Revisiting a double-Q broken-helix state in an axion-insulator candidate
Zintl-phase compounds containing divalent Eu ions have recently attracted considerable attention as platforms for unusual transport phenomena and giant magnetoresistance, owing to the strong correlation between their electronic band structures and magnetism. A representative example is EuIn2As2. This material features a layered structure of Eu triangular lattices (space group P63/mmc) and undergoes a magnetic transition at TN=17 K, exhibiting easy-plane magnetic anisotropy. First-principles calculations have proposed the realization of an axion-insulator state associated with interlayer antiferromagnetic order, making the determination of the magnetic structure a key issue. Following this theoretical proposal, neutron and resonant X-ray scattering experiments by other groups concluded that the ground state is not antiferromagnetic but rather a double-Q “broken-helix” structure characterized by the superposition of magnetic propagation vectors Q1 = (0,0,1/3) and Q2 = (0,0,1). However, the prior interpretation, particularly the modulation period and the symmetry of the magnetic structure, warrant reexamination.
In this study, we performed detailed resonant X-ray scattering experiments. Using four single crystals, we observed magnetic peaks and found that the modulation wave number of Q1, q1z, deviates from 1/3 and shows sample dependence in the range q1z = 0.25〜0.31. Crystal structure analyses revealed approximately 1% Eu deficiency in all samples, with the more deficient samples exhibiting larger q1z. These results suggest that the origin of the incommensurate Q1 modulation is an RKKY interaction mediated by hole carriers introduced by Eu vacancies. Therefore, to realize an axion state in EuIn2As2, it will be necessary to shift the Fermi level into the band gap to suppress the Q1 modulation. Eelectron doping via chemical substitution may provide an effective route. Furthermore, upon applying an in-plane magnetic field, we observed a spin-flop transition at Hc = 0.2 T, above which the high-field phase transforms into a double-Q fanlike structure. In this phase, in addition to the higher-harmonic Q2−Q1, we observe magnetic peaks corresponding to the third harmonic 3Q1, indicating the emergence of a distinctive spin configuration beyond a conventional fanlike state.
In this study, we performed detailed resonant X-ray scattering experiments. Using four single crystals, we observed magnetic peaks and found that the modulation wave number of Q1, q1z, deviates from 1/3 and shows sample dependence in the range q1z = 0.25〜0.31. Crystal structure analyses revealed approximately 1% Eu deficiency in all samples, with the more deficient samples exhibiting larger q1z. These results suggest that the origin of the incommensurate Q1 modulation is an RKKY interaction mediated by hole carriers introduced by Eu vacancies. Therefore, to realize an axion state in EuIn2As2, it will be necessary to shift the Fermi level into the band gap to suppress the Q1 modulation. Eelectron doping via chemical substitution may provide an effective route. Furthermore, upon applying an in-plane magnetic field, we observed a spin-flop transition at Hc = 0.2 T, above which the high-field phase transforms into a double-Q fanlike structure. In this phase, in addition to the higher-harmonic Q2−Q1, we observe magnetic peaks corresponding to the third harmonic 3Q1, indicating the emergence of a distinctive spin configuration beyond a conventional fanlike state.
References
[A] M. Gen et al., Phys. Rev. B 111, L081109 (2025). (Original paper [32])