  We study the magnetic oscillations (MO) in 2D materials with a buckled
honeycomb lattice, considering a perpendicular electric and magnetic field. At
zero temperature the MO consist of the sum of four sawtooth oscillations, with
two unique frequencies and phases. The values of these frequencies depend on
the Fermi energy and electric field, which in turn determine the condition for
a beating phenomenon in the MO. We analyse the temperature effect in the MO by
considering its local corrections over each magnetization peak, given by
Fermi-Dirac like functions. We show that the width of these functions is
related to the minimum temperature necessary to observe the spin and valley
properties in the MO. In particular, we find that in order to observe the spin
splitting, the width must be lower than the MO phase difference. Likewise, in
order to observe valley mixing effects, the width must be lower than the MO
period. We also show that at high temperatures, all the maxima and minima in
the MO are shift to a constant value, in which case we obtain a simple
expression for the MO and its envelope. The results obtained show unique
features in the MO in 2D materials, given by the interplay between the valley
and spin.
