Hedgehog-lattice spin texture in breathing-pyrochlore antiferromagnets

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, a mechanism other than the DM interaction has not been reported so far.
In this presentation, we will demonstrate that the hedgehog lattice is induced by magnetic frustration in the classical J_1-J_3 Heisenberg model on the breathing pyrochlore lattice without the DM interaction. 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 J_3 , 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 show 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.