  Analytical models of magnetized, geometrically thick disks are relevant to
understand the physical conditions of plasma around compact objects and to
explore its emitting properties. This has become increasingly important in
recent years in the light of the Event Horizon Telescope observations of Sgr
A$^*$ and M87. Models of thick disks around black holes usually consider
constant angular momentum distributions and do not take into account the
magnetic response of the fluid to applied magnetic fields. We present a
generalization of our previous work on stationary models of magnetized
accretion disks with magnetic polarization (Pimentel et al. 2018). This
extension is achieved by accounting for non-constant specific angular momentum
profiles, done through a two-parameter ansatz for those distributions. We build
a large number of new equilibrium solutions of thick disks with magnetic
polarization around Kerr black holes, selecting suitable parameter values
within the intrinsically substantial parameter space of the models. We study
the morphology and the physical properties of those solutions, finding
qualitative changes with respect to the constant angular momentum tori
solutions (Pimentel et al. 2018). However, the dependences found on the angular
momentum distribution or on the black hole spin do not seem to be strong. Some
of the new solutions, however, exhibit a local maximum of the magnetization
function, absent in standard magnetized tori. Due to the enhanced development
of the magneto-rotational instability as a result of magnetic susceptibility,
those models might be particularly well-suited to investigate jet formation
through general-relativistic MHD simulations. The new equilibrium solutions
reported here can be used as initial data in numerical codes to assess the
impact of magnetic susceptibility in the dynamics and observational properties
of black hole-thick disk systems.
