  The effect of magnetic modulation on thermodynamic properties of a graphene
monolayer in presence of a constant perpendicular magnetic field is reported
here. One-dimensional spatial electric or magnetic modulation lifts the
degeneracy of the Landau levels and converts into bands and their band width
oscillates with magnetic field leading to Weiss-type oscillation in the
thermodynamic properties. The effect of magnetic modulation on thermodynamic
properties of a graphene sheet is studied and then compared with electrically
modulated graphene and magnetically modulated conventional two-dimensional
electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen (dHvA)
oscillations at low and high magnetic field, respectively. There is a definite
phase difference in Weiss-type oscillations in thermodynamic quantities of
magnetically modulated graphene in compare to electrically modulated graphene.
On the other hand, the phase remains same and amplitude of the oscillation is
large when compared with the magnetically modulated 2DEG. Explicit asymptotic
expressions of density of states and the Helmholtz free energy are provided to
understand the phase and amplitude of the Weiss-type oscillations
qualitatively. We also study thermodynamic properties when both electric and
magnetic modulations are present. The Weiss-type oscillations still exist when
the modulations are out-of-phase.
