Since the discovery of topological insulators, the concept of topology has become widely recognized as an important aspect of condensed-matter physics. These materials host massless Dirac fermions on their edges or surfaces, giving rise to phenomena such as the quantum Hall effect. Recently, potential applications for highly efficient spintronic devices that exploit spin currents along these edges or surfaces have attracted significant attention. Moreover, the notion of topology has been extended from fermionic to magnonic systems, as evidenced by phenomena such as the thermal Hall effect.

Inelastic neutron scattering (INS) experiments have confirmed the existence of topological magnons in several materials. For example, in layered honeycomb-lattice ferromagnet CrI₃ [1] and three-dimensional ferromagnet Mn₅Ge₃ [2], bulk magnon dispersions exhibit gaps at the K point, and theoretical calculations predict the presence of edge states—Dirac magnons—within these gaps. Dirac magnons have also been observed in the three-dimensional antiferromagnet Cu₃TeO₆ [3] and in the ilmenite-type antiferromagnet CoTiO₃ [4], where linear band crossings at the K point create Dirac cones for both bulk and edge modes. These findings underscore the rapid expansion of topological motifs in magnonic systems that mirror those long explored in electronic counterparts.

In this study, we investigate NiTiO₃ [5], which has the same crystal structure and magnetic ordering as CoTiO₃. Magnetic-susceptibility measurements reveal that NiTiO₃ exhibits stronger interlayer interactions, whereas CoTiO₃ is dominated by intralayer coupling. To determine the spin Hamiltonian and examine the presence of Dirac magnons in NiTiO₃, we conducted single-crystal INS experiments.

Measurements were performed using the multiplex spectrometer HODACA at JRR-3 and the triple-axis spectrometer CTAX at ORNL/HFIR [6]. Figure 1(a) shows the INS spectrum measured by HODACA along the $(0, 0, l)$ direction, revealing spin-wave excitations with a band energy of 3.7 meV. Using linear spin-wave theory (LSWT), experimental data were accurately reproduced (Fig. 1(b)) by a model incorporating exchange interactions and easy-plane anisotropy. This model confirmed NiTiO₃ as a three-dimensional magnet in which interlayer coupling outweighs intralayer coupling. Moreover, whereas nearest-neighbor interactions suffice to describe CoTiO₃, modeling NiTiO₃ demands exchange paths extending to third-nearest neighbors within the $ab$ plane.

Figure 1(c) shows the INS spectra measured by CTAX along the high-symmetry path Γ₁-M-K-Γ₂. Near the K point, considering the instrumental energy resolution, the spectra were fitted by single Gaussian at the K point and two Gaussians near the K point. The dispersion relations calculated using the best fit parameters, shown in Fig. 1(d), reveal two modes that intersect linearly at the K point, confirming the formation of Dirac cones in NiTiO₃, just as in CoTiO₃. Previous work [4] argued that Dirac magnons remain stable against anisotropy and further-neighbor interactions. Our study experimentally demonstrates that Dirac magnons persist even with significant interlayer coupling and second- and third-neighbor interactions within the honeycomb layer.

References

• [1] L. Chen et al., Phys. Rev. X 8, 041028 (2018).
• [2] M. dos Santos Dias et al., Nat. Commun. 14, 7321 (2023).
• [3] W. Yao et al., Nat. Phys. 14, 1011 (2018).
• [4] B. Yuan et al., Phys. Rev. X 10, 011062 (2020).
• [5] K. Dey et al., Phys. Rev. B 103, 134438 (2021).
• [6] H. Kikuchi et al., J. Phys. Soc. Jpn. 94, 024703 (2025).

Authors

• H. Kikuchi, M. Ozeki, N. Kurita^a, S. Asai, T. J. Williams^b, T. Hong^b, and  T. Masuda
• ^aInstitute of Science Tokyo
• ^bOak Ridge National Laboratory