  The electronic properties of bilayer graphene with a magnetic quantum dot and
a magnetic quantum ring are investigated. The eigenenergies and wavefunctions
of quasiparticle states are calculated analytically by solving decoupled
fourth-order differential equations. For the magnetic quantum dot, in the case
of a negative inner magnetic field, two peculiar characteristics of the
eigenenergy evolution are found: (i) the energy eigenstates change in a
stepwise manner owing to energy anticrossing and (ii) the quantum states
approach zero energy. For the magnetic quantum ring, there is an angular
momentum transition of eigenenergy as the inner radius of the ring varies, and
the Aharonov--Bohm effect is observed in the eigenenergy spectra for both
positive and negative magnetic fields inside the inner radius.
