Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space

Efforts to find the magnetic monopole in real space have been made in cosmic rays and in accelerators, but up to now there is no firm evidence for its existence due to the very heavy mass $\sim {10}^{16}$GeV. However, we show that the magnetic monopole can appear in the crystal-momentum space of solids in the accessible low energy region ($\sim 0.1-1$eV) in the context of the anomalous Hall effect. We report experimental results together with first-principles calculations on the ferromagnetic crystal SrRuO${}_3$ that provide evidence for the magnetic monopole in the crystal-momentum space.