# Synopsis: Fingerprinting magnetic monopoles

#### Effective Magnetic Monopoles and Universal Conductance Fluctuations

Kjetil M. D. Hals, Anh Kiet Nguyen, Xavier Waintal, and Arne Brataas

Published November 11, 2010

Magnetic monopoles in real space, postulated by Dirac in 1931, have not been seen in nature. However, effective magnetic monopoles in crystal momentum space were observed in the metallic ferromagnet ${\text{SrRuO}}_{3}$ a few years ago. Here they arise from energy-band crossings; whenever a charged particle traverses a closed curve in momentum space, its wave function acquires a geometric Berry phase from the monopole fields. The fingerprint of these monopoles is an unconventional behavior in the so-called anomalous Hall effect: the transverse resistivity can show a nonmonotonic temperature dependence and even a sign change.

Writing in Physical Review Letters, Kjetil Hals, Anh Kiet Nguyen, and Arne Brataas from the Norwegian University of Science and Technology, and Xavier Waintal from CEA, Grenoble, France, show that it is possible to manipulate momentum-space magnetic monopoles in ferromagnets with strong spin-orbit coupling by external magnetic fields, and observe this in universal conductance fluctuations (UCF). In general, UCF refers to time-independent fluctuations in the conductance of metals at low temperature that vary between samples but are reproducible for a given sample at a fixed temperature. Hals et al. show that fast conductance oscillations recently observed in experiments on the ferromagnetic semiconductor $\left(\text{Ga},\text{Mn}\right)\text{As}$ are a consequence of the relocation of momentum-space magnetic monopoles. This relocation comes about due to a rotation of the magnetization and leads to a geometric phase change of closed momentum-space curves. This work offers an entirely new probe of magnetic monopoles in momentum space. – Sarma Kancharla