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Hedgehog lattice and field-induced chirality in breathing-pyrochlore Heisenberg antiferromagnets

We theoretically investigate a $J_1$-$J_3$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, $J_1$ and $J_1'$, take different values due to the breathing bond-alternation and $J_3$ is the third NN antiferromagnetic interaction along the bond direction. It is found by means of Monte Carlo simulations that for large $J_3$, a hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, emerges in the form of a quadruple-${\bf Q}$ state characterized by the ordering vector of ${\bf Q}=(\pm\frac{1}{2},\pm\frac{1}{2},\pm\frac{1}{2})$, being irrespective of the signs of $J_1$ and/or $J_1'$ as long as $J_1\neq J_1'$. It is also found that in an applied magnetic field, there appear six quadruple-${\bf Q}$ states depending on the values of $J_1$ and $J_1'$, among which three phases including the in-field hedgehog-lattice state exhibit nonzero total chirality $\mbox{\boldmath $χ$}^{\rm T}$ associated with the anomalous Hall effect of chirality origin. In the remaining two chiral phases, which are realized in the presence of ferromagnetic $J_1$ and/or $J_1'$, the spin structure is not topologically nontrivial, in spite of the fact that $\mbox{\boldmath $χ$}^{\rm T} \neq 0$. The role of the topological objects of the monopoles in $\mbox{\boldmath $χ$}^{\rm T}$ is also discussed.