. C. I. Enobio, M. Yamanouchi, S. Ikeda, S. Fukami, S. Kanai, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 105, 062403 (2014). https://doi.org/10.1063/1.4892924 show similar tendencies of Δ vs D and explain it by considering the energy barrier based on the single-domain and nucleation models for the reversal process.2121. H. Sato, E. C. I. Enobio, M. Yamanouchi, S. Ikeda, S. Fukami, S. Kanai, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 105, 062403 (2014). https://doi.org/10.1063/1.4892924 Energy barrier E for the single-domain and nucleation models can be approximated as E = KV = KtMπ(D/2)2 and E = π3AStM/4, respectively, where K denotes the effective magnetic anisotropy energy density, V is the volume of the magnetic layer, AS is the exchange stiffness constant, and tM is the thickness of the magnetic layer.21,37,3821. H. Sato, E. C. I. Enobio, M. Yamanouchi, S. Ikeda, S. Fukami, S. Kanai, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 105, 062403 (2014). https://doi.org/10.1063/1.489292437. H. Sato, M. Yamanouchi, K. Miura, S. Ikeda, R. Koizumi, F. Matsukura, and H. Ohno, IEEE Magn. Lett. 3, 3000204 (2012). https://doi.org/10.1109/LMAG.2012.219072238. Y. Takeuchi, H. Sato, S. Fukami, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 107, 152405 (2015). https://doi.org/10.1063/1.4933256 Note that the former E, which is proportional to the square of D, describes the smaller D region, whereas the latter one, which is independent of D, describes the larger D region, and the two regions are demarcated by the nucleation diameter Dn that can be approximated by π(AS/K)1/2. A procedure to reproduce the experimental Δ vs D with this scenario is as follows. First, we derive an initial Dn from a single set of parameters (K, AS). Next, Δ vs D is calculated for the same (K, AS) using the aforementioned equations of E for the single-domain and nucleation models, and the difference from the experimental results is evaluated. Then, we change (K, AS) to reduce the difference and repeat the cycle until the residual error is minimized. Since two series of Δ vs D are obtained using n of 2.00 and 1.55, where the former (latter) corresponds to the case of only K2 (K6) contribution, K2 (K6) is determined from the converged K. We find that, when (K, AS) = (K2 = 370 J/m3, AS = 3.5 pJ/m) and (K6 = 300 J/m3, AS = 3.0 pJ/m), respectively, the calculated Δ vs D for n of 2.00 and 1.55 [solid and dashed lines in Fig. 4(b)] well describes the experimental result, and this corresponds to Dn = 305 and 314 nm. The fact that the used K3232. T. F. Duan, W. J. Ren, W. L. Liu, S. J. Li, W. Liu, and Z. D. Zhang, Appl. Phys. Lett. 107, 082403 (2015). https://doi.org/10.1063/1.4929447 and derived Dn17,31,3917. Y. Takeuchi, Y. Yamane, J.-Y. Yoon, R. Itoh, B. Jinnai, S. Kanai, J. Ieda, S. Fukami, and H. Ohno, Nat. Mater. 20, 1364 (2021). https://doi.org/10.1038/s41563-021-01005-331. T. Uchimura, J.-Y. Yoon, Y. Sato, Y. Takeuchi, S. Kanai, R. Takechi, K. Kishi, Y. Yamane, S. DuttaGupta, J. Ieda, H. Ohno, and S. Fukami, Appl. Phys. Lett. 120, 172405 (2022). https://doi.org/10.1063/5.008935539. H. Bai, W. Zhu, Y. You, X. Chen, X. Zhou, F. Pan, and C. Song, Appl. Phys. Lett. 117, 052404 (2020). https://doi.org/10.1063/5.0011566 are the same orders of magnitude reported in previous works indicates the validity of our scenario. Note that we ignore the contribution of shape anisotropy because of the small spontaneous magnetization of a few mT in Mn3Sn and relatively large dot diameter. The curve based on the model could change if the magnetic anisotropy changes with the dot size. We also note that, for ferromagnetic tunnel junctions of diameter above Dn, it has been pointed out that the D value obtained by the aforementioned analysis underestimates the retention property of the device array, and the gap is mainly described by an additional energy barrier for domain wall (DW) propagation.22,2322. G. D. Chaves-O’Flynn, G. Wolf, J. Z. Sun, and A. D. Kent, Phys. Rev. Appl. 4, 024010 (2015). https://doi.org/10.1103/PhysRevApplied.4.02401023. L. Thomas, G. Jan, S. Le, Y.-J. Lee, H. Liu, J. Zhu, S. Serrano-Guisan, R.-Y. Tong, K. Pi, D. Shen, R. He, J. Haq, Z. Teng, R. Annapragada, V. Lam, Y.-J. Wang, T. Zhong, T. Torng, and P.-K. Wang, in 2015 IEEE International Electron Devices Meeting (IEDM) ( IEEE, Washington, D.C., 2015), p. 26.4.1–26.4.4. Accordingly, the actual D characterizing the retention property of Mn3Sn dots above 300 nm might be larger than the obtained value. Also, an identification of the dominant energy barrier, nucleation, or DW propagation, in antiferromagnetic systems, should be an interesting future challenge, and for this purpose, the measurement of the rare event in a large number of bits2323. L. Thomas, G. Jan, S. Le, Y.-J. Lee, H. Liu, J. Zhu, S. Serrano-Guisan, R.-Y. Tong, K. Pi, D. Shen, R. He, J. Haq, Z. Teng, R. Annapragada, V. Lam, Y.-J. Wang, T. Zhong, T. Torng, and P.-K. Wang, in 2015 IEEE International Electron Devices Meeting (IEDM) ( IEEE, Washington, D.C., 2015), p. 26.4.1–26.4.4. or random telegraph noise at elevated temperatures2424. E. C. I. Enobio, M. Bersweiler, H. Sato, S. Fukami, and H. Ohno, Jpn. J. Appl. Phys. 57, 04FN08 (2018). https://doi.org/10.7567/JJAP.57.04FN08 may be useful.

In summary, we investigated the dot-size dependence of the thermal stability factor in the 11¯00-plane oriented non-collinear antiferromagnetic Mn3Sn nanodot. We obtain the square hysteresis curves of the Hall resistance vs magnetic field. The magnetic field angle dependence of the switching field indicates a dominant contribution of the twofold magnetic anisotropy in the kagome plane of Mn3Sn. Using the switching exponent based on the rigid-body approximation, we evaluate the thermal stability factor of the Mn3Sn nanodot through the measurement of switching probability as a function of the amplitude of the pulse field. The obtained thermal stability factor is reduced below the dot diameter of about 300 nm, while it shows no significant change above 300 nm. This behavior resembles with previous reports on ferromagnetic nanodevices, suggesting an essentially similar mechanism of thermally assisted reversal. Our result offers important insight to understand the thermal activation of antiferromagnets, allowing one to design reliable and efficient antiferromagnetic devices.

The authors thank B. Jinnai, I. Morita, R. Ono, and M. Musya for technical support of fabrication of Hall devices and Y. Nakano for the measurement of inductively coupled plasma mass spectrometry (ICP-MS). This work was partly supported by JSPS KAKENHI (Grant Nos. 19H05622, 21J23061, 22K14558, and 22KK0072), MEXT Initiative to Establish Next-generation Novel Integrated Circuits Centers (X-NICS) (Grant No. JPJ011438), the Casio Science and Technology Foundation, and RIEC Cooperative Research Projects.

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Yuma Sato: Data curation (lead); Formal analysis (equal); Investigation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Yutaro Takeuchi: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (lead); Project administration (equal); Writing – original draft (equal); Writing – review & editing (lead). Yuta Yamane: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Funding acquisition (equal); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (lead). Ju-Young Yoon: Funding acquisition (equal); Investigation (equal); Writing – review & editing (equal). Shun Kanai: Funding acquisition (equal); Investigation (equal); Writing – review & editing (equal). Jun'ichi Ieda: Formal analysis (equal); Writing – review & editing (equal). Hideo Ohno: Conceptualization (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Shunsuke Fukami: Conceptualization (equal); Funding acquisition (lead); Resources (lead); Supervision (equal); Writing – original draft (equal); Writing – review & editing (lead).

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

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