# Spontaneous Quantum Hall Effect and Fractionalization in
Itinerant Chiral Magnets

### Ivar Martin, Argonne National Lab

When electrons move in a magnetic material, their transport can
be profoundly affected by scattering off magnetic ions. Converse
is also true: Itinerant electrons themselves can define the
magnetic state into which the system orders. Even though
typically these magnetic states are simple - e.g. ferromagnetic or
antiferromagnetic - sometimes, complex chiral magnetism can
appear.

Non-coplanar itinerant magnets are expected to exhibit highly
unusual transport phenomena that stem from a quantum coherent
effect of non-coplanar magnetic ordering on electrons, which is
similar to the Aharonov-Bohm effect. It can lead to the
spontaneous quantum Hall effect and ground-state electrical and
spin currents. The equivalent strength of the orbital magnetic
field can exceed 10^{4} Tesla. The stable topological
excitations (magnetic vortices) in these states can carry
fractional electronic charge and spin and realize anyonic exchange
statistics.

In this talk I will present several examples of two- and
three-dimensional itinerant models of magnetism that exhibit
complex non-coplanar ordering even in the absence of spin orbit
interaction; I will describe possible material realizations.