In some types of non-centrosymmetric magnets, spin moments are incommensurately arranged to balance Dzyaloshinskii–Moriya (DM) and Heisenberg interactions. This leads to helimagnetic spin textures and spin soliton lattice which exhibit distinctive magnetoelectric response and promising potential for applications in spintronics. A chiral-polar-corundum compound Ni₂InSbO₆ is an example for a proper-screw type spin structure realized by chirality-induced DM interaction [1], as shown in Fig. 1(a). In conventional helimagnets, a spin soliton lattice is induced in the magnetic field applied in the spin rotation plane. In contrast in Ni₂InSbO₆, the soliton lattice was proposed by a unique scenario. Suppose that additional DM interactions with the staggered vector component D₁ and D₂ along the polar c axis are assumed, as shown in Fig. 1(b). At zero magnetic field, localized magnetization components M are induced by D₁ and D₂ interacting between neighboring Ni²⁺ ions along the c axis, indicated by the light blue arrows in Fig. 1(a). In the magnetic field applied perpendicular to the spin rotation plane, they shrink or expand to minimize Zeeman energy, and hence the spin soliton lattice is realized. In previous Raman study [2], however, the spectrum was analyzed by the spin model assuming that the first and second neighbor Heisenberg interactions J₁ and J₂ were equal, corresponding that D₁ and D₂ were equal. The assumption was contradictory to the scenario based on the staggered DM vectors. Thus, in this work, we collected magnetic spectrum in wide momentum-energy space on Ni₂InSbO₆ by inelastic neutron scattering (INS) technique to identify the precise spin Hamiltonian and validate the mechanism of the spin soliton lattice [3].

Fig. 1 Schematic of (a) proper-screw type helical spin structure and (b) spin soliton lattice in Ni₂InSbO₆. The figures were adopted from Ref. [1]. (c) INS spectrum measured with E_i = 30.5 meV at T = 10 K. (d),(e) Powder averaged LSWT calculation of INS spectra using the best fit parameters for model A in (d) and model B in (e). Modes of spin wave excitation from Γ₍₀₀₃₎ to A_{(00 3/2)} and from Γ₍₁₀₁₎ to L_{(1/2 0 1/2)} points are described by red and yellow dashed lines, respectively. (f) 1D-cut of powder spectrum at E = 10.1 meV for experiment (black), model A (orange) and model B (blue).

The INS powder spectrum is shown in Fig. 1(c). Well-defined spin wave excitation is observed with the band energy of 20 meV at 10 K. Two spin models of antiferromagnetic Heisenberg Hamiltonian considering the first to fourth nearest neighbor interactions J₁ to J₄ are used to analyze the spectrum by the linear spin-wave theory (LSWT). The calculated spectra of model A with constraints J₁ = J₂ and J₃ = J₄ according to the previous Raman study [2] and model B without the constraints according to the crystallographic consideration are shown in Figs. 1(d) and 1(e), respectively. χ² and correlation coefficient R for model A were 8.8 and 0.928, and those for model B are 6.1 and 0.953, meaning that model B is more probable. Indeed, one-dimensional cuts of the experiment and calculations at the energy of 10.1 meV in Fig. 1(f) suggest that the model B reproduces the experiment better. The difference is, in fact, caused by the fast and low spin wave velocities along the c axis for model A and B, respectively. The spin model of Ni₂InSbO₆, thus, turns out to be a coupled two-dimensional lattice stacked along the c axis with intraplane interaction J₁ = 6.05 meV and interplane interaction J₁ = 0.95 meV. Since DM interaction is proportional to the corresponding exchange interaction, D₁ and D₂ are different as well, which validates the mechanism of spin soliton lattice [1].

References

• [1] Y. Araki, T. Sato, Y. Fujima, N. Abe, M. Tokunaga, S. Kimura, D. Morikawa, V. Ukleev, Y. Yamasaki, C. Tabata, H. Nakao, Y. Murakami, H. Sagayama, K. Ohishi, Y. Tokunaga, and T. Arima, Phys. Rev. B 102, 054409 (2020).
• [2] M. A. Prosnikov, A. N. Smirnov, V. Y. Davydov, Y. Araki, T. Arima, and R. V. Pisarev, Phys. Rev. B 100,144417 (2019).
• [3] Z. Liu, Y. Araki, T. Arima, S. Itoh, S. Asai, and T. Masuda, Phys. Rev. B 107, 064428 (2023).

Authors

• Z. Liu, Y. Araki^a, T. Arima^a, S. Itoh^b,c, S. Asai, and T. Masuda
• ^aThe University of Tokyo
• ^bInstitute of Materials Structure Science, High Energy Accelerator Research Organization
• ^cJ-PARC Center