Symmetry tuning topological states of the axion insulator candidate EuIn 2 As 2 by its noncollinear magnetic order

The gist: The researchers tune the magnetic symmetry of an axion insulator candidate EuIn2As2 by applying an in-plane magnetic field, revealing how this symmetry change controls topologically protected surface states and hinge states.

How it works

1. The study examines how the magnetic order of the axion insulator (AXI) candidate EuIn2As2 is tuned by an in-plane magnetic field from its broken-helix ground state to its field-polarized phase The application of this field allows for the exploration of different symmetry pathways for controlling topological states and their robust physical properties.

2. The material exhibits an A-type antiferromagnetic (AFM) order below a Néel temperature TN, which breaks time-reversal symmetry (T) but preserves inversion symmetry (P), leading to the AXI phase. This AXI is characterized by quantized bulk magnetoelectric coupling and half-quantized quantum-anomalous Hall type conductivity for gapped surfaces.

3. The magnetic order in EuIn2As2 is described by a broken-helix structure, which supports an AXI state protected by 2′ symmetry, which is the combination of a two-fold rotation and T. This magnetic space group (MSG) C2′2′21 protects the AXI phase.

Tuning Topological States via Magnetic Symmetry

The application of an in-plane magnetic field H tunes the magnetic symmetry within individual magnetic domains and examines the resulting changes to the topological surface states and hinge states existing on edges shared by certain surfaces hosting gapped Dirac states. The field can induce phase transitions, such as a transition from the broken-helix ground state to a P1 distorted-broken-helix phase, which is observed in DFT results for the [1 1 0] surface.

Key findings regarding symmetry changes include:

: Weak in-plane magnetic fields (H < 0.18 T) can switch certain surface Dirac states from gapless to gapped by reducing the bulk symmetry. This is demonstrated by DFT results showing that the gapless Dirac states for the [1 1 0] surface in the broken-helix phase become gapped for the P1 distorted-broken-helix phase. The field direction controls whether a hinge state exists on a wall between domains (f) or between other domain pairs (g). The field can affect the magnetic ordering of each domain differently, as shown in Figs. 1f and 1g. This demonstrates that H is a mechanism for continuously moving domain walls and pinned hinge states to another position in the sample, creating functionality such as a topological electric switch. The results show multiple degrees of robust tuning of topological electronic states by a weak magnetic field in a TI with noncollinear magnetic order. The analysis shows that hinge states appear on magnetic domain walls intersecting outer surfaces of the crystal if the walls separate gapped surfaces with opposite signs for m

Domain-Specific Hinge State Patterns

The presence of topologically protected chiral-conduction channels is not constrained to develop at crystalline terminations. The study predicts field-tunable complex and domain-specific hinge-state patterns.

: Hinge states pinned to domain walls occur where the wall intersects the top and bottom surfaces because the surfaces are related by 2′ regardless of the 2′ axes’ orientations in the ab plane. The researchers found that hinge states pinned to magnetic walls will persist with changing H as long as m

for the surfaces intersecting the wall and supporting the hinge states do not switch sign.

Experimental Evidence and Modeling

Neutron diffraction measurements reveal field-dependent changes in magnetic order, indicating that distinct domains can be tuned to have different magnetic symmetries. The analysis using a symmetry-constrained model shows that D3± enter the canted-A-type phase above ≈ 0.18 T based on the calculated intensity of the (1 0 2 + τ1z) Bragg peak being dominated by D3+ at low fields. Similarly, D1± transitions from a distorted-broken-helix to the cantedorthogonal phase at ≈ 0.25 T, and to the twoangle-canted phase above ≈ 0.7 T. These transitions are inferred from changes in slope of integrated intensity versus field data. The calculated magnetic structure of each domain at T = 0 K for increasing field H∥b is shown in Fig. 4, where the domains evolve through phases like C2′2′21 and P1.

Conclusion

The research demonstrates how noncollinear magnetic ordering of an AXI can be manipulated by an in-plane magnetic field to tune magnetic symmetry and, thus, the topologically protected surface states. The findings highlight a further degree of topological tunability in the existence of hinge states pinned to magnetic walls, where the associated chiral-conduction pathways can move with the domain wall.

--- Page 1 ---

arXiv:2505.22796v1 [cond-mat.mtrl-sci] 28 May 2025

Symmetry tuning topological states of an axion insulator with noncollinear magnetic order

S. X. M. Riberolles1,2, A.-M. Nedi´c1,2, B. Kuthanazhi1,2, F. Ye3, S. L. Bud’ko1,2

P. C. Canfield1,2, R. J. McQueeney1,2

Junyeong Ahn4, V. L. Quito1,2, T. V Trevisan1,2

L. L Wang1,2 P. P Orth1,26, B. G Ueland1,2

Division of Materials Sciences and Engineering, Ames National Laboratory, U.S DOE, Iowa State University Ames IA USA 50011.

Department of Physics and Astronomy Iowa State University Ames IA USA 50011.

Neutron Scattering Division Oak Ridge National Laboratory Oak Ridge TN USA 37831.

Department of Physics Harvard University Cambridge MA USA 02138.

Sao Carlos Institute of Physics University of Sao Paulo IFSC – USP Sao Carlos SP BR, 13566-590.

Department of Physics Saarland University Saarbr¨ucken DE, 66123.

/Corresponding author(s). E-mail(s): peter.orth@uni-saarland.de; bgueland@ameslab.gov; A.-M Nedi´c Present Address: Chemical Engineering and Materials Science, University of Minnesota Minneapolis MN 55455 USA †B Kuthanazhi Present Address: Department of Chemistry, University of Liverpool Liverpool L69 7ZD UK ‡Junyeong Ahn Present Address: Department of Physics, The University of Texas at Austin Austin TX 78712 1 Introduction Quantum materials with nontrivial topology can have topologically protected boundary states offering useful functional properties such as dissipationless and spin-polarized transport, quantized conductivity, or novel magnetoelectricity [1–5]. The existence and classification of a material’s topology is intimately related to its symmetry. Therefore, the application and tuning of symmetry-breaking perturbations offer different pathways for controlling topological states and their robust physical properties. Here, we examine how the magnetic symmetry of the axion insulator (AXI) candidate EuIn2As2 is tuned by an in-plane magnetic field from its complex helical ground state to its field-polarized phase and analyze how the changing symmetry controls the topologically protected boundary states. To begin, we present some examples demonstrating the relationship between symmetry and topological boundary states which will be important for understanding our results for EuIn2As2. Figure 1a shows a bulk (i.e. 3D) topological insulator (TI) located between two ferromagnets with magnetization M pointing up. In the absence of M, bulk-boundary correspondence leads to robust metallic surfaces, with each surface hosting an odd number of Dirac cones [1]. The presence of M, however, acts as a local timereversal-symmetry (T) breaking perturbation at the top and bottom surfaces. This gaps their Dirac states and their Dirac fermions acquire an effective mass m∗. m

has opposite sign for the top and bottom surfaces (represented by blue and red) because sgn(m∗) ∝ Mˆ · ˆn, where ˆn is the surface normal. The gapped top and bottom surfaces have topologically-protected quantized conductance-channels which intersect the metallic side surfaces. Topologically protected chiral-conduction channels are not constrained, however, to develop at crystalline terminations. Figure 1b shows the case of ferromagnets with opposite signs for M placed across both the top and bottom surfaces of the 3D TI. For both surfaces, this generates regions with opposite signs for m∗ which are separated by a domain wall. A chiral-conduction pathway emerges at the domain wall. In general, engineering such local T-breaking perturbations can be explored to create robust topologically protected conduction along desired pathways [6].

1. Bold header: In-plane magnetic field control of topological phase transitions. This improved system can predict field-tunable complex and domain-specific hinge-state patterns by mapping applied magnetic field directions to specific symmetry changes, as described in the abstract and Section 3.

2. Bold header: Domain-resolved topological state mapping via neutron diffraction analysis. The AI can analyze domain Averaged Theory data to infer the magnetic space group of individual domains (e.g., D1+, D2-, D3±) based on unequal domain contributions to Bragg peaks, allowing for the prediction of which surface states are gapped or gapless in a specific domain.

3. Bold header: Chiral-charge transport pathway tuning mechanism identification. The system can identify hinge states pinned to magnetic walls when intersecting certain crystal surfaces, providing a channel for tuning the chiral-charge-transport pathways by tracking the sign changes of the effective mass term, as shown in Figure 5d and Section 3.

4. Bold header: Predictive modeling of topological phase transitions via symmetry evolution. The improved system can simulate how "weak in-plane magnetic fields (H < 0.18 T) switch certain surface Dirac states from gapless to gapped by reducing the bulk symmetry, based on the evolution from broken-helix ground state to the field-polarized phase."

5. Bold header: Determination of critical field thresholds for domain switching. The AI can precisely identify specific field values, such as H = 0.18, 0.25, and 0.7 T, that correspond to transitions where domains enter new magnetic phases (e.g., D3± entering the canted-A-type phase).

Topological properties of quantum materials are intimately related to symmetry. Here, we tune the magnetic order of the axion insulator candidate EuIn 2 As 2 from its broken-helix ground state to the field-polarized phase by applying an in-plane magnetic field. Using results from neutron diffraction and magnetization measurements with ab inito theory and symmetry analysis, we assume a commensurate magnetic ground state and predict how the field tunes the magnetic symmetry within individual magnetic domains and examine the resulting changes to the topological surface states and hinge states existing on edges shared by certain surfaces hosting gapped Dirac states. We predict complex field-tunable domain-specific hinge-state patterns, with some crystal surfaces undergoing a field induced topological phase transition. We further find that domain walls can have pinned hinge states when intersecting certain crystal surfaces, providing another channel for tuning the chiral-charge-transport pathways.