  A recent laser spectroscopy experiment [J. Thielking et al., Nature (London)
556, 321 (2018)] has determined for the first time the magnetic dipole moment
of the 7.8 eV isomeric state $^{229m}$Th. The measured value differs by a
factor of approximately 5 from previous nuclear theory predictions based on the
Nilsson model, raising questions about our understanding of the underlying
nuclear structure. Here, we present a new theoretical prediction based on a
nuclear model with coupled collective quadrupole-octupole and single-particle
motions. Our calculations yield an isomer magnetic dipole moment of $\mu_{ IS}=
-0.35\mu_N$ in surprisingly good agreement with the experimentally determined
value of $-0.37(6)\mu_N$, while overestimating the ground state dipole moment
by a factor 1.4. The model provides further information on the states' parity
mixing, the role and strength of the Coriolis mixing and the most probable
value of the gyromagnetic ratio $g_R$ and its consequences for the transition
probability $B(M1)$.
