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

Abstract

We theoretically investigate a ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, ${J}_{1}$ and ${J}_{1}^{\ensuremath{'}}$, 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 $\mathbf{Q}=(\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2})$, being irrespective of the signs of ${J}_{1}$ and/or ${J}_{1}^{\ensuremath{'}}$ as long as ${J}_{1}\ensuremath{\ne}{J}_{1}^{\ensuremath{'}}$. 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 ${J}_{1}^{\ensuremath{'}}$, among which three phases including the in-field hedgehog-lattice state exhibit nonzero total chirality ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}$ 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 ${J}_{1}^{\ensuremath{'}}$, the spin structure is not topologically nontrivial, in spite of the fact that ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}\ensuremath{\ne}0$. The role of the topological objects of the monopoles in ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}$ is also discussed.