The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but by frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, $J_1^{\prime }/J_1$. A quadruple-$\mathbf{q}$ state with the ordering vector of $\mathbf{q}=(\pm \frac{1}{2},\pm \frac{1}{2},\pm \frac{1}{2})$, which is realized for a large third-NN antiferromagnetic interaction along the bond direction $J_3$, turns out to become the hedgehog-lattice state in the breathing case of $J_1^{\prime }/J_1<1$, while in the uniform case of $J_1^{\prime }/J_1=1$, it is a collinear state favored by thermal fluctuations. It is also found that in a magnetic field, the structure of the $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ hedgehog lattice is changed from cubic to tetragonal, resulting in a nonzero net spin chirality, which in a metallic system should yield a characteristic topological Hall effect.

• Received 29 September 2020
• Accepted 16 December 2020

DOI:https://doi.org/10.1103/PhysRevB.103.014406

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

©2021 American Physical Society