  We calculate the magnetic dipole moment of the Delta(1232) and Omega^-
baryons with 2+1-flavors of clover fermions on anisotropic lattices using a
background magnetic field. This is the first dynamical calculation of these
magnetic moments using a background field technique. The calculation for
Omega^- is done at the physical strange quark mass, with the result in units of
the physical nuclear magneton mu_Omega^-= -1.93(8)(12) (where the first error
is statistical and the second is systematic) compared to the experimental
number: -2.02(5). The Delta has been studied at three unphysical quark masses,
corresponding to pion mass m_pi = 366, 438, and 548 MeV. The pion mass
dependence is compared with the behavior obtained from chiral effective field
theory.
