Thermodynamic stability and magnetoelectric response of emergent magnetic monopoles in topological magnets

Topological spin textures have raised attention through their emergent electromagnetic properties, including the topological Hall effect and the topological Nernst effect. Among them, magnetic hedgehog lattices (HLs) are three-dimensional topological spin textures that host periodically arranged emergent magnetic monopoles and antimonopoles. They have been identified in metallic compounds, such as MnSi_1−xGex and SrFeO₃ [1-3]. While HLs are often modelled using either short-range (localized/insulating) or effectively long-range (itin- erant/metallic) interactions [4,5], real materials generically lie in between, with finite and material-dependent exchange ranges. Moreover, experimental probes beyond metallic transport are desirable, especially if HLs can be realized in insulating magnets. In this work, we investigate thermodynamic stability and magnetoelectric (ME) responses of these HLs using extensive Monte Carlo simulations. First, we map field–temperature phase diagrams, interpolating between the metallic and insulating limits through systematic variation of the range and spatial decay of exchange interactions. We find that HLs are stabilized over a broad interaction range; notably, an intermediate range emerges as optimal, stabilizing multiple and comparatively wide HL phases in parameter space. Next, building on the stabilized phases, we evaluate the ME effect using symmetry arguments and microscopic polarization mechanisms, such as the inverse Dzyaloshinskii-Moriya and the p-d hybridization mechanism. We show that HLs exhibit field-dependent macroscopic electric polarizations and dielectric constants, which are sensitive to topological and magnetic transitions between different HL phases. Our results enable materials-oriented predictions of HL stability from microscopic interaction models and propose the ME response as a sensitive probe for detecting emergent monopoles, particularly in candidate insulating materials.

References

[1] N. Kanazawa et al., Phys. Rev. B 86, 134425 (2012).

[2] Y. Fujishiro et al., Nat. Commun. 10, 1059 (2019).

[3] S. Ishiwata et al., Phys. Rev. B 101, 134406 (2020).

[4] S. Yang et al., Phys. Rev. B 94, 054420 (2016).

[5] S. Okumura et al., Phys. Rev. B 101, 144416 (2020).