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

Abstract

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 $J_1^{\prime }$, 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-$\mathbf{Q}$ state characterized by the ordering vector of $\mathbf{Q}=(\pm \frac{1}{2},\pm \frac{1}{2},\pm \frac{1}{2})$, being irrespective of the signs of $J_1$ and/or $J_1^{\prime }$ as long as $J_1\ne J_1^{\prime }$. It is also found that in an applied magnetic field, there appear six quadruple-$\mathbf{Q}$ states depending on the values of $J_1$ and $J_1^{\prime }$, 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 $J_1^{\prime }$, 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.

21 pages, 20 figures

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