  We uncover a new family of few-body topological phases in periodically driven
fermionic systems in two dimensions. These phases, which we term
correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by
quantized contributions to the bulk magnetization from multi-particle
correlations, and are classified by a family of integer-valued topological
invariants. The CIAFI phases do not require many-body localization, but arise
in the generic situation of k-particle localization, where the system is
localized (due to disorder) for any finite number of particles up to a maximum
number, k. We moreover show that, when fully many-body localized, periodically
driven systems of interacting fermions in two dimensions are characterized by a
quantized magnetization in the bulk, thus confirming the quantization of
magnetization of the anomalous Floquet insulator. We demonstrate our results
with numerical simulations.
