  We study the in-medium masses of the heavy quarkonium (charmonium and
bottomonium) states in isospin asymmetric nuclear matter in presence of an
external magnetic field. The mass modifications of the heavy quarkonia are
obtained from the medium modifications of a scalar dilaton field, $\chi$,
calculated within a chiral effective model. The dilaton field is introduced in
the model through a scale invariance breaking logarithmic potential, and,
simulates the gluon condensates of QCD. Within the chiral effective model, the
values of the dilaton field along with the scalar (isoscalar, $\sigma (\sim
\langle \bar u u \rangle +\langle \bar d d \rangle)$, isoscalar $\zeta (\sim
\langle \bar s s \rangle$) and isovector $\delta (\sim \langle \bar u u\rangle
  - \langle\bar d d \rangle)$) fields, are solved from their coupled equations
of motion. These are solved accounting for the effects of the Dirac sea (DS) as
well as anomalous magnetic moments (AMMs) of the nucleons. The Dirac sea
contributions are observed to lead to enhancement (reduction) of the quark
condensates (through $\sigma$ and $\zeta$ fields) with increase in magnetic
field, an effect called the (inverse) magnetic catalysis. The magnetic field
effects on the masses of the heavy quarkonia include the mixing of the
pseudoscalar (spin 0) and vector (spin 1) states (PV mixing), as well as, the
effects from (inverse) magnetic catalysis. These effects are observed to be
significant for large values of the magnetic field. This should have observable
consequences on the production of the heavy quarkonia and open heavy flavour
mesons, resulting from ultra-relativistic peripheral heavy ion collision
experiments, where the created magnetic field can be huge.
