  In this article we prove the global existence of weak solutions for a diffuse
interface model in a bounded domain (both in 2D and 3D) involving
incompressible magnetic fluids with unmatched densities. The model couples the
incompressible Navier-Stokes equations, gradient flow of the magnetization
vector and the Cahn-Hilliard dynamics describing the partial mixing of two
fluids. The density of the mixture depends on an order parameter and the
modelling, specifically the density dependence, is inspired from Abels, Garcke
and Gr\"{u}n 2011.
