A simple understanding of all-optical spin switching in Heusler ferrimagnets through the geometrical phases

For over half a century, magnetic storage technology has relied on a magnetic field to switch magnetization in magnetic drives. Banerjee and coworkers showed a single laser pulse can switch spins in Mn2RuGa Heusler compounds permanently. However, how this occurs remains unclear. Here through manganese-based Heusler ferrimagnets, we find a group of flat bands around the Fermi level act as gateway states to form efficient channels for spin switching, where their noncentrosymmetry allows us to correlate the spin dynamics to the second-order optical response. To quantify their efficacy, we introduce the third-rank Pancharatnam-Berry tensor (PB tensor), and a picture emerges: Materials such as the recently discovered Mn2RuGa, which show all-optical spin switching (AOS), always have a large PB tensor element but have a small sublattice spin moment ratio, consistent with the prior experimental small remanence criterion. This does not only reveal that the delicate balance between the large PB tensor element and the small sublattice spin ratio plays a decisive role in AOS, but also, conceptually, connects the $n$th-order nonlinear optics to $(n+1)$th-rank PB tensors in general.