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Recently, topological spin textures such as the magnetic skyrmion and its three-dimensional analogue, the magnetic hedgehog, have attracted much attention. Although the skyrmion and hedgehog have the same topological character, the latter has a singular point at its texture center, so that the hedgehog is sometimes called the magnetic monopole. Of recent particular interest is the hedgehog lattice which is a periodic array of the monopoles and anti-monopoles. Although the hedgehog lattice is known to be stabilized by the Dzyaloshinskii-Moriya (DM) interaction [1,2,3], a mechanism other than the DM interaction has not been reported so far.

In this talk, we show that the hedgehog lattice is realized in the classical J₁-J₃ Heisenberg model on the breathing pyrochlore lattice without the DM interaction [4]. A quadruple-q state with the ordering vector of q = (± 1/2, ±1/2, ±1/2), which is realized for a large third nearest-neighbor antiferromagnetic exchange interaction along the bond direction J₃, turns out to become the hedgehog-lattice state on the breathing lattice, while on the uniform lattice, it is a collinear state favored by thermal fluctuations. We will also demonstrate that in a magnetic field, the structure of the (1/2, 1/2, 1/2) hedgehog lattice is changed from cubic to tetragonal, resulting in a nonzero net spin chirality which in a metallic system, should yield a Hall effect of chirality origin.

Please access here for the registration: https://forms.gle/AMo5tqQoNoTR2e8Q9

[1] N. Kanazawa et al., Nat. Commun. 7, 11622 (2016).
[2] B. Binz and A. Vishwanath, Phys. Rev. B 74, 214408 (2006).
[3] J. H. Park and J. H. Han, Phys. Rev. B 83, 184406 (2011).
[4] K. Aoyama and H. Kawamura, Phys. Rev. B 103, 014406 (2021).

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