  Materials with the mesoscopic scales have provided an excellent platform for
quantum-mechanical studies. Among them, the periodic oscillations of the
electrical resistivity against the direct and the inverse of the magnetic
fields, such as the Aharonov-Bohm effect and the Shubnikov-de Haas effect,
manifest the interference of the wavefunction relevant to the electron motion
perpendicular to the magnetic field. In contrast, the electron motion along the
magnetic field also leads to the magnetic-field periodicity, which is the
so-called Sondheimer effect. However, the Sondheimer effect has been understood
only in the framework of the semiclassical picture, and thereby its
interpretation at the quasiquantum limit was not clear. Here, we show that
thin-film graphite exhibits clear sinusoidal oscillations with a period of
about 1-3 T over a wide range of the magnetic fields (from around 10 T to 30
T), where conventional quantum oscillations are absent. In addition, the sample
with a designed step in the middle for eliminating the stacking disorder effect
verifies that the period of the oscillations is inversely proportional to the
thickness, which supports the emergence of the Sondheimer oscillations in the
quasiquantum limit. These findings suggest that the Sondheimer oscillations can
be reinterpreted as inter-Landau-level resonances even at the field range where
the semiclassical picture fails. Our results expand the quantum oscillation
family, and pave the way for the exploration of the out-of-plane wavefunction
motion.
